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Qri)oms0n*s lixQi Ccssons. 
 
 MENTAL 
 
 ARITHMETIC, 
 
 OB 
 
 FIRST LESSONS IN NUMBERS 
 
 FOR CHILDREN. 
 By JAMES B. THOMSON, LL.D.,^ 
 
 AUTOOU Ol» PaAOTlOAI. ARITUMBTIO, BDITOB OP DAY'h SOHOOl AMHBOA 
 I.BOBNDRli'8 QBOMSTRV, BTO. 
 
 ONI HUNDRED AND FIFTIETD EDITION, REVISED AND BNLABOBD. 
 
 NEW YORK: 
 CLARK & MAYNARD, 6 BARCLAY ST. 
 
 CHICAGO : a C. GRIGGS & CO. 
 
 * * * * 
 
1 
 
 BiiUjkxI oooordlDg to Act of OongrcBe, In Uie ytor iy3€, 
 
 By JAMES B. THOMSON, 
 
 in the Clerk'u OflJoo of the Northern Dlstrlot of Now York. 
 
PREFACE 
 
 At what precise age a child should begin to gc to schoal, 
 
 or commence the different studies, it is not our province to 
 
 I decide. Whatever may be the diversity of opinion on 
 
 I this point, all practical teachers seem to agree, that Men- 
 
 \ id A^thmetic is among the first exercises which should 
 
 j be presented to the youthful mind. The correctness of 
 
 I this sentiment is corroborated by the ease with which 
 
 I children understand simple combinations of numbers, their 
 
 ! fondness for the!>e exercises, and the obvious advantages 
 
 I which may be derived from them. But in order to be- 
 
 I come interesting or profitable, it is manifest, this branch, 
 
 j as well as others, must be taught in such a manner that 
 
 the pupil shall understand it. The examples, therefore, 
 
 j must, at first, be simple, containing small numbers, and 
 
 have reference to sensible objects with which the learner 
 
 is accjuainted ; the transition from easy to more difficult 
 
 (questions must be gradual; and the reason for every 
 
 step in the solution distinctly seen. 
 
 It is believed that much dislike for the study of Arith- 
 metic, and much unnecessary discourage7nent, have been 
 occasioned by the abruptness of the transitions from easy 
 to difficult questions. It is too often forgotten that the 
 powers of the child's mind, Lke those of his body, are 
 feeble ; that while familiar mental exercises which he can 
 comprehend, afford him the highest delight, he turns from 
 intricate questions, which he does not and cannot under- 
 itand, with indifference and disgust. 
 
 It is the design of this little work to furnish a ser^^ of 
 mental exercises in numbers, adapted to the wants and 
 cnparities^of children. It commences with practical ex- 
 amples, which relate to familiar objects and require the 
 
PREFACE. 
 
 simplest combinations. The pupil is then introduced to 
 others involving the same principle but somewhat harder, 
 special care being taken to make the transition very grad- 
 ual, so that instead of being disheartened at the rugged- 
 ness of the way, he shall be stimulated to take the next 
 step by the hope of victory. 
 
 From the fact that children comprehend and remember 
 words more easily than figures, and reason upon them 
 with so much greater facility, the numbers and Tables 
 in the first part of the book are expressed in words. 
 
 After the pupil has become practically acquainted with 
 the principles of a rule, and is able to solve questions un- 
 der it with facility, the operation is then defined, and the 
 more prominent terms are briefly explained. This, it is 
 believed, teachers will be glad to see. There is no rea- 
 son why a child should not be informed, that a certain 
 operation upon numbers is called Addition ; another Sub- 
 traction ; &c., as well as to be told that a certain opera- 
 tion of his vocal organs in connection with those of his 
 mind, is called reading ; another singing ; &c. 
 
 With this brief explanation of the object and plan of 
 the work, the author commends it to the friends of edu- 
 cation, by whom his former efforts to subserve this noble 
 cause, have been so favorably received. 
 
 Although designed particularly as an introduction to 
 the *' Practical Arithmetic," it may be used as a prepar- 
 atory work to any of the larger systems of Arithmetic 
 now aefore the public. 
 
MENTAL ARITHMETIC. 
 
 SECTION I 
 
 INTRODUCTION, 
 
 The first step in acquiring a knowledge of numbers is 
 to learn to count. Most children are able to repeat the 
 na7}ies of numbers, one, two, three, (Sec, before they begin 
 to go to school ; but there are fewer who fully comprehend 
 the meaning of these terms; who perceive, for example, 
 that eleven expresses more things than seven, or fewer 
 than thirteen. While such is the case, no substantial 
 progress can be made in Arithmetic. 
 
 Great pains should therefore be taken to show young 
 pupils, in the outset, how many things thf» name of each 
 number denotes, and to establish in their minds a correct 
 idea of more and less. Counters, made of round pieces 
 of wood or leather, also beans, kernels of com, &c., may 
 be used for this purpose ; but the most convenient appa- 
 ratus is the Numerical Frame.* The bails upon the 
 wires are more easily arranged and are seen at once by 
 every member of the class, while the liability of falling 
 upon the floor and getting lost, is entirely avoided. 
 
 LESSON I. 
 
 Having slipped all the balls to the left side, the 
 teacher holds up the Numerical Frame before the 
 class and requests their particular attention. 
 
 • Every instniclor who is called upon to tearh the nidimfntfl of 
 Arithmetic, should be furniBhed wiih this useful instrument, it 
 
INTRODUCTION. 
 
 With his pointer he now moves the first ball on 
 the bottom wire to the right side and says, this is 
 oiie, the class repeating it with him. Moving across 
 another on the same wire, he says, this makes two, 
 the class repeating it with him as before ; moving 
 an )ther, this makes three ; another still, this makes 
 ' four ; and yet another, this makes Jive ; and so on 
 up to ten. 
 
 Tliis process should be repeated and varied ac- 
 cording to circumstances, u.itil the class can count 
 ten in concert and individually with readiness. If 
 this cannot be accomplished in one exercise, another 
 should be devoted to it. 
 
 Note.—U the (hil<lr»»n are young, or have never learned the 
 names of any of the numbers, when they get to three or Jive h will 
 l)e ^xp«?nient to stop and review as far as they have been. Care 
 Hhould be taken not to present too many new ideas to the young 
 mind at once, lest it become bewildered ; nor should the exercise 
 be continued so long as to weary it, and thus create a lasting dis- 
 relish for the study. 
 
 LESSON II. 
 
 Slippine a»: the balls to the left side of the frame 
 as before, move the first on the lower wire to ihe 
 right side, and ask the class to count it. 
 
 Now move out two on the second wire, taking 
 one at a time, and let the class count as you niuve 
 them, one, tioo. Then pass across three on the third 
 wire, taking one at a time, while the class coimt 
 one, two, three. 
 
 costs but a trifie, and, with proper care, will last an age. Us 
 raore important uses will be pointed out in their proper place. 
 
 The lessons in this Section are designed for pupils who have 
 not learned to count, or may not comprehend how many things 
 are dr«noted by the names of numbers. I'hose who thoroughly 
 undeti-tand tliese points, cen begin with Addition. 
 
INTRODUCTION. 7 
 
 Proceed in this manner to the iejith or Icist, in- 
 creasing one ball on each successive wire. 
 
 Again, beginning at the bottom, let the class count 
 he balls moved out on each Avire, and observe that 
 two is one more than one; that three is one more 
 than two ; that four is one more than three, &c. 
 
 Next, let the class retrace this process ; that isj | 
 beginning at the top, let them count the balls moved 
 out on each wire till they arrive at the bottom one. 
 
 Let them also begin at ten and count backwards 
 to one, several times in quick succession. Thus, 
 teji, nine, eight, seven, six, &c. 
 
 Finally, move out any number of balls under ten 
 promiscuously, and call upon some one to count 
 them ; then move out a different number, and let 
 another count them ; and thus continue to vary the 
 exercise, till every one in the class can count ten 
 understandingly. 
 
 LESSON III. 
 
 Note. — As soon as the class clearly comprehend how many thinffs 
 are expressed by the name of each of the numbers up to ten, they 
 are then prepared to learn to count from ten to twenty, &,c. 
 
 Flaving counted out ten balls on the lower wire, 
 move across one on the second wire saying, this 
 makes eleven, the class repeating it with you. Pass- 
 ing across another, this makes twelve ; another, this 
 makes thirteen ; another still, this makes fourteen ; 
 and so on up to twenty. 
 
 Repeat this process, at the same time explaining 
 to the class that the term thirteen, is composed of 
 the words three and ten, and means the same as ihvf'e 
 counted on to ten, or three and ten put together. 
 Also, that the term fourteen is con.posed of the 
 
INTRODUCTION. 
 
 words four and ten, and means the same as four and 
 ten put together; that fifteen means five and ten; 
 sixteen^ six and ten ; seventeen, seven and ten; eiyh- 
 teen, eight and ten; nineteen, nine and ten; and 
 twenty means two tens. 
 
 Next, having counted off twenty balls ; that is, 
 ten apiece on each of the two lower wiies, pass 
 across one on the next wire, saying this makes twen- 
 ty-one, the class repeating it with you as before. 
 Passing across another, this makes tioenty-two ; an- 
 other, this makes tioenty-three ; another still, this 
 makes twenty-four ; and so on to thirty. 
 
 Here again tlie teacher should be careful to ex- 
 plain that the term twenty-one, is composed of the 
 words iiventy and one, and means the same as one 
 counted on to twenty, or twenty and one put together. 
 Also, that the term twenty-two, is composed of the 
 words twenty and two, and means the same as twenty 
 and two put together; that tzoenty- three mea.ns twen- 
 ty and three ; «fec. 
 
 In a similar manner children may be easily taught 
 to count from thirty to forty, fifty, sixty, &c., to a 
 hundred, and to comprehend Iiow 7nany tilings are 
 expressed by the name of each number. 
 
 Nott to tht Teacher. — It is advisable to exercise the pupil 
 in writing the Jigures upon his slate, or the black-board, in 
 the early part of his course. This will afford him pleasing 
 occupation, and at the same time, will be of great assistance 
 in enabling him to understand and apply them when he 
 shall have occasion for their use 
 
SECTIOJN II. 
 ADDITION. 
 
 LESSON I. 
 
 1. How many little hoys are there in this class? 
 
 2. How many little girh are there ? 
 
 3. How many little girls and boys are there, 
 counted together ? 
 
 4. Will each of you show n e your right hand ? 
 Now if you put your left hand by the side of it, how 
 many hands will each one show me ? Why ? 
 
 Ans. Because one and one more make tv:o. 
 
 5. If you show me two fingers on your left hand 
 and one on your right, how many fingers will you 
 show me ? Why ? 
 
 Ans. Because two and mie more make three. 
 
 6. If you open three fingers on your left hand and 
 one on your right, how many fingers will you have 
 open ? Why ? 
 
 7. How many fingers have you on your right 
 hand ? How many thumbs ? How many fingers 
 and thumbs counted together, are there on your right 
 hand? 
 
 8. If I move out five balls on the lower wire of 
 Tfiy Numerical Frame and one on the next, how 
 many will they all make ? Why ? 
 
 Note. — When a general question ia asked whicl is not desi^Hd 
 to be answered in concert, it is an excellent way to have afi who j 
 think they know, raise a hand ; the i call upon some one promifl- j 
 cuously to answer it. This methcxJ prevents much confusion and | 
 secures the attention, wliile it effectually avoids the temp'ation , 
 to learn the answers to certain questions which will fall to »>ach, 
 if the teacher always begins at the same end of the cla^^ and 
 proceeds through it iii regular rotation. 
 
10 
 
 ADDITION, 
 
 9. I^ I move out six on the lower wire and one 
 on the next, how many will they make ? Why ? 
 
 10. If I move out seven on the lower and one on 
 the next, how many will they make ? Why ? 
 
 11. If I move out eight on the lower and one on 
 the next, how many will they make ? 
 
 12. If I move out wne on the lower and one on 
 the next, how many wi 1 they make ? 
 
 Note. — A« loon m a child learns a principle in Arithmetic, it i« 
 iniportajit for him to see ita application, ana begin to practice it. 
 For this reason, it js recommended to let the class iludy the next 
 eight lessons in connection with the corresponding paru of the Ta- 
 ble be.ow. Thus, as soon as they learn to add twos, let them take 
 lesson second yvhich contains exercises in adding two ; as soon as 
 they learn to add threes, let them take lesson third, &c. In this 
 way the Table is kept together, which is essential for reference 
 ana review, ar.d at the same time we secure all the advantages 
 of studying it jx connection with examples which put it into prac- 
 tice, as fast as it is leamexi. 
 
 ADDITION TABLE. 
 
 One 
 
 •nd 
 
 oae wr. 
 
 twa 
 
 One 
 
 •nd six V seven. 
 
 One 
 
 u 
 
 two " 
 
 threek 
 
 One 
 
 " seven « eight. 
 
 One 
 
 u 
 
 three " 
 
 four. 
 
 One 
 
 " eight " nine. 
 
 One 
 
 U 
 
 four " 
 
 five. 
 
 One 
 
 " nine " ten. 
 
 One 
 
 u 
 
 five " 
 
 six. 
 
 One 
 
 « ten " eleven. 
 
 Two 
 
 and 
 
 OJtB •« 
 
 three. 
 
 Two 
 
 u»d six Ml eight. 
 
 Two 
 
 u 
 
 two " 
 
 four. 
 
 Two 
 
 " seven " nine. 
 
 Two 
 
 (1 
 
 three " 
 
 five. 
 
 Two 
 
 " eight " ten. 
 
 Two 
 
 H 
 
 four " 
 
 six. 
 
 Two 
 
 •' nine " eleven. 
 
 XW) 
 
 n 
 
 five '* 
 
 seven. 
 
 Two 
 
 " ten " twelve. 
 
 Ihree 
 
 •Ad 
 
 on«J «• 
 
 four. 
 
 Three 
 
 Hid six u* nine. 
 
 Three 
 
 u 
 
 two " 
 
 five. 
 
 Three 
 
 " seven " ten. 
 
 Three 
 
 u 
 
 three " 
 
 six. 
 
 Thr«e 
 
 " eight " eleven 
 
 Three 
 
 II 
 
 four " 
 
 seven. 
 
 Three 
 
 " nine " tweha 
 
 Three 
 
 II 
 
 five . " 
 
 eight. 
 
 Three 
 
 " ten " thirteen. 
 
1 
 
 1 
 
 
 ADDITION. 
 
 11 
 
 Four 
 
 and one 
 
 art five. 
 
 Four and six 
 
 are ten. 
 
 1 Four 
 
 " two 
 
 » «x. 
 
 Four " seven 
 
 " eleven. ( 
 
 1 Four 
 
 ' three 
 
 " seven. 
 
 Four " .eight 
 
 " twelve. 
 
 ! Four 
 
 ' four 
 
 " eight. 
 
 Four " nine 
 
 «♦ thirf.'en. | 
 
 i Four 
 
 « five 
 
 " nme. 
 
 Four " ten 
 
 ** fourteen. 
 
 ; Five 
 
 and one 
 
 are six. 
 
 Five and six 
 
 are eleven. 
 
 Five 
 
 " two 
 
 " seven. 
 
 Five " seven 
 
 " twelve. 
 
 Five 
 
 " three 
 
 " eight. 
 
 Five " eight 
 
 " thrrieen. 
 
 Five 
 
 « four 
 
 " nine. 
 
 Five " nine 
 
 " fourteen 
 
 Five 
 
 " five 
 
 " ten. 
 
 Five " ten 
 
 " fifteen. 
 
 Six 
 
 ana one 
 
 ar« seven. 
 
 Six and six 
 
 are tWclve. 
 
 Six 
 
 » two 
 
 " eight. 
 
 Six '" seven 
 
 " thirteen. 
 
 1 Six 
 
 " three 
 
 " nine. 
 
 Six " eight 
 
 " fourU^en. 
 
 Six 
 
 " four 
 
 " ten. 
 
 Six '< nine 
 
 « fifteen. 
 
 Six 
 
 " five 
 
 *' eleven. 
 
 Six " ten 
 
 " sixteen. 
 
 Seven 
 
 aud one 
 
 are eight. 
 
 Seven and six 
 
 are thirteen. 
 
 Seven 
 
 '» two 
 
 " nine. 
 
 Seven " seven 
 
 " fourteen. 
 
 Seven 
 
 " three 
 
 " ten. 
 
 Seven " eight 
 
 " fifteen. 
 
 Seven 
 
 " four 
 
 " eleven. 
 
 Seven " nine 
 
 " sixteen. 
 
 Seven 
 
 " five 
 
 " twelve. 
 
 Seven " ten 
 
 " seventeen. 
 
 Eight 
 
 and one 
 
 are nine. 
 
 Eight and six 
 
 are fourteen. I 
 
 Eight 
 
 " twn 
 
 " ten. 
 
 Eight " seven 
 
 " fifteen. | 
 
 Eight 
 
 " thific 
 
 " eleven. 
 
 Eight " eight 
 
 " sixteen. 
 
 Eight 
 
 « fom 
 
 '* twelve. 
 
 Eight " nine 
 
 " seventeen. 
 
 Eight 
 
 " five 
 
 ** mirteen. 
 
 Eight " ten 
 
 *• eighteen, j 
 
 ! Nine 
 
 and one 
 
 are ten. 
 
 Nine anu six 
 
 are fifteen. - 
 " sixteen. 
 
 Nine 
 
 " two 
 
 " eleven. 
 
 Nine " seven 
 
 Nine 
 
 " three 
 
 " twelve. 
 
 Nine " eight 
 
 " seventeen. 
 
 Nine 
 
 « four 
 
 " thirteen. 
 
 Nine " nine 
 
 '* eighteen, j 
 
 j Nine 
 
 1 
 1 
 
 « five 
 
 " fourteen. 
 
 Nine " ten 
 
 " nineteen. 
 
12 ADD7TI0N. 
 
 LESSON II. 
 
 1. If a pear costs two cents, and an apple costs one 
 cent, ho^ many cents will they both cost ? Why ? 
 
 2. Charles had ttao books, and his father gave him 
 two more: how many books did he then have? — 
 Why? 
 
 3. Robert brought in three sticks of wood, and 
 George two sticks : how many sticks did both boys 
 bring in ? Why ? 
 
 4. Let each one in the class open all his. fingera 
 on his left hand, and two on his right : how many 
 fingers has each one open ? How many are four 
 and two ? 
 
 5. Sarah had Jive dresses, and on her birthday 
 her aunt gave her two more : how many dresses had 
 she then ? Why ? 
 
 6. In this class there are two girls, and six boys : 
 how many scholars does the class contain ? 
 
 7. John has seven brothers, and two sisters : how 
 many brothers and sisters has he together ? 
 
 d. A little boy gave a blind man eight cents, and 
 his sister gave him two cents more : how many cents 
 did they both give him ? 
 
 9. William has two marbles in his hand, and nint 
 in his pocket : how many marbles has he in all ? 
 
 10. Mary recited two perfect lessons last week and 
 
 ^1 Nole. — llje process of addins and the structure of the Table 
 raay be easily illustrated by the Numerical Frame. Thus, to show 
 that five and four make nine, mi-ve out five balls on one wire and 
 four on another, and let the pupil count them together. But as 
 I soon as the pupil understands the principle of the oiHiration, he 
 should tlien learn to i»crforra it without the assistance of visible 
 objects. Nothing is more deleterious to mental growth and dis- 
 cipline, than the habit of solving questions by counters, by the 
 fingers, marks upon a slate, &c. (S^n. 
 
ADDITION. 13 
 
 tfifi this wee.i : how many perfect lessons has sK-e re- 
 cited in two weeks ? 
 
 LESSON III. 
 
 1 If you pay three cents for a pint of nuts, and I 
 one cent for an apple, how many cents do you pay 
 for boili ? Why ? 
 
 2. Henry has tkree young doves, and two old j 
 ones : how many doves has he ? Why ? 
 
 8. A begjxar met some generous little boys, one 
 of whom gave him four cents, and another gave him 
 three cents: how many cents did they both give 
 him ? Why ? 
 
 4. Susan bought three yards of blue ribbon, and 
 three yards of white : how many yards of ribbon did 
 
 I she buy in all ? Why ? 
 
 5. Harriet gave her teacher Jive pinks, and three 
 roses : how many flowers did she give her teacher ? 
 
 6. Matthew sold a quart of chestnuts for 6ix cents, 
 and a pint of beechnuts for three cents: how much 
 did his nuts come to ? i 
 
 7. flenry picked three ripe peaches from one lree> I 
 and s€i'>en from another : how many peaches did lie ' 
 pick from both trees ? I 
 
 8. Frank has nme walnuts in his pocKet, and he j 
 lost three coming to school : how many had he when 
 he started from home ? 
 
 9. How many are eight and three ? I 
 
 10. Jane read ten pages of hislory in the morning, ' 
 and three in the afternoon : how many pages did slm i 
 read during the day ? I 
 
 Ncte. — It is ad\l8able lo have the class review iIjc prerrdinjr i 
 part of the Table, and thus continue to do at every re-itati(jn, ! 
 till they get through it. { 
 
14 ADDITION. 
 
 LESSON IV. 
 
 1. Joseph received four peaches from his couiiin. 
 and one from his sister : how many peaches had he ? 
 
 2. A boy paid four cents for an orange and two 
 cents for a pear : how much did he pay for both ? 
 
 3. Emily bought a yard of silk for five shillings, 
 and a pair of gloves for four shillings : how many 
 shillings did she pay for both ? 
 
 4. Dick's father gave him six marbles, and he 
 gained four more : how many had he then ? 
 
 5. Henry gave four cents for a lemon, and four 
 cents for an orange : how many cents ^lid he give 
 for both ? 
 
 6. A farmei g^yefour dollars for a hog, and eight 
 dollars for a cow : how much did he pay for both ? 
 
 7. How many are four and three ? 
 
 8. A market boy soldybwr shillings worth of milk, 
 and vegetables to the amount of ^even shillings: how 
 much money did he have to carry home ? 
 
 9. James g&yefour shillings for a knife, and nine 
 shillings for a pair of skates: what did he pay for 
 both? 
 
 10. Henrietta bought a slate for ten cents, and a 
 sponge for four cents : how much did she pay for 
 both? 
 
 LESSON V. 
 
 1. A man bought a plough for fve dollars; and a 
 •hovel for two dollars : how many dollars did he pay \ 
 for both ? j 
 
 2. A farmer raised three bushels of plums n one | 
 tree, and j?re bushels on another : how many bushels 
 did he raise on both trees ? 
 
ADDITION. 15 
 
 I 3. A man sold a bushel of plums fear five dollars, 
 and a bushel of peaches (or four dollais: how much 
 did both come lo ? 
 
 4. There are six sweet apples, said five sour ones , 
 I in the fruit dish: how many apples does the dish 
 
 contain ? j 
 
 5. A man paid^t'e shillings for a turkey, &nd five 
 shillings for a peck of peas: how much did he pay 
 for both ? 
 
 6. A man caught eight red squirrels, erndfive grey 
 ones : how many did he catch in all ? 
 
 7. A cabinet-maker asks five dollars for a rock- 
 ing chair, and seven dollars for a table : what is the 
 price of both ? 
 
 8. If I pay five shillings postage on letters, and 
 nine shillings on pamphlets, what is the amount of 
 my postage ? 
 
 9. Harriet bought a comb for ten cents, and a pa- 
 per of needles ioT five cents : how much did she pay 
 for both ? 
 
 LESSON VI. 
 
 1. Charlotte picked six white roses, and two red 
 ones : how many roses did she pick ? 
 
 2. Harriet gave three cents for a sponge, and six 
 cents for a slate : how many cents did she pay for 
 both? 
 
 3. IIow many are six and six ? 
 
 4. How many are six ^nd five ? Y 
 
 5. How many are six and ybwr? 
 
 6. If you read six pages in the morning, and seven 
 in the evening, how many pages will vou read in a 
 day 1 
 
1 8 ADDITION. 
 
 7. John hoed ei^ht rows of cca*n in one day, and 
 s,x in another day: aow many rows did he hoe in 
 bolh days ? 
 
 8. His employer gave him nine pence for liis first 
 day's work, and six pence for the second day 's work : 
 how many pence did John receive ? 
 
 9. A lady bought a muff for J^n dollars, and a hat 
 for six dollars : what was the amount of her bill ? 
 
 LESSON VII. 
 
 1. Sarah had seven pins on her cushion, and she 
 afterwards found two more : how many pins had she 
 then? 
 
 2. How many are seven and three ? 
 
 3. If seven flower pots stand in one window, and 
 foiir in another, how many are there in both win- 
 dows ? 
 
 4. How many are seven and six? 
 
 5. How many are seven snid Jive? 
 
 6. How many are seveii and seven? 
 
 7. Oliver paid seven cents for a writing-book, and 
 eig/it cents for a slate: how much did he pay for 
 both? 
 
 8. How many are seven and ten ? 
 
 9. How many are seven and nine ? ft 
 
 LESS jN VIII. 
 
 1. If a barrel of flour cost eight doLars, and a keg 
 cf lard 'wo dollars, how much will Wh cost? 
 
 *2. A merchant tailor asks eight liars for a pair 
 of pants, and three dollars for a vest: what is the 
 price of both ? 
 
ADDITION. 17 
 
 3. If you pay eight cents a mile for the use of a 
 horse, and Jive cents for a buggy, how much will you j 
 pay a mile for both ? i 
 
 4. How many are 6(i0'/i/ and yb?/r? ! 
 f>. Julius gave one of his companions six ap* '*3, i 
 
 and had eight left : how many had he at first ? | 
 
 6. Henry had eight marbles, and his brother gave 
 him eight more : how many did he then have ? 
 
 7. A shopkeeper sold eight yards of satin to one 
 lady, and seven to another: how many yards did he 
 sell to both ? 
 
 8. Catharine's book has eight pictures in it, and 
 iMary's has 7une : how many pictures do both books 
 contain ? 
 
 9. If you pay eight cents for a pound of sugar, 
 and ten cents for a pound of figs, what must you 
 pay for both ? 
 
 LESSON IX. 
 
 1. There are nine shade trees standing in front of 
 the school house, and two have been cut down : how 
 many trees were set out ? 
 
 2. Alexander's kite line is now nine yards long, 
 i by accident he broke off three yards: how long was 
 
 his line at first ? 
 
 3. flow many are ni?ie and Jive? 
 
 4. IIow many are iwie smd four? 
 
 5. If a ton of coal costs nine dollars, and a co.-d 
 of wood costs s^ix dollars, how much will they both 
 
 jCOSt? 
 
 I 6. A hunter gave nine dollars for a gun, and 
 I seven dol ars for a dog : how much did he pay for 
 
 \ both ? 
 
 I 
 
18 
 
 ADDITION, 
 
 7. If you have nine chestnuts in cne pile and nine 
 in another, how many will they make i( you put 
 thtm all into one pile ? 
 
 8. In Margaret's flower garden there are nine 
 lady's slippers, *nd eight bachelor's buttons: how 
 many flowers has she ? 
 
 9. Sophia wrote nine lines at the last exercise, 
 and Henrietta wrote ten : how many lines did both 
 write ? 
 
 LESSON X* 
 
 1 . Ilow many are one and ten ? Three and ten ? 
 Six and ten 1 Four and ten ? Seven and ten. Five 
 and ten ? Eight and ten ? Nine and ten ? 
 
 2. How many are eleven and ten ? Twenty-one 
 and ten ? Forty-one anjd ten ? Thirty-one and ten ? 
 Fifty-one and ten ? Seventy-one and ten ? Sixty -one 
 and ten ? Eighty-one and ten ? Ninety-one and ten ? 
 
 3. Two and ten ? Twelve and ten ? Twenty-two 
 and ten ? Forty-two and ten ? Thirty -two and ten ? 
 Fifty-two and ten ? Seventy -two and ten ? Sixty-two 
 and ten ? Eighty-two and ten ? Ninety-two and ten ? 
 
 4. Three and ten ? Thirteen and ten ? Twenty- 
 three and ten ? Forty-three and ten 1 Thirty-three 
 
 ! and ten ? Sixty-three and ten ? Eighty-three and 
 ten ? Fifty-three and ten ? Seventy-three and ten ? 
 Ninety-three and ten ? 
 
 5. Four and ten? Fourteen and ten? Twenty-four 
 and ten ? Fifty-four and ten ? Thirty-four and ten ? 
 Sixty-four and ten ? Forty-four ar d ten ? Eighty-four 
 
 * TJiis and the following Lesson should he studied, 1 11 the ques- 
 tions can be answered with great faril'ty. 
 
ADDITION. 19 
 
 1 and ten ? Seventy-four and ten ? Ninety-four and 
 Iten ? 
 
 I 6. Five and len ? Twenty-five and ten ? Fifteen 
 , and ten ? Seventy-five and ten ? Sixty-five and ten ? 
 ! Fifty-five and ten ? Forty-five and ten ? Ninety-five 
 and ten ? Eighty-five and ten 1 
 
 7. Six and ten ? Eight and ten ? Twenty-six and 
 ten ? Twenty-seven and ten ? Seventeen and ten ? 
 Sixty-eight and ten ? Thirty-six and ten ? Fifty- 
 seven and ten ? Seventy-six and ten ? Eighty-eight 
 and ten ? 
 
 8. Seven and ten ? Twenty-nine and ten ? Forty- 
 seven and ten ? Thirty-six and len ? Ninety-seven 
 and ten ? Seventy-six and ten ? Sixty-nine and ten ? 
 Seventy-seven and ten ? Eighty-seven and ten ? 
 
 9. Nine and ten ? Eighteen and ten ? Twenty- 
 nine and ten ? Thirty-eight and ten ? Sixty-nine 
 and ten ? Fifty eight and ten ? Seventy-nine and 
 ten ? Forty-nine and ten ? Eighty-nine and ten ? 
 Ninety-nine and ten ? 
 
 LESSON XI 
 
 1 . How many are twelve and. five ? Twenty-two 
 and five ? Forty-two and five ? Thirty -two and five ? 
 Fifty-two-and five? Seventy-two and five ? Sixty- 
 two and five ? Eighty-two and five ? Ninety-two 
 and five ? 
 
 2. How many are thirteen and six ? Twenty-three 
 and six ? Thirty-three and six? Forty-three and 
 six ? Seventy-three and six ? Fifty-three and six ? 
 Eighty-three and six f Sixty-three and six ? Ninety- 
 three and six ? 
 
 8. How many are fourteen and seven ? TAventy- 
 four and seven ? Forty-four and seven ? Thirty-four 
 
*20 ADDITION. 
 
 and seven ? Fifty- four and seven? Seventy-four and 
 seven ? Sixty-four and seven ? Eighty-four and 
 ^even ? Ninety-foui and seven ? 
 
 4. How many are fifteen and eight ? Twenty. five 
 And eight ? Sixty-f^ve and eight ? Forty-five and 
 eight ? Seventy-five and eight ? Thirty-five and 
 eight? Ninety-five and eight? Eighty-five and 
 eight? 
 
 5. How many are sixteen and nine ? Thirty-six 
 and nine ? Twenty-six and nine ? Forty-six and 
 
 I iiine ? Eighty-six and nine ? Sixty-six and nine ? 
 Ninety-six and nine ? 
 
 6. How many are seventeen and three ? Twenty- 
 jseven and four ? Thirty-seven and five ? Forty- 
 seven and six ? Fifly-seven and seven ? Sivty-seven 
 and eight ? Eighty-seven and nine ? 
 
 7. How many are eighteen and two ? Twenty- 
 eight and three ? Thirty-eight and four ? Forty- 
 eight and five ? Fifty-eight and eight ? Sixty-eight 
 and seven ? Seventy-eight and six ? 
 
 8. How many are nineteen and nine ? Twenty- 
 nine and eight ? Thirty-nine and seven ? Forty-nine 
 and six ? Fifty-nine and five ? Sixty-nine and four ? 
 3eventy-nine and three ? 
 
 9. How many are five, thirteen, two, and one ? 
 
 10. How many are six, fourteen, five, and ten f 
 
 11. How many are two, three, sixteen, and four? 
 
 12. How many are three, four, seven, and two* 
 
 13. How many are fifteen, and ten, and seven, I 
 And five, and three ? | 
 
 14. How many are thirteen, and seven, and five, 
 and ten, and four ? i 
 
 15. How many are sixteen, and four and three, j 
 and seven ? I 
 
ADDITION. 21 
 
 LEiSSON XII 
 
 i 
 
 1. A grocei sent me a pound of t^a worth seven I 
 shillings, a gallon of molasses worth three shillings, ! 
 and a pound of honey worth one shilliiig : how many | 
 shillings did they all amount to ? | 
 
 2. IIow many are ten, and fourteen, and two ? ' 
 
 3. IIow many are seven, and fifteen, and three ? 1 
 
 4. How many are sixteen, and three, and two, ! 
 and one ? 
 
 5. Charles bought a pound of raisins for ten cents, 
 a quart of strawberries for six cents, and a stick of 
 candy for one cent : what was the cost of all ? 
 
 6. One of Samuel's hens has sixteen chickens, 
 another has seven, and the other three : how many 
 chickens has he in all ? 
 
 7. In my walk this morning I saw nineteen wild 
 geese in one flock, eight in another, and five in an- 
 other : how many wild geese did I see ? 
 
 8. Sixteen, and five, and three are how many ? 
 
 9. Seventeen, and six, and fuur are huw many ? 
 
 10. Ten, and seventeen, and three are how many ? 
 
 11. Horatio paid ten cents for a peukaife, ten cents 
 for a slate, five cents for an inkstand, and one cent 
 for a pencil : how many cents did he pay for all ? 
 
 12. A man paid fifteen dollars* for a cow, eight dol- 1 
 lars for a load of hay, three dollars for a calf, and i 
 two dollars for a sheep : how many dollars did he ' 
 pay for all ? j 
 
 13. Henry bought a Spelling- Bo :)k fcr ten ccntS; , 
 I an Arithmetic for twenty cents, and a slate for nine 
 
 ! cents : how nmch did he pay for all ? 
 
 j 14. Twenty, and ten, and seven, and three, and ! 
 
 ; five are how many ? 
 
 J 
 
22 ADDITION. 
 
 LESSON XIII. 
 
 1. Q. What is the operation called, by which the 
 precedinsj examples have been solved ? 
 
 Ans. It is called Addition, 
 
 2. Q. What is addition ? 
 
 Ans. Addition is tlie process of uniting two or more 
 numbers in one sum. 
 
 3. Q. What is the answer^ or number obtained, by 
 addition, called ? 
 
 Ans. The sum or ammint. 
 
 4. Q. When we say fve and four are nine ; which 
 of these number is the sum or amount ? 
 
 When we say eleven and eight are nineteen^ which is 
 the sum or amount ? 
 
 5. Q. What is the sum of six, and four, and two ? 
 Solution. — Six and four are ten, and two are 
 
 twelvie. Ans. Twelve. 
 
 6. What is the sum of five, and three, and one ? 
 
 7. What is the sum of eight, and four, and three ? 
 
 8. What is the sum of ten, and fifteen, and two 1 
 
 9. What is the f^m of twenty, and six, and four ? | 
 
 10. What is the ^um of thirty-one, and tf.n, and | 
 six, and one, and four ? I 
 
 11. What is the sum of twenty-seven, and three, j 
 and one, and six, and five ? I 
 
 '12. What is the sum of forty-three, and four, and j 
 ten, and six, and seven ? 
 
 13. What is the sum of fifty-four, and five, and j 
 nine, and three, and six ? j 
 
 14. What is the sum of seventy-two, and three, j 
 ind five, and seven, and eight ? 
 
 IT). What is the sum of sixty-eight, and ten, and 
 two, and five, and three, and nine ? 
 
ADDITION. 23 
 
 EXAMPLES FOR PRACTICE. 
 
 Note. —The examples for practice may be divided into two or 
 more lessons according to tlie capacity of the learner. | 
 
 I 
 
 I . It cost a traveler ten shillings a day for his 
 i board, seven shillings for his horse, and three shil- 
 i lings for incidental expenses : how much were his 
 j daily expenses ? 
 
 j 2. If one little girl should give rne "Jeven roses, 
 
 j another five tulips, and another four pinks, how many 
 
 I flowers should 1 have 1 
 
 j 3. Mow many are three, and seventeen, and four ? 
 
 ! 4. How many are sixteen, and four, and five ? 
 
 I 5. How many are eighteen, and four, and two ? 
 
 I 6. A man bought a pound of sugar for ten cents, 
 
 j a pound of raisins for eight cents, and a pound of 
 
 i butter for six cents : what was the cost of all ? 
 
 I 7. Henry bought a quart of cherries for eight 
 
 I cents, an orange for tliree cents, and an ounce of 
 
 ! pep})ermints for six cents : how much did he pay 
 
 i for all ? 
 
 I 8. Five, and three, and seventeen, and one, are 
 
 I how many ? 
 
 ' 9. Sixteen, and two, and seven, and three, are 
 
 how many ? 
 
 10. Three, and nineteen, and seven, and two, are 
 
 how many ? 
 
 II . f larry bought a pound of raisins for ten cents, 
 a pound of figs for fifteen cents, and an orange for 
 five cents : what did they all amount to ? 
 
 12. Louisa gave twenty cents for her slate, ten 
 cents for her writing-book, six cents for 8 bunch of 
 
24 ADDITION. 
 
 . ! 
 
 quills, and three cents for some pencils : what did 
 she pay for all ? 
 
 13. How many are four, and five, and one ? Six, 
 and seven, and three ? Three, and eiji^ht, and four ? 
 Six, and ten, and five ? Ten, and eight, and three ? 
 
 14. How many are eight, and two, and four ? Six, 
 and one, and two ? Seven,' and four, and ten ? 
 Nine, and ten, and five ? 
 
 <?15. A farmer sold a cow for eleven dollars, a calf 
 for four dollars, and a sheep for three dollars : how 
 much did he receive for all ? 
 
 16. A gentleman had several apple-trees in h's 
 garden ; frofn one he gathered seven hushels, from 
 another ter. and from another five bushels: how 
 many bushels did he gather from all ? 
 
 17. Dick bought a knife for twenty-five cents, and 
 sold it for five cents more than he gave for it : how 
 much did he sell it for ? 
 
 15. A man bought a sleigh for thirty dollars, and 
 paid seven dollars to have it painted, and ten dollars 
 for other repairs : how much did it cost him ? 
 
 19. A farmer bought a cart for thirty-five dollars, 
 a plough for nine dollars, and a shovel for two dol- 
 lars : what was the cost of the whole ? 
 
 20. A man bought a horse for sixty dollars, a sad- 
 dle for ten dollars, and a bridle for three dollars : 
 how much did he pay for all ? 
 
 21. William boughi a i^eography for seventy-five 
 cents, a slate for ten c»^nLs, a sponge fo' three cents, 
 and a lead pencil for two cents : what was the 
 amount of his purchase ? 
 
 22. A farmer sold a horse and saddle for a hun 
 dred and twenty-five dollars, which was ten dollars 
 less than they cost him : what did he pay forjLhem? 
 
SECTION m. 
 
 S UBTRACTION. 
 LESSON I. 
 
 1. Suppose I have two peaches, and give one of 
 tl;jm away, how many shall 1 have left i 
 
 Solution. — One peacli taken from two peaches, 
 leaves one. Therefore if I have two peaches and give 
 one of them away, I shall have one left. 
 
 2. Open three fingers on your left hand ; now if you 
 shut ofie of thera, how many will remain open ? Oiie 
 taken from three leaves how many ? 
 
 3. George having four marbles in his hand, dropped 
 one of them : how many had he left ? 
 
 iVof«.— The principle of subtracting one number from another, 
 may be easily explained to the pupil by the Numerical Frame. 
 Thua, to show kow nuvny three taken from eigkt will leave, move 
 across eight balls, then moving three of thorn part way back, let 
 the pupil count those that are left. 
 
 4. Leonard had five cents and gave on*, ^r a pen- 
 cil : how many cents had he left ? One from five 
 leaves how many ? 
 
 5. Cornelia had fiix apples and gave one to her 
 brother : how many had she left ? 
 
 6. There are seven scholars belonging to this class ; 
 yesterday one of them was absent : how many were 
 present ? 
 
 7. Martha had eigkt roses, but on her way to school 
 she lost oi^£ : how muny had she left ? 
 
 8. If )ou have ten apples, und give away one of 
 thera, how many wUl .^u have left ? 
 
26 
 
 SUBTRACTION. J! 
 
 
 SUBTRACTION TABLE. 
 
 .Vote.— It U advisable tor the pupil to study this Table in the ' 
 ' wime manner aa he did ths Addition Table. (See Note, p. 10.) t| 
 
 One from 
 
 one ie*Te. naught. 
 
 One from six le>TM five. 
 
 One " 
 
 two " one. 
 
 One " seven " six. ' 
 
 One " 
 
 threj •' two. 
 
 One " eight " seven, j 
 
 One " 
 
 four " three. 
 
 One " nine " eight. 
 
 One " 
 
 five •' four. 
 
 One " ten " nine. 
 
 Two from 
 
 two leare. naUght. 
 
 Two frwn seven learei five. 
 
 ' Two " 
 
 three " one. 
 
 Two " eight " six. 
 
 Two " 
 
 four two. 
 
 Two " nine " seven. 
 
 Two " 
 
 five " three. 
 
 Two "ten " eight, i 
 
 Two " 
 
 six " four. 
 
 Two ** eleven " nine. 1 
 
 Three from three UaTe. naught. 
 
 Three fiora eight leavei five. ; 
 
 i Three " 
 
 four " one. 
 
 Three " nine • " six. 
 
 Three " 
 
 five " two. 
 
 Three " ten " seven. | 
 
 1 Three " 
 
 six " three. 
 
 Three " eleven " eight. | 
 
 ! Three " 
 
 seven *' four. 
 
 Three " twelve " nine. ! 
 
 i Four from 
 
 four it*rs» naught. 
 
 Four from nine lea»et five. 1 
 
 i Four « 
 
 five '■ one. 
 
 Four "ten " six. | 
 
 ! Four " 
 
 six " two. 
 
 Four " eleven " seven, i 
 
 Four " 
 
 seven " three. 
 
 Four " twelve " eight. , 
 
 i Four " 
 
 eight " four. 
 
 Four " thirteen " nine. | 
 
 ; Five 'rom 
 
 five leiTM naught. 
 
 Five from 'en iea»e. five. 
 
 Five " 
 ! Five " 
 
 six " one. 
 
 Five " eleven " six. 
 
 seven " two. 
 
 Five " twelve " seven i 
 
 Five " 
 
 eight " three. 
 
 Five ** thirteen •' eight 1 
 
 Five " 
 
 nine '* four. 
 
 Five " fourteen " nine. ■ 
 
 ; Six fnw. 
 
 six iea»et naught. j Six from eleven itaT«t five. 
 
 Six " 
 
 seven " one. j Six " twelve " six. j 
 
 i Six " 
 
 eight " two. Six " thirteen " seven. '. 
 
 1 Six " 
 
 nine " t iree. Six " fourteen " eight. | 
 
 Six ' 
 
 ten " fom. Six *« fifteen " nine, i 
 
SUBTRACTION. 
 
 27 
 
 .- I 
 
 Seven 
 
 from seven 
 
 leares naUght. 
 
 Seven from twelve leare 
 
 five. 
 
 Seven 
 
 " eight 
 
 " one. 
 
 Seven " thirteen " 
 
 six. 
 
 Seven 
 
 " nine 
 
 " two. 
 
 Seven " fourteen " 
 
 seven. 
 
 Seven 
 
 " ten 
 
 " three. 
 
 Seven " &iieen " 
 
 eight. 
 
 Seven 
 
 •' eleven 
 
 " four. 
 
 Seven " sixteen " 
 
 nine. 
 
 Eight 
 
 row eight 
 
 leaTM naught. 
 
 Eight from thirteen ieaTe«five. 
 
 Eight 
 
 " nine 
 
 " one. 
 
 Eight •' fourteen " 
 
 six. 
 
 Eight 
 
 " ten 
 
 " two. 
 
 Eight " tifteen " 
 
 seven 
 
 Eight 
 
 " eleven 
 
 " three. 
 
 Eight " sixiean " 
 
 eight 
 
 Eight 
 
 " twelve 
 
 " four. 
 
 Eight " seventeen " 
 
 nine. 
 
 Nine 
 Nine 
 Nine 
 Nine 
 Nine 
 
 trom nine leares 
 
 •' ten " 
 
 ■* eleven " 
 
 '• twelve " 
 
 " thirteen " 
 
 naught. 
 
 one. 
 
 two. 
 
 three. 
 
 four. 
 
 Nine 
 Nine 
 Nine 
 Nine 
 Nine 
 
 fruiu fourteen leav«. 
 
 " fifteen " 
 
 " sixteen " 
 
 '* seventeen " 
 
 " eighteen " 
 
 five. 
 
 six. 
 
 seven 
 
 eight. 
 
 nine. 
 
 LESSON I 
 
 1. William had two apples when he started from 
 home, and has given two away : how many has he 
 rn)\v I Two from two leaves how many ? 
 
 2. Eliza had four cents, and has spent two of them 
 for candy : how many cents has she left ? 
 
 Note. — The pupil should think what number added to two 
 makes four, and that will be the number of cents she now has. 
 
 3. There were three doves upon the roof of a 
 barn, but two of them have flown away : how many 
 remain upon the roof? Two from three leaves how 
 many ? One from three leaves how many ? 
 
 4. Marbles were formerly five cents a dozen, but 
 now they are two cents cheaper : what do they now 
 cost a dozen? Two and what number make five? 
 Three from five leaves how many ? 
 
 5. Joseph having seven cents, gave two of them 
 
29 
 
 SUBTRACTION. 
 
 for a peach : how many cents had he left? Two 
 and what number make seven ? Five from seven 
 leaves how many ? 
 
 6. A boy bou«Tht six tumblers, and broke two of 
 them in carrj'ing them home; how many whole 
 ones were left ? Two and what number make six ? 
 Four from six leaves how many 1 
 
 7. Formerly there were nine shade trees in front 
 of the school house, but two have been cut down : 
 how many remain ? 
 
 8. There are eight scholars in the Geography 
 class ; two of them missing their lesson, were de- 
 tained : how many were permitted to take their 
 seats ? 
 
 9. A boy having ten rabbits, lost two of them : 
 how many had he left ? 7\vo and what number 
 make ten ? Eight from ten leaves liow many ? 
 
 LESSON in 
 
 1. Edwin nad three oranges, and gave each of his 
 three sisters one apiece : how many had he left i 
 Three from three leaves how many ? 
 
 2. If Edwin had four oranges, and should flfive 
 away three, how many would he have left? I'Lee 
 from four leaves how many ? 
 
 8. A boy was sent to buy six eggs, by careless- 
 ness he broke three of them: how many whole ones ij 
 had he left ? Three and what number make six ? :| 
 
 4. A man put five cows in a pasture, but .nree 
 of them jumped out : how many remained in the 
 pasture ? 
 
 5. Louisa havin^r seven shillings, gave three of 
 
SUBTRACTION. 29 
 
 them for a pair of gloves : how many shillings had 
 she then ? 
 
 6. Frank had nine chickens, but three of them 
 were kille«i by the hawks : how many had he left ? 
 
 7. Eight boys were permitted to go out, but only 
 tkree of them chose to go : how many staid ir. 
 school ? 
 
 8. Eleven boys were called up to be punished for 
 bad conduct, all but three of them confessed and 
 were pardoned : how many escaped the punish- 
 ment ? 
 
 9. Julia finding ten roses on her bush, picked off 
 three : how many remained on the bush ? 
 
 10. There were twelve peaches in a fruit basket, 
 three of which had begun to decay : how many 
 sound ones were there I 
 
 LESSON IV. 
 
 1. Joseph having five lemons, gave foui of them 
 for a knife : how many had iie left ? 
 
 2. There were seven chairs in a school room, 
 four of which were bioken : how many whole ones 
 were there ? 
 
 '3. Mary having six pears, gave four of them to 
 her brothers : how many had she left ? 
 
 4. On a training day, nine boys formed themselves 
 into a military company, four of them were officers 
 and the remainder were privates: how many pri- 
 vates were there ? 
 
 5. John made eight marks on his sla*e, and then 
 rubbed out four of them : how many marks remain- 
 ed ? 
 
 6. A pouni of sugar is worth tep *»nta, and a 
 
30 SUBTRACTION, 
 
 quart of vinegar is worth four cents: hrf)W much 
 more is the sugar worth than the vinegar ? 
 
 7. Lucretia had twelve flower pots standing ic the 
 window, and four of them fell out : how many re- 
 mained in the window ? 
 
 8. Edward exchanged his kite worth eleven ceuts 
 for an inkstand worth four cents, and received the 
 balance in money : how much money did he re 
 ceive ? 
 
 9. William gave thirteen cents for a slate, and 
 four cents for a sponge : how much more did his 
 slate cost than his sponge ? 
 
 10. There are fourteen pages in Henrietta's wri- 
 ting-book, and she has written four of them : how 
 many pages remais to be written ? 
 
 LESSON V. 
 
 1. If an orange costs six cents, and a lemon costs 
 five cents, how much more does an orange cost than 
 a lemon ? 
 
 2. A man having bought eight yards of cloth. 
 , used five yards to make a suit of clothes : how many 
 
 yards had he left ? 
 
 3. Frank has seven marbles, and John has five : 
 how many more marbles has Frank than John ? 
 
 4. A man bought a cow for ten dollars, and gave j 
 a barrel of flour worth five dollars, and paid the rest 
 in money : how much money did he pay ? 
 
 5. If a bushel of wheat costs nine shillirjgs, and a 
 bushel of corn five shillings, what is the difference 
 in their price ? 
 
 6. A man bought a quantity of butter for twelve 
 dollars, but finding it damaged, sold it for five dol- 
 
SVBTRACTION. 31 
 
 lars less than he gave for it : for how much did he 
 sell it ? 
 
 7. If you had eleven dollars and should pay five 
 dollars for a hat, how many dollars would you have 
 left? 
 
 I 8. John answered thirteen questions and Peter 
 only five : how many more questions did John an- 
 swer than Peter ? 4> 
 
 9. A trader bought a keg of tobacco for fourteen 
 dollars, and sold it for five dollars less than he gave : 
 how much did he sell it for ? 
 
 LESSON VI. 
 
 1. There were seven passengers in a stage, six of 
 whom got out : how many were left in the stage ? 
 
 2. George bought nine quills, and used up six of 
 them in a week : how many had he left ? 
 
 3. A boy liaving eight cents, bought six cents 
 worth of figs : how many cents had he left ? 
 
 4. Jane having eleven walnuts, cracked bix of 
 them : how many whole ones has she ? 
 
 5. Moses sold his knife for ten cents, which vvas 
 six cents more than he gave for it : how much did it 
 cost him ? 
 
 6. A writing-book costs thirteen cents, and an 
 inkstand six cents : how much more must I pay for 
 a writing-book than an inkstand ? 
 
 7. Harriet bought twelve knots of yarn, and used 
 six knots in knitting herself a pair of stockings : how 
 many knots had she left ? 
 
 j 8. During the last fourteen days it has rained six 
 days : how many fair days have there been ? Eight 
 I from fourteen leaves how many ? 
 
32 SUBTRACTION. 
 
 9. A watermelon costs fifteen cents, and a musk- 
 melon six cents : what is the difference in their 
 prices ? 
 
 LESSON Vll 
 
 1. Sarah had eight pins, but she has lost seven of 
 them : how many has she left ? 
 
 2. Catharine having a present of nine peachea, 
 gave away seven of them, and kept the remainder : 
 how many did she keep ? 
 
 3. Seven from eleven leaves how many ? Four 
 from eleven leaves how many ? 
 
 4. A merchant had ten yards of cloth in a piece, 
 and sold seven yards of it ; how many yards were 
 left? 
 
 5. If you had twelve apples and should give 
 away seven of them, how many would you have 
 left? 
 
 6. John had thirteen marbles and lost seven of 
 them at play • how many had he left ? 
 
 7. A farm" drove fourteen sheep to market, but 
 could sell 01 dy seven of them : how many had he 
 left ? 
 
 8. Seven from sixteen leaves how many ? Nine 
 from sixteen leaves how many ? 
 
 9. A man bought a keg of molasses containing 
 fifteen gallons, and having used a quantity of it, 
 
 I found he had seven gallons left : how much nad he 
 used ? 
 
 10. There were seventeen caps hung up in the 
 entry, but during recess seven of them were knocked 
 down : how many of them were left hanging ? Ten 
 from seventeen leaves how many ? 
 
SUBTRACTION. 
 
 LESSON VIII. 
 
 1. Frank bought a book for eight cents, and sod 
 I it for eleven cents : how much did he make by his 
 
 bargain ? 
 
 2. A lady bought a dress for eight dollars, and 
 handed the shopkeeper a ten-dollar bill : how much 
 chanjje ought she to receive back ? 
 
 3. John bought a sled for nine cents, and paid 
 eight cents down : how many cents does he still 
 owe for it ? 
 
 4. There are twelve weeks in a quarter, and 
 eight of them are past : how many weeks before the 
 quarter will end ? 
 
 5. Eight Trom fifteen leaves how many ? Seven 
 fiom fifteen, how many ? 
 
 6. Ei<rht from thirteen leaves how many ? Five 
 from thirteen, how many ? 
 
 7. Margaret's vacation is fourteen days long, and 
 she has been at home eight days : how many days 
 before she must return to school ? Eight from 
 fourteen leaves how many ? 
 
 8. A boy having sixteen oranges in his basket, 
 sold eight of them to the Railroad passengers : how 
 many has he left ? 
 
 9. A little girl went a shopping with seventeen 
 cents in her purse, and on her j^eturn, found she had 
 eight cents left : how much did she spend ? Eight 
 from seventeen leaves how many ? 
 
 10. A man selling a cow for eighteen dollars, took 
 eight dollars hi goods and the rest in money : how 
 much money did he receive ? Eight from eighteen 
 leaves how many ? 
 
34 SUBTRACTION. 
 
 LESSON IX. 
 
 1 - If ) ou buy a pound of sugar for nine cents, 
 and give the shopkeeper a ten-cent piece, how much 
 change ought he to give you ? 
 
 2. In the Algebra class there are twelve schol- 
 ars, and nine of them recited their lesson perfectly ; 
 how many failed ? Three from twelve leaves how 
 many ? 
 
 3. Susan has eleven pmks and nine tulips : how 
 many tulips must she receive to*make them equal 
 in number to her pinks ? Two from eleven leaves 
 how many ? 
 
 4. Harriet's age is thirteen years, and Lucy's is 
 nine years: how much older is Harriet ^han Lucy? 
 Four from thirteen leaves how many ? 
 
 5. Nine from fifteen leaves how many ? Six 
 from fifteen, how many ? 
 
 6. Nine from fourteen leaves how many ? Five 
 from fourteen, how many ? 
 
 7. Albert has sixteen plums, and James nine : 
 ' how many must James receive to make his number 
 i equal to that of Albert ? 
 
 I 8. A merchant bought a quantity of beef at sev- 
 I enteen dollars a barrel, and finding it damaged, sold 
 I it for nine dollars a barrel ; how much did he lo 
 > on a barrel ? 
 
 j 9. William had eighteen cents in his pocket, and 
 ' on h.'s way to school he spent nine of hem : how 
 
 many cents had he left? 
 
 10. in school street there are nineteen shade trees, 
 
 nine of which are elms, and the rest are maples : 
 
 how many maple trees are there ? 
 
SUBTRACTION. 35 
 
 1.ESS0N X* 
 
 1. One from ten leaves how many? One fir«i 
 twenty ? One from thirty ? One from forty 1 One 
 from seventy ? One from sixty ? One from eighty ? 
 One from fifty ? One from ninety ? One from a 
 hundred ? 
 
 2. Two from ten leaves how many ? Two from 
 twenty ? Two from thirty ? Two from forty ? Two 
 from sixty ? Two from eighty ? Two from fifty ? 
 Two from seventy ? Two from ninety ? Two from 
 a hundred ? 
 
 3. Four from ten leaves how many ? Four frori 
 twenty 1 Four from thirty ? Four from sixty 1 Four 
 from forty? Four from fifty? Four from ninety? 
 Four from seventy ? Four from eighty ? F'our from 
 a hundred ? 
 
 4. Three from a ^hundred leaves how -many ? 
 Three from ninety ? Three from eighty ? Three 
 from seventy ? Three from sixty ? Three from fifty ? 
 Three from forty ? Three from thirty ? Three from 
 twenty ? ' 'Three from ten ? 
 
 5. Five from a hundred leaves, how many ? Five 
 from ninety "? From eiglUy ? Seventy? Sixty? 
 Fifiy ? Forty ? Thirty ? Twenty ? 
 
 6. Six from fourteen leaves how many ? Six from 
 Twenty? From thirty ? Fifty? Forty? Sixty? 
 Eighty? Ninety? Seventy? A hundred? 
 
 7. Seven tVom ten leaves how many ? Seven from 
 Twenty ? From forty ? Thirty ? Seventy ? Sixty ? 
 Eighty ? Fifty ? Ninety ? A hundred ? 
 
 * Th^i pupil should be able to answer the questions in tliis and the 
 following I>efl9on, with readiness, before he proceeds to tlie next. 
 
36 SUBTRACTION. 
 
 8. Eight trom ten leaves how many ? Eight from 
 twenty f From thirty ? Fifty ? Forty ? Sixty ? 
 Eighty ? Seventy ? Ninety ? A hundred ? 
 
 9. Nine from ten leaves how many ? Nine from 
 twenty ? From forty ? Eighty ? Ninety ? Seventy ? ' 
 Fifty? Sixty? Thirty? A hundred? | 
 
 LESSON XJ 
 
 1. Ten from twelve leaves how many ? Ten from 
 twenty-three ? Ten from thirly-four ? Ten from for- 
 ty-five ? Ten from fifty-six ? Ten from sixty-seven ? 
 Ten from seventy-eight ? Ten from eighty-nine ? 
 Ten from a hundred ? 
 
 2. Five from twelve leaves how many ? Five 
 from twenty-two ? Five from thirty-two ? Five from 
 sixty-two ? Five from forty-two ? Five from seven- 
 ty-two? Five from fifty-two? Five from eighty-two? 
 Five from ninety-two ? 
 
 3. Three from eight leaves how many ? Three 
 from eighteen ? Three from twenty-eight ? Three 
 from fifty-eight ? Three from forty-eight ? Three 
 from sixty-eight ? Three from thirty-eight ? Three 
 from seventy-eight ? Three from ninety-eight ? 
 Three from eighty-eight ? 
 
 4. Four from nine leaves how many ? Four from 
 nineteen ? Four from thirty-nine ? Four from twen- 
 ty-nine ? Four from sixty-nine ? Four from seventy- 
 
 ' nine ? Four from fifty -nine ? Four from forty-nin« ? 
 j Four from eighty-nine ? Four from ninety-nine ? 
 
 5. Six frDm seventeen leaves how many ? Six 
 from twenty-eight ? Six from fifty-four? Six from 
 thirty-eight ? Six from eighty-seven ? 
 
 6. Seven from twenty- five leaves h >w many ? 
 
SUBTRACTION. 37 
 
 Seven from forty-nine "^ Seven from thirty-six ? 
 Seven from sixcy-three ? Seven from eighty-lour t 
 Seven from ninety-eight ? 
 
 LESSON XII. 
 
 1. A mm boii<:ht a cow for ten dollars, and sold 
 I it a<rain for twelve dollars : how much did he make 
 ; by his bariiain ? Ten from twelve leaves liow 
 j many ? Two from twelve, how many ? 
 I 2. Ten from eleven leavers how many ? One 
 I from eleven, how many ? 
 
 ! 3. William's x\rithmetic lesson contained thirteen 
 I questions, and he rociied ten of them perfectly : how j 
 I many did he miss ? . 
 
 I 4. Charles paid fifteen cents for a knife, and sold 
 I it for ten cents : how much did he lose by his bar- 
 1 gain ? 
 
 j 5. A robber was sentenced to the State's prison 
 ! for fourteen years, and after ten years had elapsed 
 I he was pardoned out : how many years of his sen- 
 I tence still remained ? 
 
 : 6. A lady vvent a shopping with sixteen dollars 
 in her purse, and having paid ten dollars for a dress, 
 gave ihe rest for a bonnet : what was the price of 
 ' the bonnet ? 
 
 7. Heniy having eighteen canary birds, wishes 
 to keep ten of them and sell the remainder : how 
 i many can he sell ? 
 
 I 8. Ten from seventeen leaves how many ^ Seven 
 I from seventeen, how many ? 
 
 ■ 9. In an orchard containing nineteen trees, ten of 
 I them are apple-trees, and the rest are peach treea : [ 
 I how many peach-trees are there ? 
 
can the car go/than tie Wse »" """"^ ""-« ""il- 
 yards did he hat; ?eft f ^'""^'' ^^^^^^ • ^ow many I 
 LESSON XIII. 
 
 ^-. It is called S.U.IZ^"^''" been solved? / 
 ^;fg^^'"'ti^S"I>traction? I 
 
 subu£til?eii;:dt "'"""■ •"■ ""»''«' °*'-wby I 
 
 ^- What is the (^Irenct ,. f ""'" -^'^ ^'^i '""« ? 
 
 a Kron, twenty aubrct Ltr ^" ^"<^ "^"•'-' ' I 
 10^- J,,'""" 'i^Wy-five subtract si 
 10. i rom 6«y.ti.,,e take ten. I 
 
 1. hrom forty-se.en tate four. 
 
SUBTRACTION. 39 
 
 EXAMFLES FOR IRACTICE. 
 
 1. James gave twelve cents for a quart of cher- 
 ries, and eight cents for a quart of chestnuts : how ' 
 much more did he pay for his cherries than for his I 
 chestnuts? ! 
 
 2. A man gave seventeen dollars for a cow, and j 
 nine dollars for a load of hay : how much more did I 
 he give ihr the cow than for the hay ? ] 
 
 3. Horace having thirty-six marhles, gave ten to j 
 his cousin : how many had he left I 
 
 4. Susan had twenty. four peaches; she gave six I 
 to Harriet, and four to Ann : how many peaches had i 
 she left ? 
 
 5. On a training day a little boy had fifty cents ; 
 he spent ten cents for pea-nuts and lost five cents : 
 how many cents had he lefl ? 
 
 6. A man bought a wagon for th:rty.six dollars, 
 and sold it for ten dollars less than cost : how nmch 
 did he get for it ? 
 
 7. A merchant bought a hogshead of molasses 
 containing sixty-three gallons, and found that eight 
 gallons had leaked out: how many gallons were 
 left ? 
 
 8. A barrel of brandy cc«ts twentv-nine dollars, 
 and a barrel of flour costs six CK.jt k vhat is the 
 difference in their price ? 
 
 9. The cost of a cloak is forty-five dollars, and 
 the cost of a hat eight dollars: what is the differ- 
 ence in their cost ? 
 
 10. A man bought a horse for seventy-five dollars, 
 and sold it for ton dollars less than he paid : how 
 much did he get fcTr his horse ? 
 
40 SUBTRACTION. 
 
 11. Samuel is nineteen years old, and his sister is 
 six years younger : how old is she ? 
 
 12. The cost of an Arithmetic is twenty-five cents, 
 and the cost of a slate is twenty cents : what is the 
 difference in their cost ? 
 
 18. Henry having thirty-six marbles, lost six and 
 gave away five : how many had he left ? 
 
 14. George having twenty-eight apples, gave three 
 to one companion, two to another, and four to an- 
 other : how many had he left? 
 
 15. A man bought a sleigh for twenty dollars and 
 paid ten dollars ibr painting it ; he then sold it for 
 thirty-two dollars: did he make or lose by the bar- 
 gain ? How much ? 
 
 16. A man owning forty acres of land, sold twenty 
 acres of it: how many acres had he left ? 
 
 17. Henry's kite line is fifty yards long, and Wil. 
 liam's is forty yards long : what is the dillerence in 
 their length ? 
 
 18. A farmer having a hundred bushels of wheat, 
 sold fifty bushels : how many bushels had he left ? 
 
 19. If I have seventy-five cents, and give ten to 
 Charles, six to James, four to Susan, and six to 
 Harriet, how many cents shall I have left? 
 
 20. If you have fifty peaches, and give ten to one 
 com[)anion, ten to a second, ten to a third, and ten 
 to a fourth, how many peaches will you have lefl ? 
 
 21. George having twenty -one marbles lo«*t eight of 
 them, and afterwards gained twelve : how many did I 
 he then have ? ; 
 
 22. Sarah has twelve roses, Mary has five less^ than ' 
 Sarah, and Susan three less than Mary : bow many | 
 have all ? j 
 
 23. If you take sixteen from twenty, and add twen- ! 
 ty-five to the remainder, what will the sum be ! i 
 
SECTION IV 
 MULTIPLICATION. 
 
 LESSON I. 
 
 ^. What will two apples cost, at one cent apiece ? 
 
 Solutio-n. — If one apple costs one cent, two apples 
 w 11 cost two times one cent : and two times one cent 
 ar3 two cents. Ans. Two cents. 
 
 2. What will two pears cost, at two cents apiece ? 
 
 Note. — The learner should be required to give the reaaoning in 
 the solution of every example. 
 
 3. At three cents a yard, what will two yards of 
 ribbon cost ? 
 
 4. At four cents apiece, what will two oranges 
 come to ? 
 
 5. George bought two melons, at five cents apiece : 
 how much did he pay for them ? 
 
 6. if one lemon is worth six cents, how many 
 cents are two lemons worth ? 
 
 7. What will two muffs cost, at seven dollars 
 apiece ? 
 
 8. What cost two quarts of cherries, at eight cents 
 j a quart ? 
 
 9. At nine cents a pound, \''hat will two pounds 
 I of sugar cost ? 
 
 Note — The principle of miiW/jZymg cannot be loo carefully ex- 
 plained to young pupils. To show ihem, for eiainple, that tvo 
 times ten are twenty, move out ten balls on one cf the wires of the 
 iNuraerical Frame, tlien move out tew on anolhei wire and let him 
 liim '".ouut these two tens togetht>r. 
 
 While learning the Muliiplication Table, the ;lass may study 
 to advantage the Lessons corresponding with its different parts, 
 as in Addition and Subtraction. 
 
j 
 
 1 43 MULTIPLICATION. 
 
 1 
 
 MULTIPLICATION TABLE. 
 
 Two timet One are tWO. 
 
 Two Ume. six are twelve. 
 
 Two " two " four. 
 
 Two " seven " fourteen. 
 
 Two " three " six. 
 
 Two " eight " sixteen, j ' 
 
 1 Two " four " eight. 
 
 Two " nine " eighteen. 
 
 ^ Two '' five " ten. 
 
 Two "ten " twenty. 
 
 Three time, one are three. 
 
 Three Ume. six are eighteen. 
 
 j Three " two " six. 
 
 Three " seven" twenty-one. ' 
 
 i Three " three «' nine. 
 
 Three " eight " twenty-four. 
 
 Three " four " twelve. 
 
 Three " nine " twenty-«uir. 
 
 Three " five " fifteen. 
 
 Three " ten " thirty. 
 
 Pour timM one are four. 
 
 Four time, six are twenty-four. 
 
 ! Four " two " eight. 
 
 Four ** seven " twenty-ei^ht. 
 
 Four •' three " twelve. 
 
 Four " eight " thirty-two. 
 
 Four " four " sixteen. 
 
 Four " nine " thirty-sir 
 
 Four " five " twenty. 
 
 Four " ten " forty. 
 
 P'ive timeiOne are five. 
 
 Five limes six are thirty. 
 
 Five " two " ten. 
 
 Five " seven" thirty- five 
 
 Five " three " fifteen. 
 
 Five " eight " forty. 
 
 Five " four " twenty. 
 
 Five " nine " forty-five. 
 
 Five " five " twenty-five. 
 
 Five " ten " fifty. 
 
 Six time, one are SIX. 
 
 Six ime. six are thirty-six. 
 
 Six " two " twelve. 
 
 Six " seven " forty-two. ( 
 
 Six " three " eighteen. 
 
 Six " eight " forty-eight 
 
 Six " four " twenty-four. 
 
 Six " nine " fifty-four. >, 
 
 Six = fiTe " thirty. 
 
 Six " ten " sixty. 
 
 Seven iin»e« one are seven. 
 Seven " two " fourteen. 
 Seven " three" twenty -one. 
 Seven " four " twenty-eight. 
 Seven " five " thirty-five. 
 
 Seven time, six ar« forty-two. 
 Seven " seven " forty-nine. 
 Seven " eight " fifty-six. 
 Seven " nine " sixiy-three 
 Seven " ten " sf "enty. 
 
MULTIPLICATION. 
 
 43 
 
 ' Eight time* one aw eight 
 Eight " two " sixteen. 
 
 Eight 
 Eight 
 Eight 
 Nine 
 Nine 
 Nine 
 Nine 
 Nine 
 
 three " twenty- fou. 
 four " thirty-two, 
 live " forty. 
 
 I Eight tirae. six M« forty-eight. 
 Eight " seven " fifty-six. 
 Eight " eight " eixty-four. 
 
 one are nine, 
 two " eighteen, 
 three " twenty -sev, 
 four " thirty-six. 
 five " forty-five. 
 
 Eight 
 Eight 
 
 nine " seventy-two. 
 ten " eighty. 
 
 Nine time, six «« fifty- four. 
 Nine *' seven " sixty-three. 
 Nine " eight " seventy-two. 
 Nine " nine '* eighiy-one. 
 Nine " ten " ninety. 
 
 Ten u»»»M one are ten. Ten umo* six are sixty. 
 
 Ten " two " twenty. Ten " seven " seventy. 
 
 Ten " three " thirty. Ten " eight " eighty. 
 
 Ten " four " forty. Ten " nine " ninety. 
 
 Ten " five " fifty. Ten " ten '• one hundred. 
 
 Note. — It is an interesting and profita})le exercise, for yoimg 
 pupils, to recite tables in concert. But it will not do to depend 
 'jpon this method al»ne. It is indisprasable for every scholar who 
 desires to be accurate either in arithmetic or business, to have the 
 cfinmon arithmetical tables distinctly and indtlihlif fixed in \\\» 
 .n'ii«i. Hctice, after a table has been repealed by the class in 
 oor Tiert, or individually, the Teacher should ask many prorais- 
 e^oua questions, to prevent its being recited mechanically, [rota 
 a knowledge of the regular increase of numbers. 
 
 LESSON II. 
 
 1. What will three quarts of strawberries cost, at 
 one shilling a quart ? 
 
 2. At two cents apiece, what will three lead pen- 
 cils come to ? 
 
 3. In one yard there are tlnoc ieet : how many 
 feet are there in three yards ? 
 
 4. At four cents apiece, what will three oranges 
 cost ? 
 
 5. What cost three quarts of milk, at five cents a 
 quart ? 
 
44 MULTIPLICATION . 
 
 6. What cost three ounces of snufT, at six cents 
 an ounce ? 
 
 7. At seven cents a pound, what will three pounds 
 of cheese come to ? 
 
 8. In one peek there are eight quarts : how many 
 quarts are there in three pecks? 
 
 9. If it requires nine yards of calico to make one 
 dress, how many yards will it require to make three 
 d'2sses? 
 
 10. A man gave three boys ten apples apiece : 
 how many did he give them all ? 
 
 LESSON III. 
 
 1. At one dollar a bushel, how much will four 
 bushels of wheat cost ? 
 
 2. What cost four lemons, at two cents apiece ? 
 
 3. If Frederic obtains four credit marks a day, 
 how many will he have in four days? 
 
 4. What cost four quarts of cider, at three cents a 
 quart ? 
 
 5. Jane bought four skeins of sewing silk, at five 
 cents a skein : how much did she piy for them all?.j 
 
 6. In one week there are seven days : how many 
 days are there in four weeks? 
 
 7. Henry had four class-mates, and gave them six 
 apples apiece : how many did he give to all ? 
 
 8. What cost four hats, at nine dollars apiece ? 
 
 9. Wha cost four barrels of flour, at eight dollar* | 
 a barrel ? 
 
 10. At ten dollars a ton, what wi.l four tons of 
 hay cost? 
 
MrLTTILJCATTON. 45 
 
 I 
 
 LESSON IV. 
 
 1. At one do lar a yard, what will five yards ol 
 gilk cost ? 
 
 2. What cost five lemons, at three cents apiece ? 
 
 3. My board costs me two dollars a week : what 
 will it amount to in five weeks ? 
 
 4. A man hired a horse for six cents a mile : how 
 much must he pay for going five miles 1 
 
 5. Saralj's cloak contains five yards of merino, 
 whic.i cost five shillings a yard : how much did hei 
 cloak cost ? 
 
 6. What cost five pair of boots, at four dollars a 
 pair? 
 
 7. I'^ight quarts make one peck : how many quarts 
 are there in five pecks ? 
 
 8. If a stage goes seven miles an kour. how far 
 will it go in five hours? 
 
 9. At nine cents a pound, what will five pounds 
 of butter cost ? 
 
 10. ^Vhat cost five yards of cloth, at tei shillings 
 a yard ? 
 
 LESSON V. 
 
 1. What cost six yards of calico, at one shilling a 
 yard ? 
 
 2. What cost six oranges, at three cents apiece? 
 
 3. There are four weeks in a month ; how many 
 weeks are there in six months 1 
 
 4. What cost six yards of cloth, at two dollars a 
 yard ? 
 
 5. What cost six spools of cotton, at five cents a 
 spool ? 
 
46 MULTIPLICATION. 
 
 6. At seven cents a pound, what will a quarter I 
 ol Iamb weighing six peunds, come to ? I 
 
 7. What cost six quarts of plums, at ten cents a ! 
 quart ? I 
 
 8. Sarah bought six yards of ribbon, at seven ! 
 cents a yard : how much did she pay for it ? ! 
 
 9. If one inkstand costs six cents, how much will | 
 six ccsl ? I 
 
 10. What cost six pounds of raisins, at eight cents I 
 a |>ound ? 
 
 LESSON VI. 
 
 1. Helen's dress contains seven yards of calico, 
 which cost one shilling a yard : what was the cost 
 of her dress ? 
 
 2. At three cents a skein, what will seven skeins 
 of sewing silk cost ? 
 
 j 3. At two cents a stick, what will seven sticks of 
 twist cost ? 
 
 4. The fare by Railroad from Boston to Albany 
 is six dollars for one person: what wiil it be for a 
 family of seven persons ? 
 
 5. Four farthings make one penny : how many 
 farthings are there in seven pence ? 
 
 6. If a stage runs five miles in one hour, how far 
 will it run in seven hours ? 
 
 7. Harriet had seven rose bushes, and one morn- 
 ing she found eight roses upon each : how many 
 were ticre upon all ? 
 
 8. What cost seven pounds of lard, at seven cents 
 a pound 1 
 
 9. What .cost seven dozen chairs, at nme dollars 
 per tiozen i 
 
 10. At ten shillings a >ard, what is the cost of 
 seven yai Is of cloth ? 
 
I 
 
 MULTIPLICATION. 47 
 
 LESSON VII. 
 
 1 . What will eight bushels of peaches co&t, at one 
 dollar a bushel ? 
 
 2. If a quart of milk costs four cents, what will 
 be t'le cost of eight quarts ? 
 
 8. If you recite three perfect lessons a day, how 
 many will you recite in eight days ? 
 
 4. At two shillings a gallon, what will eight gal- 
 lons of molasses come to ? 
 
 5. In New Kngland, six shillings make a dollar : 
 how many shillings are there in eight dollars? 
 
 6. At five cents a pound, what cost eight pounds 
 of figs ? 
 
 7. There are eight rows of trees in an orchard, 
 and seven trees in a row : how many trees are there 
 
 j in the orchard ? 
 
 I 8. In New York, eight shillings make a dollar : 
 
 [ how many shillings are there in eight New York 
 
 I dollars ? 
 
 I 9. A farmer sold eight tons of hay, at nine dol- 
 
 ; lars per ton : how much did he receive for his hay ? 
 
 i 10. What is the value of eight cows, at ten dollars 
 
 i apiece ? 
 
 ; LESSON VI 11. 
 
 i 
 
 1. In one quart there are two pints : liow many 
 
 '■ pints are th<^re in nine quarts? 
 ! 2. What cosi nine caps, at one dollar apie/ce ? 
 ■ 3. Thr'i.e feet make a yard : how many feet are 
 therp m nine yards ? 
 I 4. A traveler n^t nine beggars and gave each of 
 j them four shillings : how many shill-ngs did he give 
 I to all ? 
 
48 MULTIPLICATION. 
 
 5. If a hunter kills five pigeons at every shot, and 
 fires nine times, low many will he kill ? 
 
 6. How much will nine quarts of blue-berries : 
 cost, at eight cents a quart ? 
 
 7. Henry's mother gave him six cents apiece for: 
 carrying nine billets : how many cents did he receive 
 for all ? 
 
 8. Susan received sev^n shillings a week fordoing 
 the work of the family : how much did she earn in 
 nine weeks ? 
 
 9. If a family consumes ten pounds of butter in 
 a week, how many pounds will last them nine 
 weeks '( 
 
 10. What fosi nuie cords of wood, at nine shillings 
 a cord ? 
 
 LESSON IX. 
 
 1. How mu(,h will ten sheep cost, at two dollars 
 a head ? 
 
 2. How much will ten barrels of flour cost, at five 
 dollars a barrel ? 
 
 3. At four dollars a yard, what will ten yards of 
 cloth cost ? 
 
 4. VVhat cost ten bushels of corn, at three shil- 
 lings a bushel ? 
 
 5. What cost ten coats, at eight dollars apiece ? 
 
 6. A farmer gave three bushels of wheat foi a 
 yard of cloth : how many bushels must he give for 
 ten yards ? 
 
 7. A dairy- woman bought ten yards of silk and 
 paid for it in butter, giving seven pounds for ayc^d : 
 how many pounds of butter did her silk cost ? 
 
 8. At six dollars a yard, how much will ten yards \ 
 of clcth cost ? i 
 
MULTIPLICATION. 49 
 
 9. Ten dollars make an eagle : how many dollars 
 are there in ten eagles ? 
 
 10. My neighbor's peach-orchard contains ten rows 
 of trees, and there are nine trees in a row : how 
 many peach-trees has he? 
 
 LESSON X.* 
 
 1. How many times two make eight? How many 
 times two make twelve? Ten? Fourteen? Eigh- 
 teen? Sixteen? Twenty? 
 
 2. How many times three make twelve? Nine? 
 Fifteen? Twenty-one? Eighteen? Twenty-four? 
 Thirty? Twenty-seven? 
 
 3. Hpw many times four make twenty? Sixteen? 
 Twelve? Eight? Twenty-four? Thirty-two? Thirty- 
 six? Forty? 
 
 4. How many times five make twenty ? Thirty ? 
 Twenty -five? Thirty -five ? Forty? Forty-five? 
 Fifty? 
 
 5. How many times six make eighteen ? Thirty ? 
 Twenty-four? Forty-two? Thirty-six? Sixty? For- 
 ty-eight? Fifty-four? 
 
 6. How many times seven make twenty-eight? 
 Thirty-five? Twenty-one? Forty-two? Seventy? 
 Sixty-three? Fifty-six? 
 
 7. How many times eight make twenty-four? 
 Thirty-two ? Forty-eight ? Seventy -two ? Forty ? 
 Fifty-six? Eighty? Sixty-four? 
 
 8. How many times nine make twenty-sevtn ? 
 Forty-five? Thirty-six? Fifty-four? Seventy-two? 
 Sixty-three? Eighty -one? Ninety? 
 
 * This and the following lesson should be studied, till the class 
 can answer the questions with great promptitude. This they 
 will soon be al.le to do, if they have thoroughly learned the Mul- 
 tiplication Table, 
 
50 MULTIPLICATION. 
 
 9. 3ow many timea ten make thirty ? Twenty? 
 Forty? Sixty? Fifty? Ninety? Eighty? Seventy? 
 One hundred? 
 
 LESSON XI . 
 
 1. Eight* is how many times two? Hew many 
 times four ? How many times one ? 
 
 2. Twelve is how many times two? How many 
 times three? How many times four? How many 
 times six ? How many times one? 
 
 3. Eighteen is how many times two? How'^many 
 times six ? How many times three ? How many 
 times nine ? 
 
 4. Sixteen is how many times eight? How many 
 times four ? F\ow many times two ? 
 
 5. Twenty ;s how many times two ? How many 
 times five ? How many times ten ? How many times 
 four ? 
 
 6. Thirty is how many times five? How many 
 times ten ? How many times six ? How many times 
 three ? 
 
 7. Twenty-four is how many times four? How 
 many times three ? How manv times six ? How 
 many times eight ? How many tinir* twelve ? How 
 many times two ? 
 
 8. Thirty-two is how many tim&s eight? How 
 many times four? 
 
 9. Thirty-six is how many times six? How many 
 times four? How many times three? How many 
 times twelve ? How many times nine ? 
 
 10. Twenty-seven is how many times hree ? Hew 
 many time? nine ? 
 
 * The number eight, &.c., is M)nsidered a collective noun, con- 
 veying the idea of unity, and »h>refore requires a verb in the 
 singular numb*r. 
 
MULTIPLICATION. 51 
 
 1 1 . Forty -two is how many times six ? How many 
 times se\en ? 
 
 12. Fifty-six is how many times seven? How 
 many times eight ? 
 
 13. Thirty-five is how many times seven? How 
 many times five ? 
 
 14. Seventy -two is how many times nine ? How 
 many times eight ? 
 
 LESSON XII. 
 
 1. What cost five oranges, at three cents apiece ? 
 
 2. What cost six tfiimbles, at four cents apiece ? 
 
 3. A teacher bought ten inkstands, at six cents 
 apiece : what did they come to ? 
 
 4. If four boys sit on one bench, how many can 
 sit on five benches ? On seven benches ? 
 
 5. Jane bought five yards of silk braid, at four 
 cents a yard : how much did it come to ? 
 
 6. Horace bought four young rabbits for eight 
 shillings, and sold them for three shillings apiece : 
 did he gain or lose by his bargain ? How much ? 
 
 7. VVhat will ten pounds of figs cost, at eight 
 cents a pound ? At nine cents ? 
 
 8. When beef is six dollars a hundred, what 
 will a fatted ox co»ne to which weighs nine hundred 
 pounds ? 
 
 9. If one stage can carry nme pasvsengers, now 
 miny can four stages carry ? 
 
 10. What cost nine pounds of tea, at six shillings 
 a pound ' 
 
 11. if five yards of cloth will make one cloak, 
 Kjw many yards wili six olouiws re^-.'i'^ "^ 
 
 12. If a horse travels six miles an hour, how far 
 will he travel in ten hours ? 
 
62 MULTIPUCATION. 
 
 LESSON XIII. 
 
 1. Q' What is the operation called, by which the 
 preceding examples in this section have been solved ? 
 
 Ans, It is called Multiplication. 
 
 2. Q. What is Multiplication ? 
 
 Ans. Multiplication is the process of finding the 
 avnount of a given number repeated or added to itself, 
 a given number of times. 
 
 3. Q. What 16 the number to be repeated, or mul- 
 tiplied, called ? 
 
 Ans. The Multiplicand. 
 
 4. Q. What is the number by which we multiply, 
 called f 
 
 Ans. The Multiplier. 
 
 5. Q. What is the answer, or number produced by 
 multiplication, called ! 
 
 Ans. The Product. 
 
 6. Q. What is meant by the term product ? 
 Ans. Something that is jyrodu4;ed or formed. 
 
 Y. When we say, three times six are eighteen ; 
 which is the number to be multiplied ? Which is the 
 number to multiply by? Which the product? 
 
 8. When we say, four times five are twenty; 
 which is the answer? What is the four called? 
 What is the five called ? What is the iweyity 
 called ? 
 
 9. What is the product of seven multiplied hy 
 six ? 
 
 10. What is the product of nine multiplied bv 
 five? 
 
 11. What is the product of eight multiplied by 
 
 SIX 
 
I MULTIPLICATION. 
 
 I 12. What is the product of seven times nine 1 Of 
 I eight .imes eight ? Of seven times six ? 
 1 13 What is the product of eight times seven ? Of 
 j nine times eight ? Of nine times seven ? Of six 
 times nine ? Of seven times five ? Of nine tinnes 
 I five ? Of seven times ten ? 
 
 14. Which is the most, three times four, or four 
 times three ? 
 
 Note. — To iUiistrate ttiis point, move out four balls on the lower 
 wire, and four apiece on the seroinl and third wires. This will 
 denote three times four, or four added to itself three times, which 
 the pupil will perceive make twelve. 
 
 Again, letting these remain in their present place, move out 
 three balls on the upper wire, also three apie<e un the next three 
 wires. This will denote four times three, or three added to it- 
 self four times, whicli the pupil will see make twelve, and is 
 therefore the same a.s three times four. 
 
 15. Which is the most, five times three, or three 
 times five ? 
 
 16. Which is the most, five times six, or six times 
 five ? Six times seven, or seven titnes six ? 
 
 EXAMPLES FOR PRACTICE. 
 
 1. What will six pair of skates cost, at five shil- 
 
 ] lings a pair ? , 
 
 2. What will four caps cost, at eight shillings j 
 apiece ? i 
 
 3. How much will nine quarts o^ t' erries come 
 to, at seven cents a quart ? 
 
 4. A ten dollars apiece, how much yfiW three 
 ploughs cost ? I 
 
 5. A farmer sold nine lambs, at eight shillings I 
 apiece : how much did they come to 1 I 
 
 6. If a man gives six bushels of oats foi one pair | 
 
54 MULTIPf ICATION. 
 
 of boots, how many bushels must be give ibr seven 
 pair of boots ? 
 
 7. If six men do a piece of work in ten days, how 
 long V* ill it take one man to do it ? 
 
 8. At seven cents a bunch, how much will eight 
 bunches of radishes cost ? Nine bunches ? Ten ' 
 bunches ? I 
 
 9. VV^hich is the most, eight times seven, or nine ; 
 times six ? Six times six, or four times nine ? Eight 
 times eight, or seven times nine ? 
 
 10. A farmer bought six pair of shoes, at two dol- 
 lars a pair, and paid four cords of wood worth two 
 dollars a cord : how much did he still owe for his 
 shoes ? 
 
 1 1 . Twenty-eight is how many times seven ? How 
 many times four ? Sixty-three is how many times 
 nine ? Forty-eight is how many times six ? 
 
 12. Fifty-six is how many times eight? Forty-five 
 is how many times nine ? Forty-two is how manv 
 times six ? Forty-nine is how many times seven ? 
 
 18. Kighty-one is how many times nine ? Forty is 
 how many times ten ? Eigiity is how many times 
 ten ? 
 
 14. VV^hich is trlie most, four times eight, or three 
 times nine ? 
 
 15. Which is the most, five times seven, or four 
 times ten ? 
 
 16. Which is the most, six times eii^nt, or nine 
 times six ? 
 
 17. Which is the most, seven times nine, or eight 
 .. *imes seven ? 
 
 { 18. If side Combs cost nine cents a pair, what will 
 five pair cost? Eight pair? Nine pair? Seven 
 ! pair ? Ten pair ? 
 
MULTIPLICATION. 55 
 
 19. VVhat cost nine papers ot* pins, at two shillings 
 a paper ? At four shillings ? 
 
 20. Nine times three are how many ? Nine timet< 
 focir ? Nine times six ? 
 
 21. If a barrel of maple sap will make eight 
 pounds of sugar, how many pounds will four barrels 
 mako ? Seven barrels ? Right barrels ? 
 
 2'2. What cost seven penknives, at six shillings 
 apiece ? 
 
 23. Kdwin bought six pencils and gave two apples 
 apiece for them ; also four quills and gave three ap- 
 ples apiece for them : how many apples did he give 
 for his pencils and (juills together? 
 
 24. If one acre of ground produces ten bushels of 
 wheat, how many bushels will six acres produce ? 
 Ten acres ? 
 
 2.5. Seven times six are how many ? Seven times 
 eight ? Seven times nine ? Eight times nine '' Six 
 times nine ? 
 
 26. Charlotte bought six primers, at nine cents 
 apiece : what did they come to ? 
 
 27. A lady bought ten yards of calico, at ten cents 
 a yard ; and four spools of cotton, at five cents a 
 spool : what did her bill amount to ? 
 
 25. A man bought ten sheep, at two dollars a 
 head ; and four cows, at ten dollars a head : how 
 much did he give for all ? 
 
 29. Henry bought seven quarts of cheiiies, a* 
 nine cents a quart ; and ten quarts of strawberries, 
 at six cents a quart : which cost the most ? 
 
 30. VVhich will cost the most, nine slates at eight 
 centn apiece^ or ten inkstand* at seven cents apiece ? 
 
SECTION V. 
 
 DIVISION. 
 
 LESSON I. 
 
 1. How mau} pears, at two cents apiece, can you 
 buy for six cents $ 
 
 Analysis. — Since two cents will buy one pear, six 
 cents will buy as many pears, as two cents are con- 
 tained times in six cents ; and two cents are contained 
 in six cents, three times. Therefore six cents will buy 
 three pears, at two cents apiece. 
 
 2. At two cents a yard, how many yards of tape 
 can you buy for four cents ? 
 
 Suggestion. — To find how many times two cents 
 are contained in four cents, the learner must think 
 how many times two make /owr. 
 
 3. At two cents apiece, how many oranges can be 
 bought for six cents ? 
 
 4. George bought ten marbles, which he divided 
 among his little brothei-s, giving them two a}>iece : 
 how many brothers had he ? 
 
 Suggestion. — Since he gave two maibles to each, 
 he manifestly had as many brothers, as two marbles \ * 
 are contained times in ten marbles. 
 
 Note.—'^\\Q principle of dividing may be illustrated in the fol- 
 lowinsr manner : Pass acrosR ten balls on one of the wires, which 
 may represent the ten marbles. Now since he gave two marbles 
 to each brother, moving: out two balls will denote one brother; 
 movinor out two more will denote another share, and so on, every 
 two I alls will denote one brother, till all the balls are removed or 
 exliai ?ted. Finally, counting the number of twos or pair of l5;dls 
 moved out, it will sliow how many times two marbles are con- 
 tained in ten marbles, which is the number of brothers he had. 
 
DIVISION. 
 
 57 
 
 5. How many load pencils, at two cents apiece, 
 can you buy for eiglit cents ? 
 
 6. Henry had twelve shillings which he laid out 
 in books, at two shillings aj)iece : how many books 
 did he buy ? 
 
 7. Julius had fourteen marbles which he wished 
 to divide into two equal piles : how many must he 
 pat in a pile ? 
 
 8. How many pounds of ginger, at two shillings 
 a pound, can be bought for sixteen shillings ? 
 
 9. A tnan laid out eigliteen shillings in apples, at 
 two shillings a bushel : how many bushels did he 
 buy ? 
 
 10. A man bought twenty dollars worth of shoes, 
 at two dollars a pair : how many pair did he buy ?* 
 
 Note. — The Divismn Table should be studied in the same man- 
 ner as the preceding Tables. 
 
 DIVISION TABLE. 
 
 Two ui two, 
 
 Two " four, 
 
 Two " Bix, 
 
 Two •' eight, 
 
 Two " ten, 
 
 once. 
 
 two limf* 
 
 three " 
 four " 
 five " 
 
 Two in twelve, 
 
 Two " fourteen. 
 
 Two " sixteen, 
 
 Two " eighteen, 
 
 Two " twenty. 
 
 SIX tiniM 
 
 seven ** 
 eight " 
 nine " 
 ten " 
 
 ! Three 
 
 ill three, 
 
 once. 
 
 Three 
 
 ineiguteen, six time.. 
 
 Three 
 
 "six, 
 
 two time.. 
 
 Three 
 
 " twenty-one, seven " 
 
 Three 
 
 " nine. 
 
 three " 
 
 Three 
 
 " twenty-four, eight •' 
 
 i Three 
 
 " twelve, 
 
 four " 
 
 Three 
 
 * twenty-sev,, nine " | 
 
 1 Throe 
 
 " tilleon, 
 
 five " 
 
 Three 
 
 " thirty, ten " 
 
 Four 
 
 iK four, 
 
 once. 
 
 Fo'ir 
 
 in twenty- four, six ti»e.. 
 
 Four 
 
 " eight, 
 
 two tmiei. 
 
 Foot 
 
 " twenty-eigh) seven ** 
 
 Pour 
 
 " twelve, 
 
 three " 
 
 Four 
 
 "thirty-two, eight " 
 
 Four 
 
 " sixteen. 
 
 four " 
 
 Four 
 
 " thirty-six, nine " 
 
 Pour 
 
 '« twenty, 
 
 five " 
 
 Four 
 
 " forty, .n " 
 
58 
 
 
 DIVISION. 
 
 
 
 Five tofivs, 
 
 once. 
 
 F'ive in thirty, 
 
 six tiaM. 
 
 Five 
 
 'ten, 
 
 two timet 
 
 Five 
 
 ' thirty -five, 
 
 seven " 
 
 ! Five ' 
 
 ' fifteen, 
 
 three " 
 
 Five 
 
 ' forty, 
 
 eight " 
 
 Five 
 
 ' twenty, 
 
 four " 
 
 Five 
 
 ' forty-five, 
 
 nine " j 
 
 Five 
 
 ' twen.y-five, 
 
 five " 
 
 Five 
 
 'fifty. 
 
 ten " I 
 
 Six . 
 
 nsix. 
 
 once. 
 
 Six in thirty-six, 
 
 six ttoM. 
 
 : Six 
 
 ' twelve, 
 
 two Ume. 
 
 Six 
 
 ' forty-two. 
 
 seven " 
 
 j Six 
 
 ' eighteen, 
 
 three " 
 
 Si<x 
 
 ' forty-eight. 
 
 eight « 1 
 
 Six 
 
 ' twenty-four, 
 
 four " 
 
 Six 
 
 ' fifty-four. 
 
 nine " 
 
 Six 
 
 ' thirty, 
 
 five " 
 
 Six 
 
 ♦ sixty, 
 
 ten " 
 
 Seven 
 
 in seven, 
 
 once. 
 
 Seven 
 
 11. forty-two, 
 
 six tlBBM. 
 
 Seven 
 
 ' fourteen, 
 
 two timei. 
 
 Seven 
 
 ' forty- nine. 
 
 seven " 
 
 Seven 
 
 ' twenty-one. 
 
 three " 
 
 Seven 
 
 'fifty -six, 
 
 eight " 
 
 Seven 
 
 " twenty-eight, four " 
 
 Seven 
 
 ' sixty-three. 
 
 nine " 
 
 Seven 
 
 ' thirty-five, 
 
 five " 
 
 Seven 
 
 ' seventy. 
 
 ten " 
 
 Eight 
 
 1. eight. 
 
 once. 
 
 Eight 
 
 n forty-eight, 
 
 six tUDM. 
 
 1 Kight 
 
 ' sixteen. 
 
 two times. 
 
 Eight 
 
 ' fifty-six. 
 
 seven " 
 
 Eight 
 
 ' twenty- four, 
 
 three " 
 
 Eight 
 
 ' sixty-four. 
 
 eight " 
 
 1 Right 
 
 ' thirty-two, 
 
 four " 
 
 Eight 
 
 ' seventy-two 
 
 nine " 
 
 ' Eight 
 
 ' forty, 
 
 five " 
 
 Ei^ht 
 
 " eighty. 
 
 ten " 
 
 INine 
 
 n nine, 
 
 once. • 
 
 Nine 
 
 n fifty-fitur, 
 
 six tin.e». 
 
 iNinc 
 
 " eighteen, 
 
 two limea. 
 
 Nine 
 
 " sixty-three. 
 
 seven " 
 
 j Nine 
 
 ■'twenty-sev., 
 
 three " 
 
 Nine 
 
 '' seventy-two 
 
 , eight " 
 
 iNine 
 
 "thirty-six, 
 
 four " 
 
 Nine 
 
 " eighty-one, 
 
 nine « i 
 
 Nine 
 
 " forty-five 
 
 five " 
 
 Nine 
 
 " ninety, 
 
 ten « 
 
 Ten 
 
 111 ten. 
 
 once. 
 
 jTen 
 
 uisixtv, 
 
 six timet j 
 
 Ten 
 
 " twenty. 
 
 two timaa. 
 
 Ten 
 
 " seventy, 
 
 seven " I 
 
 Ten 
 
 " thirty, 
 
 three " 
 
 Ten 
 
 "eighty, 
 
 eight " 1 
 
 Ten 
 
 "forty, 
 
 four " 
 
 Ten 
 
 ■•' ninety 
 
 nine " j 
 
 Ten 
 
 "fifty, 
 
 five ' 
 
 Ten 
 
 "a hundred, w 
 
 ten " 1 
 
 1 
 1 
 
DIVISION. 59 
 
 •& 
 
 I LESSON II 
 
 \ 1. When oranges are three cents apiecej how I 
 many can you buy for six cents ? How many times i 
 three make six ? I 
 
 2. At three cents a yard, how many yards of rib- 
 bon can you buy for nine cents ? How many times i 
 three make nine ? | 
 
 3. George has twelve apples which he wishes to i 
 ' divide equally among three of his companions : how 1 
 j many will each receive ? How many times three \ 
 
 make twelve ? i 
 
 I 4. A man divided eighteen oranges equally amon 
 his three sons : how many did each receive ? 
 
 5. If you walk three miles an hour, how long j 
 will it take you to walk fifteen miles ? How many ! 
 times three make fifteen ? | 
 
 6. If you had twenty-one marbles to give three \ 
 of your companions, how many could you give them 
 apiece ? 
 
 7. How many barrels of cider, at three dollars a 
 barrel, can I buy for twenty-four dollars? How 
 many times three in twenty-four ? 
 
 8. A man wishes to set out twenty-seven peach- 
 irees in three rows : how many must he put in a 
 
 , row ? 
 
 ' 9. Three boys caught thirty fishes, and agreed 
 i to divide them equally : how many will each one j 
 I have ? 
 
 10. If one man can do a piece of work in twen- 
 I ty-one days, how long will it take three men to 
 I do it ? 
 
60 DIVISION. 
 
 LESSON III. 
 
 1. How many lemons, at four cents apiece, can 
 be bought for eight cents ? How many times four 
 make eight ? 
 
 2. At four shillings a gallon, how many gallons 
 of molasses can be bought for twelve shillings? 
 
 3. William desires to divide twenty apples equal- 
 ly among four boys : how many must he give them 
 
 i apiece ? 
 
 4. Four scholars recited twenty-four questions in 
 arithmetic : how many questions did each recite ? 
 
 5. The price of a pair of boots is four dollars : 
 how many pair can I buy for sixteen dollars? 
 
 6. If a man walks four miles an hour, how long 
 will it take him to walk thiily-two miles ? 
 
 7. How long will it takf> him to walk twenty- 
 eight miles, at four miles an hour? 
 
 is. Four boys find a piirse containing thirty-six 
 cents, which they wish to divide equally : how many 
 cents will each one receive ? 
 
 9. A school which contained forty scholars, was 
 divided into four equal classes : how many scholars 
 were there in a class ? 
 
 LESSON IV. 
 
 1. How many spools of cotton at five cents a 
 •^pool, can be bought for ten cents ? How many 
 times five nmke ten ? 
 
 2. How ujany barrels of flour, at five dulars a 
 barrel, can you buy for twenty dollars? 
 
 8. At five shillings a pound, how many pounds 
 of tea can I buy for fifteen shillings ? 
 
DIVISION. 61 j 
 
 4. At five cents a pound, how many pouncUi of 
 lard can be bought for thirty cents ? 
 
 5. James has twenty-five cents which he wishes 
 to lay out in lemons, which cost five cents apiece * 
 how many can he buy ? 
 
 6 When milk is five cep*s a quart, how many ; 
 quaits can you buy for fort} cents ? 
 
 7. If you have fifty cenU how many tops can you , 
 buy, at five cents apioce ? I 
 
 8. If a man travels fiv* miles an ho«r, how long j 
 will it take him to travel forty-five miles? 
 
 9. How lotijir will it take a man to travel fifty 
 I miles, if he travels five miles an hour? 
 
 j LESSON V. 
 
 I 1. If I had twelve cents, how many bunches of 
 i quills could I buy, at six cents a bunch ? 
 I 'Z, If you had twenty-four peaches to give to six ! 
 . of your companions, how many could you give them i 
 j apiece ? i 
 
 I 3. At six dollars a yard, how many yards of cloth ' 
 j can I buy for eighteen dollars? j 
 
 j 4. At six cents an ounce, how many ounces of i 
 ! peppermints can you buy for thirty cents? j 
 
 j 5. How many hats, at six dollars apiece, will I 
 forty-two dollars buy ? 
 
 6. How many pounds of tea, at six shillings a 
 ! pound, will thirty-six shillings buy? 
 
 7. A man laid out sixty shillings for lambs, at gix 
 shillings apiece : how many did he buy ? 
 
 8. A merchant paid fifty-four dollars for six mufTs 
 i how much was that apiece ? 
 
 ' 9. At six shillings a bu«hel, how many bushels of 
 j wheal will forty-eight shillings buy ? 
 
.»2 DIVISION. 
 
 LESSON VI. 
 
 1. Sarah bought seven yards of silk braid for 
 twenty-eight cents : how much did she give a yard ? 
 
 2. Susan laid out forty-two cents for ribbon worth 
 seven cents a yard : how many yards did she get ? 
 
 3. If seven yards of cloth make one suit of clothes, 
 how many suits will twenty-one yards make ? 
 
 4. A teacher wishes to give fourteen pencils to a 
 class of seven scholars : how many pencils can he 
 give to each ? 
 
 5. George has thirty-five pears to give to seven 
 boys : how many can he give them apiece ? 
 
 6. At seven cents a pound, how many pounds of 
 cotton can be bought for fifty-six cents ? 
 
 7. Seven days make a week : how many weeks 
 are there in forty-nine days ? 
 
 8. If a stage goes seven miles an hour, how long 
 will it be in going seventy miles ? 
 
 9. A man paid sixty-three cents for seven pounds 
 of sugar, wliat was that a pound ? 
 
 LESSON VII. 
 
 1. A man gave sixteen shiliings to eight oeg- 
 gars : how much did he give to each ? 
 
 2. Sarah has twenty-four roses to give to eight 
 little girls: how many can she give them apiece? 
 
 3. How many sheep, at eight shillings a head, can 
 I buy for forty shillings ? 
 
 4. Eight quarts make a peck : how many pecks 
 are there in thirty-two quarts ? 
 
 5. At eight dollars a ton, how much coal can I 
 buy for sixty.four dollars? 
 
DIVISION. 63 
 
 6. When cherries are eight cents a quart, hoM' 
 many quarts can you buy for fifty six cents ? 
 
 7. If you have forty-eight cents, how many slates 
 can you buy, at eight cents apiece ? 
 
 8. If you read eight pages a day, how long will 
 it taiie you to read a book through, which has sev- 
 enty-two pages ? 
 
 9. If a school contains eighty scholars, how many 
 classes can be formed containing eight scholars 
 apiece ^ 
 
 LESSON Vlll. 
 
 1. When butter is nine cents a pound, how many 
 pounds, will twenty-seven cents buy ? 
 
 2. At nine dollars a barrel, how many barrels of 
 beef can I buy for thirty-six dollars? 
 
 8. If nitie yards of cloth will make one cloak, 
 how many cloaks will eighteen yards make ? 
 
 4. If yoii can buy a quart of molasses for nine 
 cents, how man) {uarts can you b'l.y for forty-five 
 cents 1 
 
 5. If nine yards of silk cost seventy-two shillings, 
 what will one yard cost? 
 
 6. A man paid sixty-three dollars for nine tons 
 of hay : what was that per ton ? 
 
 j 7. A tavern-keeper gave fifty-four quarts of oats 
 
 ' to nine horses : how many quarts did he give to 
 
 I each horse ? 
 
 I 8. If you recite nine questions in arithmetic a day, 
 
 i how many days will it take you to recite eighty -one 
 
 , questions? 
 
 j 9. How many cows, at nine dollars apiece, can a 
 
 I man buy for ninety dollars ? 
 
 J 
 
64 DIVISION. 
 
 LESSON IX. 
 
 1. How many cows, at ten dollars a head, can a 
 man buy for twenty dollars "? 
 
 2. A certain school contained forty scholars, which 
 the teacher formed into classes of ten scholars each : ! 
 how many classes did he form ? 
 
 3. At ten dollars per acre, how many acres of 
 land can be bought for nfty dollars? 
 
 4. A man paid eighty cents for a horse and chaise 
 to ride ten miles : how much was that a mile ? 
 
 5. How many sheep, at ten shillings a head, can 
 be bought for ninety shillings ? 
 
 6. A man laid out sixty dollars for hay, at ten 
 dollars per ton : how many tons did he buy ? 
 
 7. If I pay ten cents a quart for blackberries, 
 how many quarts can I buy for thirty cents ? 
 
 8. A dairy- woman has seventy pounds of butter, 
 which she wishes to divide equally among ten cus- 
 tomers : how many pounds can she send to each ? 
 
 9. If you divide a hundred marbles into ten equal 
 piles, how many will there be in a pile ? 
 
 LESSON X 
 
 I 1. In eight, how many times four? How many 
 times two ? How many times one ? 
 
 2. In six, how many times two ** How many 
 times three ? One ? Six ? 
 
 3. In twelve, how many times two? Three? 
 Four ? Six ? 
 
 4. In ten, how many times five ? Two ? One ? 
 
 5. In sixteen, how many times eight? Four? 
 Two? One? 
 
1 
 
 1 
 
 1 
 
 
 DIVISION. 
 
 
 
 1 
 65, 
 
 1 
 
 1 
 
 ' 6. 
 
 In twenty. 
 
 four, how many 
 
 times two ? 
 
 Three ? 
 
 Four 
 
 ? Six? P 
 
 :ight ? 
 
 
 
 
 -r 
 
 In eighteen, how maii}' 
 
 limes 
 
 two? 
 
 Three ? 
 
 Sx? 
 
 Nine ? 
 
 
 
 
 i 
 
 8. 
 
 In twenty, 
 
 how many times two 
 
 ? Ten 
 
 ? Five? 
 
 9. 
 
 In thirty-six, how nnany 
 
 times six ? 
 
 Nine ? | 
 
 Three ? Four ? 
 
 Two? 
 
 
 
 1 
 
 i ^<^ 
 
 In thirty- 
 
 two, how many 
 
 times eijjht ? 
 
 Four ? 
 
 ! n 
 
 Jn l'.venty-ei<rht, how many 
 
 times 
 
 seven ? i 
 
 Four ? Two ? 
 
 12. In forty, how many tijufs ten? Fight ? Five ? 
 18. In forty-eitrht how many times eight? Six ? 
 
 14. In sixty-three, how many times seven ? Nine ? 
 
 15. In fifty -six, how many times seven ? Eight ? 
 
 LESSON XI . I 
 
 1. How many t''mos is three contained in twelve ? j 
 I T citrhleen ? In fiJ^oon? In twontvone? In twenty- i 
 fc' ir ? In thirty ? in twenty-seven ? I 
 
 J. IIow many times is five contained in fifteen ? ' 
 In twenty-five ? In thirty five? In fifty ? 
 
 8. IIow many times is four contained in sixteen ? 
 In twenty. four ? In thirty two? In forty? In thirty- i 
 six? In twenty-eight ? .; 
 
 4. How many times is six contained in eighteen ? ' 
 In thirty? In twenty-four? In thirty-six? In forty- \ 
 two ? ^ In fifty- four ? ! 
 
 5. How many times is eight contained in twenty ' 
 four? In thirty-two? In forty-eight ? In sixty-four ? j 
 Inffty-six? In seventy-two ? I 
 
 6. IIow many times is seven contained in twenty- ■ 
 eight? In thirty-five ? In forty-two? In fifty-six ? 
 In fort} -pine ? In sixty-three ? ! 
 
1^ ■ 
 
 DIVISION. 1 
 
 j 
 
 1 
 
 1 7. 
 
 [low many times is nine contained in twenty. 
 
 seven 
 
 ? In forty-five? In thirty-six? In fifty four? 
 
 In sixtv-three ? | 
 
 H. 
 
 In thirteen, how many times four, aid how 
 
 many 
 
 over ? 1 
 
 Ans. Three times, and one over. |i 
 
 9. 
 
 Why ? 1 
 
 Am. Because, three times four are twelve, acd 1 
 
 twelve from thirteen leaves one. || 
 
 1« 
 
 In seventeen, how many times five, and how 1 
 
 many over ? !| 
 
 11 
 
 in twenty.six, how many times six, and how j 
 
 1 many 
 
 over ? } 
 
 i-i. 
 
 In twenty, how many times three, and how i 
 
 many 
 
 over ? 
 
 18 
 
 In forty-three, how many times five, and how 
 
 many 
 
 over ? 
 
 14. 
 
 In thirty-nine, how many times six, and how 
 
 many 
 
 over? 
 
 1. 
 
 LESSON XII. 
 
 How many oranges, at four cents apiece, can 
 
 you h 
 
 uy /or twenty cents ? 
 
 2. 
 
 How many thimbles can Sarah buy for t: irty- 
 
 five cents, if she pays seven cents apiece? | 
 
 3. 
 
 George paid twenty-four cents for six lead pen- 
 
 cils: 
 
 how much was that apiece? 
 
 ! 4. 
 
 A man gave fcrty-five dollars for nine sheep: 
 
 i what 
 
 was the price of the sheep per head? 
 
 5. 
 
 It a man travels soven miles an hour, how lonti 
 
 vvjl. ii take him t) travel sixtv-three miles? l| 
 
 ; 6. 
 
 A gentleman divided thirty-five cents equally 
 
 1 amon 
 
 g five boys : how many cents did each receive ? j 
 
 
 -.-. .- - J 
 
DIVISION. 67 
 
 7. How many barrels of flour, at six dollars a bar- 
 rel, can be boui^ht for forty -eight dollars? 
 
 8. A hatter had forty hats, which he packed in five 
 boxes : how many did he put in a box ? 
 
 9. A man wishes to walk from New Haven to Hart- 
 ford, a distance of thirtv-six miles '. how long will it 
 take him, if he walks four miles an hour ? 
 
 10. Seven boys found a pocket-book containing 
 forty-nine dollars, which they shared equally: how 
 much did each receive? 
 
 11. When c<:»al is eight dollars a ton, how much 
 can I buy for fifty -six dollars? 
 
 12. If one man can b li! 1 a barn in forty days, how 
 ; long would it take four men to build it ? 
 
 LESSON XIII. 
 
 1. Q. What is the operation called, by which the 
 preceding examples in this section have been solved ? 
 
 I Ana. It is called Divuion. 
 
 2. Q. What is Division ? 
 
 Ans. Division is tht process of finding how many 
 times one given number is contained in another, 
 
 3. Q. What is the number to be divided, called ? 
 Ans. The Dividend. _f'\ 
 
 4. Q. What is the number by which we' divide, 
 called ? 
 
 Ans. The Divisor. 
 
 5. Q. What is the answer, or number obtained oy 
 iivision, called ? 
 
 A718. The Quotient. I 
 
 6. Q. What ii^ the number that is sometimes left 
 after dividing, called ? 
 
 Ans. The Remainder. 
 
69 DIVISION. 
 
 7. When we say four is contained in twenty- 
 seven, six times and three over, wliich is the num- 
 ber to be divided ? Which the number we divide 
 by? Which the quotient ? Which the remaindei ? | 
 
 H. When we say, five is contained in tiiirty-eight. 
 seven times and nree over, what is the five called 't 
 What is the thir y-e'itrht called ? What is the seven 
 sailed? What is the three called? 
 
 y. What is the quotient of twenty-three divided 
 by tour, and what the remainder ? | 
 
 10. Five in twenty-eight, how many times, and 
 what the remainder? 
 
 11. Six in thirty-four, }k)w many times, and how 
 many over? 
 
 \-z. Eight in fifty, how many times, and how many 
 over ^ 
 
 EXAMPLES FOR PRACTJCK. 
 
 1. itcorge )>nid twenty-four cents for six Jemons: 
 how muon did they cost apiece ? 
 
 2. It a man walks five miles an hour, how long 
 will it taKc him to go forty mihs? 
 
 .3. How many yards of ribbon, at seven cents a 
 yard, can v^ou purchase for twenty-one cents? For 
 thirty-five cents? For forty-two cents? 
 
 4. How many thimbles, at six cents apiece, can 
 Mary buy tor twenty-four cents? For thirty cents? 
 For forty-two cents? For fifty- four cents? 
 
 ^^. At eight cents a quart, how many quarts of j 
 blackberries can you buy tor sixteen cents? For 
 thirty-two cents? For forty-eight cents? For 
 twenty-four ceiils? 
 
^ DIVISION. 69 
 
 6. A man paid forty dollars for eight yards of j 
 cloth : hDW much was that per yard 1 
 
 7. Henry had sixty-four marbles, which he ^ave 
 to eight companions: how much did each receive? ' 
 
 8. In three times four, hv)w many times two? 
 So/utio7i.—r-Thri'.e times four are twelve : and two 
 
 is contained fii twelve, six times, ^ns. Six times. 
 
 9. In two tin»es eight, hew many limes four ? 
 
 10. In three times six, how many times nine ? 
 
 11. In eight times three, how many times six ? 
 
 12. In four times ten, how many times eight? i 
 
 13. In five times four, how many tin>es ten t | 
 
 14. In six times six, how many times nine ? j 
 
 15. Three times six are how many times two? 
 
 I 16. Four times six are how many tinies eight ? 
 
 17. Six times six are how many times four ? 
 
 18. How many weeks are there in forty-two days, 
 there being seven days in a week? In thirty-five 
 days, how many weeks ? 
 
 19. A man laid out twenty-eight shillings in wheat. 
 at seven shillings a bushel : how many bushels did 
 he buy ? 
 
 20. I f slates cost eight cents apiece, how many can 
 you buy for sixty-four cents ? 
 
 21. If the price of coffee is nine c^-^.ts a pound, 
 how many pounds can I buy for forty-five cents? 
 For sixty-three cents ? For seventy-two cents? | 
 
 22. If land is ten dollars an acre, how many acres | 
 can a man buy for eighty dollars ? 
 
 2H. At seven dollars a yard, how many yards of 
 cloth can be bought for sixty-three dollars? 
 
 24. How long will it takf a stage to go seventy- 
 fHo miles, if it goes at the rate of eight miles an ' 
 hour ? 
 
1 
 
 SECTION VI. 
 
 
 ARABIC NOTATION. 
 
 fn the pieceding lessons, numbers have been ex- 
 
 fiessed by words. In business calculations, how- | 
 
 ever, they are 
 
 commonly denoted by the following 
 
 ten characters or figures ; viz : || 
 
 1 2 3 
 
 4 5 6 7 8 9 
 
 one, two, three 
 
 , feur, five Bix, aeren, eight, nine, n»aght.* 
 
 To express 
 
 len, we use 1 and 0, thus 10 ; to ex- 
 
 press eleven^ 
 
 we use two Is, thus 11 ; to express 
 
 twelve^ we use 1 and 2, thus 12 ; and so on, as in || 
 
 the foliowing 
 
 
 
 TABLE. 
 
 ! l,one. 
 
 21, twenty-one. 
 
 41, forty-one. 
 
 % two. 
 
 22, twenty-two. 
 
 42, forty-two. 
 
 i 3, three. 
 
 2;i, twenty-three. 
 
 43, forty-three. 
 
 4, four. 
 
 24, twenty-four. 
 
 44, forty- four. 
 
 i 5, five. 
 
 2,5, twenty-five. 
 
 45, forty-five. 
 
 1 (i, six. 
 
 '^\, tw.nty-Kix. 
 
 46. forty-six, SiC. 
 
 1 7 «evcn. 
 
 27, twenty-seven. 
 
 50. fifty. 
 
 j ^. exgUi. 
 
 2H, twenty-eight. 
 
 51, fifty-one, &c. 
 
 j 9, nin«. 
 
 21). twenty-nine. 
 
 HO, sixty. 
 
 \ 10, ten. 
 
 30, thirty. 
 
 61, sixty-one, &c. 
 
 j 11, tJeven, 
 
 31, thirty -one. 
 
 70, seventy. 
 
 I 12, twflve. 
 
 32, thirty-two. 
 
 71, seventy-one, &c. 
 
 ■ 13, thirteen. 
 
 33, thirty-three. 
 
 80, eighty. 
 
 14, fourteen!. 
 
 34, thirty -four. 
 
 81, eighty-one, &c. 
 
 15^ fifteen. 
 
 35, thirty-five. 
 
 90, ninety. 
 
 16, sixl*M»n. 
 
 St), thirty-sii. 
 
 91, ninety -one, &c. 
 
 17, seventeen. 
 
 37, thirty-seven. 
 
 100, one hundre*!. j 
 
 IK njjhter.n. 
 
 :W. thirty-eight. 
 
 200, two hunJntl. ! 
 
 ii^. nineteen. 
 
 3l», thirty-nine. 
 
 500, three hundred, &c. 1 
 
 2^ twenty. 
 
 40, forty. , 1000, one thou^Mi,nd. | 
 
 • Th*- pupil sha . 
 
 d be able to distiincuinh and to tpnte these ten flarure*, : 
 
 b»fo!>> I..X attfmvt* fc 
 
 p ••sj»itw; larpsr nunjh^r* By a frw hlntu frtm ti> 
 
 r^Micber mi to th^ cua 
 
 Lnn^T of ccmbintng th«m, he will eaaily ieam vO ex 
 
 pr«w any namb«.r. 
 
 i 
 
NOTATION. 
 
 71 
 
 ROxMAN NOTATION. 
 Another method of expressing numbers is by tho 
 follovvin^r letters; viz: I, V, X, L, C, D, M. 'The 
 rriBnner of doin^ this may be learned from tne fol- 
 lowing 
 
 TABLE. 
 
 I denotes one 
 
 XXX denote thirty. 
 
 II 
 
 i( 
 
 two. 
 
 XL 
 
 (1 
 
 forty 
 
 III 
 
 (( 
 
 three. 
 
 L 
 
 IC 
 
 fifty 
 
 IV 
 
 (( 
 
 four. 
 
 LX 
 
 It 
 
 sixty. 
 
 V 
 
 (i 
 
 five. 
 
 LXX 
 
 " 
 
 seventy. 
 
 VI 
 
 (( 
 
 six. 
 
 LXXX 
 
 " 
 
 eiirlity. 
 
 VII 
 
 (( 
 
 eleven. 
 
 xc 
 
 " 
 
 ninety. 
 
 VIII 
 
 '< 
 
 eight. 
 
 c 
 
 " 
 
 one hundred. 
 
 IX 
 
 " 
 
 nine. 
 
 CI 
 
 u 
 
 one hunil red nnd one. 
 
 X 
 
 1« 
 
 ten. 
 
 ex 
 
 (1 
 
 one hundred and ten. 
 
 XI 
 
 u 
 
 eleven. 
 
 CO 
 
 i( 
 
 two hundred. 
 
 XII 
 
 C( 
 
 twelve. 
 
 ccc 
 
 (( 
 
 three hundred. 
 
 Xlil 
 
 l( 
 
 thirteen,^ 
 
 cccc 
 
 <l 
 
 four hundred. 
 
 XJV 
 
 (( 
 
 fourteen'. 
 
 I) 
 
 (( 
 
 five hundred, 
 
 XV 
 
 (( 
 
 fifteen. 
 
 DC 
 
 II 
 
 six hundred. 
 
 XVI 
 
 (( 
 
 sixteen. 
 
 DCC 
 
 << 
 
 seven hundrinl. 
 
 XVll 
 
 II 
 
 seventeen. 
 
 DCCC 
 
 l< 
 
 eijfht hundred. 
 
 XVIII" 
 
 eighteen. 
 
 IXJCCC 
 
 u 
 
 nine hurulred. 
 
 XIX 
 
 '» 
 
 nim^leen. 
 
 M 
 
 II 
 
 one lhi)Usand. 
 
 XX 
 
 (( 
 
 twenty. 
 
 MC 
 
 (1 
 
 one thou^^and v.^^ one hund. 
 
 XXI 
 
 (1 
 
 twenty-one. 
 
 MI) 
 
 (I 
 
 one thousand iV fivehund 
 
 XXII 
 
 II 
 
 twenty-two. 
 
 MDCCCXLVI, one ihoufiand eijfhi 
 
 
 
 
 
 
 hundrev. and forty-six. 
 
 EXERCISES IN NOTATION. 
 
 I. Write the following numbers in figures U}w r? 
 your slate, or black-board : 
 1. Kleven. 
 
 3. TMenty-one. 
 
 5. Forty -seven. 
 
 7. Spventv-ei^ht. 
 
 9. Si.xty-five. 
 
 11. Eighty-nine. 
 
 2. Seventeen. 
 
 4. Sixty. three. 
 
 6. Kiglily-six. 
 
 8. Kifiy-seven. 
 
 10. Niiiety-thre^i. 
 
 12. Ninety-hve. 
 
72 NOTATION. 
 
 13. One hundred and one. 
 
 14. One hundred and five. 
 
 15. One hundred and seven. 
 
 16. One hundred and ten. 
 
 17. Two hundred and fourteen. 
 
 18. Four hundred and twenty three. 
 
 19. Three hundred and nineiy-five. 
 
 20. Three hundred. 
 
 21. Two hundred and thirty. 
 
 22. Six hundred. 
 
 23. Four hundred and fifty-five. 
 
 24. Seven iiundred and sixty. 
 
 25. Ki^^ht hundred and sixty-five. 
 
 26. Nine hundred and eighty-seven. 
 
 27. One thousand. 
 
 1. Q. What is the an of expressing numbers, by 
 t;i;ures and h'Hers, called i 
 
 A71S. It is calhid iNotation. 
 
 2. Q. What is the method of expressing numbers 
 by figures, called ? 
 
 Ans. The Arahic Notation. 
 
 3. Q. Why is it called tiie Arabic notation. 
 Ans. Because it was invented by the Arabians. 
 
 4. Q. VV'.at is the method of expressing numbers 
 by letters, called ? 
 
 Ans. The Rivnian Notation. 
 
 5. Q. Why is it called the Roman Notation? 
 Ans. Because it Mas invented by the Rymans. 
 
 6. Q. Which of the alM)ve systems of Notation, is 
 commonly used 1 
 
 Ans. The Arahic Notation. 
 
 7 Q. What is the art of reading numbers ex- 
 pressed by figures, called? 
 
 Ans, It is called Numeration. 
 
1 
 
 
 
 
 
 1\ 
 
 1 
 
 1 
 
 NOTATION. 
 
 
 i 
 
 EXERCISES 
 
 IN NUMERATION. | 
 
 Read the 
 
 numbers 
 
 expressed by 
 
 the iDliowing , 
 
 figures : 
 
 
 
 
 13 
 
 57 
 
 10() 
 
 310 
 
 17 
 
 39 
 
 101 
 
 295 
 
 25 
 
 76 
 
 119 
 
 430 
 
 52 
 
 48 
 
 116 
 
 375 
 
 36 
 
 79 
 
 107 
 
 537 
 
 1 "^1 
 
 91 
 
 121 
 
 426 
 
 ' m 
 
 37 
 
 110 
 
 111 
 
 27 
 
 81 
 
 130 
 
 239 
 
 19 
 
 65 
 
 126 
 
 685 
 
 43 
 
 58 
 
 140 
 
 491 
 
 34 
 
 83 
 
 129 
 
 507 
 
 56 
 
 89 
 
 105 
 
 810 
 
 41 
 
 92 
 
 150 
 
 740 
 
 65 
 
 78 
 
 162 
 
 936 
 
 24 
 
 94 
 
 201 
 
 845 
 
 68 
 
 86 
 
 214 
 
 987 
 
 73 
 
 98 
 
 196 
 
 1000 1 
 
 1 Read the 
 
 numbers 
 
 expressed by 
 
 the followinf» 
 
 figures : 
 
 
 
 
 1845 
 
 1850 
 
 1«55 
 
 1^60 
 
 2167 
 
 4101 
 
 6705 
 
 6200 
 
 578 
 
 5060 
 
 7039 
 
 7000 
 
 1 2861 
 
 2805 
 
 4000 
 
 6203 
 
 1 3420 
 
 6729 
 
 7210 
 
 8000 
 
 1 1605 
 
 2508 
 
 6400 
 
 8400 
 
 4(J8 
 
 3091 
 
 1601 
 
 7609 
 
 4376 
 
 2930 
 
 8700 
 
 3491 i 
 
 2024 
 
 6238 
 
 4890 
 
 9000 1 
 
 5230 
 
 7304 
 
 5000 
 
 8468 ) 
 
 j 1040 
 
 7490 
 
 8245 
 
 9999 j 
 
74 MISCELLANEOUS 
 
 MISCELLANEOUS EXAMPLES. 
 
 1. James bought a lemon for 4 cents, and a pouud 
 of figs for 8 cents : how much did he pay for both ? 
 
 j Solution. — 4 cents and 8 cents are 1 2 cents. Tbero- 
 I fore, if he paid 4 cents for his lemon, and 8 cents for 
 I his figs, he must have paid 12 cents for both. 
 
 2. A man bought a pound of tea for 4 shillings, 
 and a gallon of molasses for 3 sbiUings : how many 
 
 I shillings did he pay for both ? 
 
 3. Uorace })aid 6 cents for some marbles, 3 cents 
 fo^ a top, and 1 cent for a whis».'e : how many cents 
 did he pay for all i 
 
 I 4. How many are 5 and 13 ? 22 and 4 ? 3 and 16 ? 
 4 and 13! 
 
 5. Uow many are 6 and 12 1 5 aU 14 ? 4 and 17 ? 
 16 and 5? 
 
 6. llow much will three oranges cost, at 4 cents 
 apiece ? *^- 
 
 Analysis. — If 1 orange costs 4 cents, 3 oranges will 
 vv^t three times as much : and 3 times 4 cent^^ are 12 
 cents. Therefore 3 oranges, at 4 cent* apiece, will 
 cost 12 cents. I 
 
 7. If 1 quart of strawberries cost 6 cents, what will ■ 
 2 quarts cost ? 2 times 4 are how many * | 
 
 8. What cost 3 barrels of flour, at 5 dol ars a bar- 
 rel ? 4 barrels? 5 barrels? ^ . 
 
 9. What cost 10 lambs, at 7 slillings apiece ? i 
 
 10. What cost 4 bushels of cr: uberrie*) at 3 dollars ' 
 a bushel ? 6 bushels ? j 
 
 11. What cost 6 sheep, at 4 dollars a Km'i ? 
 
 12. What cost 8 cords of wood, at 3 doU^it d^ <?.C'd ? 
 7 cords ? 10 cords? | 
 
BXAMPLES. 15 
 
 I 13. How many are 7 times 3 ? 5 times 8 ? 6 times 
 I 4 ? 4 times 8 « i 
 
 I 14. Henry had 9 apples, and gave away 4 : how 
 
 many had he left ? j 
 
 I Solution. — 4 apples taken from 9 apples leave 6 
 '. apples. Therefore if he had 9 apples, and gave away 
 I 4, he must have had 5 left ? j 
 
 I 15. Sarah had 10 peaches, and gave away 3 : how 
 , many had she left ? I 
 
 I 16. If you have 12 marbles, and lose 5 of them, 
 i how many will you have left ? 
 I 17. 3 from 17 leaves how many ? 5 from 18 ? 
 18. 5 from 11 leaves how many ? 6 firom 10? 7 
 
 from 12 ? 8 from 13 ? 6 from 15 ? 
 I 19. William bought a knife for 18 cents, and sold 
 
 it for 5 cents less than cost : how much did he sell it 
 
 for? 
 
 20. How many yards of ribbon, at 6 cents a yard, 
 
 can be bought for 30 cents ? 
 
 Anali/sis. — If 6 cents will buy 1 yard, 30 cents will 
 
 buy as many yards as 6 is contained times in 30 : 
 
 and 6 is contained in 30, 5 times. Therefore, 30 cents 
 
 wiU buy 5 yards of ribbon, at 6 cents a yard. 
 
 21 How many bushels of corn, at 4 shillings a 
 
 bushel, can a man buy for 16 shilUngs? 
 
 22. If I have 18 peaches to give to 6 boys, how 
 many can I give them a})iece ? 
 
 23. How many hats, at 5 dollars apiece, can you 
 buy for 20 dollars? 
 
 24. How many times 6 in 24 ? In 30 ? In 42 ? 
 
 25. How many times 4 in 28 ? In 20 ? In 36 ? 
 
 26. A man l>ought 8 yards of cloth, at 3 dollars a 
 yard, and paid for it in tiour, at 4 dollars a barrel : how 
 many barrels did it take ? 
 
76 MISCELLANKOUS 
 
 Sufi j/eaHov — Firet find how much tne cloth comes to 
 If 1 yard is worth 3 dollars, 8 yards are worth 8 
 times as much ; and 8 times 8 dollars are 24 dol- 
 lars. Now it will manifestly take as many barrels 
 of flour to pay for the cloth, as 4 dollars are con 
 rained times in 24 dollars ; and 4 in 24, 6 times 
 Atis. 6 barrels. 
 
 27. A farmer bought 6 pounds of tea, at 4 shil- 
 lings a pound, and paid for it in whtat, at 8 shillings 
 a bushel ; how many bushels did it take ? 
 
 28. A man bought a cow for 10 dollars, and sold 
 it for 16 dollars : how much did he make by his 
 bargain ? 
 
 2ii. If Horatio buys 6 oranges, at 8 cents apiece, 
 and sells them again for 4 cents apiece, how much 
 will he make by his bargain ? 
 
 80. In 5 limes 8, how many times 10? 
 
 81. In 6 titnes 0, how many times 4 ? 
 
 82. In 8 times 8, how many times 6 ? 
 
 ! 88. A butcher sold 8 pounds of beef for 56 cents : 
 
 what was that a pound ? 
 i 84. A dairy-man sold 10 pounds of butter for 80 
 I cents : how much did he get a pound ? 
 I 85. A fanner sold 10 bushels of oats, at 3 shil- 
 I lings a bushel, and took 7 yards of flannel, at 4 
 
 shillings a yard, and the rest in money : how much 
 I money did he receive ? 
 I 86. What is the ditTerence between 3 times 6, and 
 
 7 times 8 ? 
 '. 87. What is the diflference between 5 times b 
 
 and 4 times ^ ? 
 
 88. In 21, how many times 5, and how many 
 I over? Ans. 4 tiuies and 1 over. 
 
 39. In 18 how many times 4, and how many over? 
 
EXAMPLES. . 77 
 
 40. In 80, how many times 7, and how many over ? 
 
 41. In 87, how many times 9, and how many over ? 
 
 42. In 4.5, how mar.y times "i , and how many over ? 
 48. In 6f>, how ntany times 9, and how many over '? 
 4l. If 3 coals cost 24 dollars, how much will 1 
 
 coat cost ? 
 
 Solution. — If 8 coats cost 24 dollars, 1 coat will 
 cost as many dollars as 8 is contained times in 24 : 
 and 8 is contained in 24, 8 times. Ans. 8 dollars. 
 
 j 45. How many hats, at five dollars a piece, can 
 
 I be bou^iit for 85 dollars ? 
 
 46. How much flour, at 7 dollars a barrel, can a 
 man buy for 42 dollars ? 
 
 47. How many yards of cloth, ai 9 dollars a 
 yard, will 86 dollars buy ? 
 
 48. How many tons of coal, at 8 dollars a ton, 
 will 64 dollars buy ? 
 
 49. A man bought 8 pair of boots at 8 dollars 
 a pair, and paid for them in flour, at 6 dollars a bar- 
 rel : how many barrels diJ it take ? 
 
 50. If you buy 4 penknives at 10 cents apiece, 
 and pay for them in beechnuts, at 5 cents a quart, 
 
 ! how many quarts will it take ? 
 
 I 51. A farmer sold 6 pounds of butler for 10 cents i 
 
 ! a pound, asid took his pay in njolasses, at 6 cents a | 
 
 quart: how many quarts did he receive? | 
 
 1 .52. When wlu^ai is 7 shiliin«rsa bushel, how many 
 
 bushels can be boujrht for 68 shillings ? 
 ' 58. Six boys found a purse of money containing 
 ' 48 dollars, W'hich they divided among themselves 
 
 3<]ually : how many dollars did each receive? j 
 
 54. If a man has 45 dollars, how many whole 
 
 barrels of flour can he buy, at 6 dollars a barrel, and 
 
 how many dollars will he have over ? 
 
78 MISCELLANEOUS 
 
 55. Ai 5 dolla-s a yard, how many whole yards 
 of cloth can be bought for 28 dollars, and how many 
 dollari-- o>er ? 
 
 56. In 85, how many times 9, and how many 
 over? 
 
 57. In 107, ho>* many times 10, and how many 
 over? 
 
 58. In 95, how many times 9, and how many 
 I over? 
 
 59. In 83, how many times 8, and how man) 
 over ? 
 
 60. In 109, how many times 10. and how many 
 over ? 
 
 61. Henry bought a Geography for 5(> cents, and a 
 Reader for 20 cents : h jw much did he give tor both ? 
 
 Analysis. — 50 is equal to 5 tens, and 20 is equal 
 to 2 tens : now 5 tens and 2 tens are 7 tens ; and 
 7 tens are equal to 70. Ans. 7(^ cents. 
 
 62. How many tens in 30 ? In 70 ? 
 
 63. How many tens m 40 ? In 90 ? 
 
 64. How many tens in 80 ? In 100 ? 
 
 65. 4 tens are equal to how many ? 
 
 66. 6 tens are equal to how many ? 
 
 67. 7 tens are erjual to how many ? 
 
 68. 9 tens are equal to how many ? 
 
 69. 8 tens are equal to how many ? 
 
 70. 10 tens are equal to how many ? 
 
 71. 3 tens and 5 tens are how many? 
 Solution, — 3 tens and 5 tens are 8 tens and 8 
 
 tens are equal to 80. 
 
 72. 6 tens and 4 tens are how many ? 
 
 73. How many are 30 and 50 ? 
 
 74. How many are 60 and 30 ? 
 
 75. How many are 40 and 40? 
 
EXAMPLES. 79 
 
 76. Henry bought 30 marhles, atuJ his uncle gave 
 him 40 more : how many marbles had he then ? 
 
 77. If a pound of lea costs M cents, and a g^allon 
 of molasses 40 cents, how much will both oaxl 
 
 78. A man gave 40 dollars for a ran, ar^ 50 
 ! dollars for a yoke of oxen : how much did he j,ive 
 j for both ? 
 
 I 79. A farmer sold a horse for 90 dollars, and a 
 
 cow for 30 dollars : how much did he get for both ? 
 I Analysis. — 90 is equal to 9 tens, and 30 is equal 
 
 to 3 tens : 9 tens and 3 tens are 12 tens; and 12 
 ! lens are equal to 120. Aiis. 120 dollars. 
 j 80. James gave 60 cents for a sled, 90 cents for 
 
 a pair of skates, and 8 cents for a knife: how much 
 
 did he give for all ? 
 
 81. If a man travels 70 miles the first day, and 
 40 the next day, how far will he travel in both 
 
 I days ? 
 
 82. Harriet gave 25 cents for her ReadfTr, and 
 37 cents for her Practical Arithmetic: how much 
 did she give for both ? 
 
 Analysis. — 25 is composed of 2 tens and 5 units, 
 and 37 is composed of 3 tens and 7 units : now 2 
 lens and 3 tens are 5 tens or 50 ; and 5 units and 7 
 units are 12 units, which added to 50 make 62, 
 ^iis. 62 cents. 
 
 83. I low many are 32 and 45 ? 
 
 84. How many are 56 and ?H ? 
 
 85. How many are 72 and 47 ? 
 
 86. How many are 61 and 82 ? 
 
 87. A man bought a horse for 75 dollars, and a 
 buggy for 63 dollars : how much did he pay for 
 both ? ; 
 
 88. A farmer raised 54 bushels of corn on one I 
 
8^) MISCELLANEOUS 
 
 acre, and 48 bushels on another : how many bush- 
 els dii he raise on both acres ? 
 
 89. A man gave 90 cents for a bushel of wheal, 
 and 40 cents for a buahol of rye : how much more 
 did he pay for his wheat than for iiis rye ? 
 
 Solution. — 90 is 9 tens, and 40 is 4 tens : now 4 
 tens from 9 tens leave 5 tens ; and 5 tens are equal 
 to 50. Ans. 50 cents. 
 
 90. Frank gave 80 cents for a Dictionary, and 50 
 cents for a Geography : how much more did he pay 
 for his Dictionary than for his Geography? 
 
 91. William, having 100 cents, spent 60 of them : 
 how many cents had he left ? 
 
 92. If ►^a. ah reads 80 pages in a day, and Susan 
 reads 50, hew many more pages will Sarah read 
 than Susan ? 
 
 98. A man put 75 sheep into a pastidre, but 20 of 
 them jumped out : how many remauied in the pas- 
 ture ? 
 
 94. 25 from 45 leaves how many ? 
 
 95. 36 from 76 leaves how ;i>any ? 
 
 96. 72 from 85 leaves how many ? 
 
 97. 63 from 79 leaves how many ? 
 
 98. 84 from 97 leaves how many ? 
 
 99. A farmer sold 5 cows, at 30 dollars a head : 
 how much did they come do ? 
 
 Aruilyais. — If 1 cow costs 30 dollars, 5 cows will ; 
 cost 5 times as much. Now 30 is equal to 3 tecs, and 
 6 times 3 tens are 15 tens; and 15 tens are equal to 
 150. Therefore, 5 cows, at 30 dollars a head, will cost ; 
 150 dollars. 
 
 100. What cost 20 sheep, at 8 shillings a head? ! 
 
 101. A dairy- woman sold 40 pounds of cheese for 7 j 
 cents a |x>und : how much ».lid it come to ? 
 
KXAMPLE8. 81 
 
 102. A merchant sold 60 pounds of sugar for 8 
 cotits a pound : how much did it come to? 
 ! 103. A manufacturer sold 100 yar^ls of muslin, at 
 I 9 c«nts a yard : how much did it con e to ! 
 
 104. What cost 3 melons, at 15 cc nts apiece ? 
 Awilysis. — If 1 melon costs 15 ceuts, 3 melons will 
 
 cost >t times as much. Now 15 is composed of 10 
 and 5 : but 3 times 10 are 30, and 3 times 5 are 
 15 ; and 15 added to 30 make 45. Therefore 3 mel- 
 ons, at t5 cents aj^iece, will cost 45 cents. 
 
 105 What will 4 slates cost, at 14 cents apiece ? 
 
 106. vVhat cost 5 pounds of butter, at 16 cents a 
 pound ? 
 
 107. What will Y yards of cloth come to, at 15 
 shillings a yard ? 
 
 105. A. farmer sowed 6 acres of oats, which yielded 
 25 bushels per acre ; how many bushels of oats did 
 he have ? ^-- 
 
 Analysis. — 25 is composed of 2 tens and 5 units : 
 now 6 times 2 tens are 12 tens, or 120, and 6 times 
 5 are 30; and 30 added to 120 make 150. There- 
 fore 6 acres will yield 150 bushels, at 25 bushels per 
 acre? 
 
 109. At 35 dollars apiece, how much will 5 acres 
 '^^ land cost ? 
 
 110. At 42 dollars apiece, how much will 7 sleighs 
 cost ? 
 
 111. Joseph bought 7 oranges, at 4 cents apiece, 
 and sold them at 5 cents apiece : how much did he 
 make by his bargain ? 
 
 Sng^jestion. — The learner should first find how 
 
 ! much he paid for the oranges, then how much he 
 
 received for them; finally, taking the sum he pail 
 
82 MISCELLANEOUS 
 
 from the sum he received, the remainder will be his 
 gain. 
 
 112. A man bought 10 sheep at 7 shillings a 
 head, and sold them again at 9 shillings a head : 
 how much did he gain by the bargain ? 
 
 113. A merchant bought "i barrels of flour, at 9 
 dollars a barrel, and sold them at () dollars a barrel : j 
 how much did he lose by his bargain ? 
 
 114. A man bought 6 hats at 4 dollars apiece, 
 and .5 yards of cloih at 6 dollars a yard : how much 
 did he pay for both ? 
 
 115. A farmer sold 7 pounds of veal at 8 cents a 
 pound, and 4 pounds of butter at b cents a pound : 
 how much did he receive for both ? 
 
 116. If 1 buy 8 pounds of sugar at 7 cents a 
 pound, and 10 lemons at »i cents apiece, how much 
 must I pay for both ? 
 
 117. If 5 boys can saw a cord of wood in 4 hours, 
 how long will it take 1 boy to saw a cord ? 
 
 118. If 10 men can do a job of work in 20 dajs, 
 how long will it take one man to do it ? 
 
 110. If a barrel of flour will last 6 men 15 days, 
 how long will it last 1 man ? I 
 
 120. If 6 men can dig a cellar in 4 days, how j 
 many men will it lake to dig it in 1 day ? \ 
 
 ril. James divided 100 oranges equally among! 
 10 companions: how many oranges did he give to! 
 each ? ! 
 
 122. A man paid 63 dollars for 9 yards of cloth : | 
 how much was that a yard ? v | 
 
 123. A farmer sold 9 lambs for 72 shillings: how ' 
 much did he receive apiece ? 
 
 124. A merchant sold 9 hats, at 4 dollars apiece, 
 
EXAMPLES. d3 
 
 and agreo I to take his pay in flour at 6 dollars a bar- 
 rel : hoA* many barrels did he receive for his hats? 
 
 125. A cobbler sold 8 pair of boots at 5 dollars a 
 pair, and tooli 4 tons of coal worth 9 dollars a ton, 
 and the rest in cash : how much cash did he re- 
 ceive ? 
 
 126. How many bunches of quills can I purchase, 
 at 8 cents a bunch, for 12 slates worth 6 cents apiece ? 
 
 127. In 7 times 8, how many times 6, and how 
 many over? 
 
 128. In 9 times 5, how many times 7, and how 
 many over ? 
 
 129. In 7 times 9, how many times 6, and how 
 many over ? 
 
 130. In 8 times 9, how many times 10, and how 
 many over ? 
 
 131. In 10 times 6, how many times 7, and how 
 many over ? 
 
 1.S2. In 8 times 10, how many times 9, and how 
 many over ? 
 
 133. In 9 times 9, how many times 8, and how 
 many over ? 
 
 134. In 8 times 7, how many times 10, and how 
 many over ? 
 
 13.5. In S times 8, how many times 7, and how 
 manv over ' 
 
 I'dii. Charles bouj[yht a history for 27 cents, a ilate 
 for 10 cent^ less, hikI a geograpliy for 10 centa more; 
 ibaii his history: how much did he pay for all? i 
 
 137. llt'nry had 3 ap})les, (xporge had 4 times as 
 many as lienrv, and William had twice as many as 
 t)oth: how many did George and William have^ 
 apiece ; and how many had all of them ? i 
 
SECTION VII. 
 
 FRACTIONS. 
 LESSON I. 
 
 1. If I divide any number or thing, as an apple 
 or a pear, into two equal parts, what is each of those 
 pans called ? 
 
 Ans. One half. 
 
 2. What is then meant by one Imlf? 
 
 3. I low many halves make a w/io/e one ? 
 Ans. Two. 
 
 4. If I cut a sheet of paper into halves and give 
 , you 1 half, what part of the sheet shall I have left ? 
 j U 1 give you 2 halves, how much would be left? 
 
 Note. — The meaning of the terms one half, one third, one 
 ' fourth, &.C.., flhouKl l)e illustrated to tlie pupil by artnally cutting 
 I some familiar object, as an apple or a {»ear, into kuhex, thirds, 
 j fourths, &c. In this way, he will easily citrnprehnnd the mean- 
 ; ing of the terms used in fractions, and will lie able to perform 
 j operationu in them with as much fatiliiy aa in whole nurabcra. 
 
 j 5. If any number or thing is divided into three 
 
 equal parts, what is each of the parts called ? 
 ! Ans. One third. 
 
 6. What then is meant by (me third? What is 
 meant by two thirds ? 
 
 7. If 1 cut an apple into thirds and give away 1 
 third, what pan will be left ? If I give away 2 thirds, 
 what part will be left ? 
 
 8. How many thirds make a whole one? 
 
 9. If a number or thing is divided intoybu*- equal 
 parts, what is each of the parts called ? 
 
 i Atis. One fourth, or one quarier. 
 
 I 10. What is meant by 2 fourths? By 3 fourth*? 
 
FRACTIONS. 
 
 85 I 
 
 11 If you divide a stick of candy in fourths, and 
 give 3 fourths of it to your companions, what part 
 of it would you have left? 
 
 12. If you give away 1 fourth, what part would 
 be left ? I 
 
 13. Tv'o fourths and one fourth make how many | 
 fourths ? Three fourths and one fourth, make how j 
 many fourths ? i 
 
 14. How msiny fourths make a whole one ? , 
 
 LESSON II. 
 
 1. What is meant by 1 fifth ? I 
 Ans. When any thing is divided into Jine equal \ 
 
 parts, one of these parts is called 1 fifth. | 
 
 2. What is meant by 2 fifths? By 3 fifllis ? B> i 
 
 4 fifths ? 
 
 3. If you cut a pie into fifths, and take away 2 
 fifths, how many fifths will remain ? 
 
 4. 3 fifths and 2 fifths make how many fifths ? 
 
 5. How many Jiff hs make a whole one? 
 
 0. What is ojeant by 1 sixth ? By 2 sixths ? By 
 
 5 sixths ? By 3 sixths ? 
 
 7. James had 2 sixths of a dollar, and his father 
 gave him 3 sixths more : what part of a dollar had 
 he then ? 
 
 I 8. How many sixtJis make a whole one ? 
 
 , 9. What is meant by 1 seventh ? By 2 sevenths ? 
 
 • By 3 sevenths ? By 5 sevenths ? 
 
 10. What part of a dollar will 2 sevenths and 4 
 sevenths make ? 
 
 I 11. A man hoed 3 sevenths of an acre of corn in 
 
 i one day, and 2 sevenths of an acre the next day . 
 
 ! what part of an acre did he hoe in boLn days? 
 
86 FRACTIONS. 
 
 12. How many seventJis make a whole one ? 
 11^. What is meant by 1 eighth? By 2 eighths? 
 By 8 eighths ? By 5 eighths ? By 7 eighths ? 
 
 14. How many eighths make a whole one? 
 
 15. What is meant by 1 ninth ? By 2 nitiths ? By 
 8 ninths ? 
 
 16. How many ninlhs make a whole one ? 
 
 17. What is meant by 3 tenths? By 5 tenths? 
 By 7 tenths ? * • 
 
 18. What is meant bv 1 fifteenth ? By 2 fifteenths ? 
 By 8 fifteenths ? By 7''fifteenths ? By 10 fifteenths ? 
 
 19. What is meant by 1 twentieth ? By 2 twenti- 
 eths ? By 8 twentieths? By 12 twentieths? 
 
 20. How many thirtieths make a whole one ? How 
 ma.ny forty -fifths make a whole one ? How many 
 sixty fourths make a whole one ? How many hun- 
 dredths make a whole one ? 
 
 I LESSONIII. 
 
 1. If one half of a pear costs 1 cent, how much 
 will two halves or a whole pear cost ? 
 
 Suggestion. — 2 halves or a whole pear will cost 
 twice as much as 1 half. Now if 1 half costs 1 cent, 
 2 halves or a whole one will cost 2 times 1 cent, and 
 2 times 1 cent are 2 cents. Ans. 2 cents. 
 
 2. If 1 half an orange costs 2 cents, how much | 
 will a whole orange cost ? i 
 
 8. If i half a yard of ribbon costs 3 cents, what i 
 will a whole yard cost ? j 
 
 4. If 1 third of a pie costs 2 cents, how much will | 
 2 thirds of a pie cost ? How much will 3 thirds or I 
 a whole pie cost ? I 
 
 5. If 1 fourth of a poui.d of sugar costs 2 cenjs, j 
 
FRACTIONS. 87 I 
 
 how much will 2 fourths cost ? 3 fourths ? A whole 
 |x>und ? 
 
 6. A man sold 1 fifth of a cord of wood for 3 shil- 
 iinjTs : how much would 3 fifths come to at the same 
 rate ? A whole cord ? 
 
 7. If I sixth of a barrel of flour costs 1 dollar, 
 how much will 4 sixths of a barrel cost ? 6 sixths ? 
 
 S. If 1 seventh of a ton of hay is worth 2 dollars, 
 what is 8 sevenths worth ? 4 sevenths ? 6 sevenths ? 
 I 7 sevenths ? 
 
 9. If 1 eighth of a yard of cloth costs 1 dollar, 
 how much will 5 eighths cost ? 3 eighths I 7 
 eighths ? 8 eighths ? 
 
 10. If 1 ninth of an acre of land is worth 3 dollars, 
 how much is 4 ninths worth ? 5 ninths? 7 ninths? 
 H ninths ? 
 
 11. One tenth of a hogshead of molasses is worth 
 3 dollars : how much is 5 tenths of a hogsheaii 
 worth? 7 tenths ? 9 tenths? [low much is a hogs- 
 head worth ? 
 
 LESSON IV. 
 
 1. If a yard of tape is worth 2 cents, how much 
 
 is 1 half a yard worth ? 
 I So/uf?on. — Since a whole yard is worth 2 cents, 
 I 1 half of a yard is worth 1 half as much : and I 
 
 half of 2 cents is 1 cent. Ans. 1 cent. 
 I 2. What is 1 half of 4 cents? Ans. 2 cents. 
 i Why? 
 
 i Ans If 4 cents are divided into two equal par^s, 
 ! one of the parts is 2 cents. 
 
 j 3. If an r.*-ange costs 4 cents, how much will half 
 j an orange cost ? 
 
88 FRACTIONS. 
 
 I 4. What is 1 half of 6 cents ? What is 1 half of I 
 S cents ? Of 10 cents ? Of 12 e-^.nts ? Of l« cents ? j 
 Of 20 cents? j 
 
 I 5. If a lemon costs 6 cents, how much will 1 third \ 
 of a lemon cost 1 What is 1 third of 6 cents? , 
 
 e>. What is 1 third of 9 cents ? What is 1 third I 
 of 12 cents? Of 18 cents? Of 15 cents? Of 24 
 cents ? Of :iO cents ? 
 
 Observation. — From the preceding examples, the 
 learner will perceive that a half o{ a number is equal 
 to as many units as 2 is contained times in that num- 
 ber ; a tkird of a number is ecjual to as many units 
 
 ; as 8 is contained times in that number ; 2i fourth of a 
 number is equal to as many units as 4 is contained | 
 times in that number, &c. 
 
 7. How do you find a ha/f of a. number ? 
 Ans. Divide the number by 2. 
 
 8. How find a third of a number? How find a ! 
 fourth of a number ? A fifth ? A sixth ? A seventh ? 
 
 An eighth ? A ninth ? A tenth ? 
 
 9. What is 1 fourth of 12 dollars? Of 16 dollars? 
 Of 20? Of 82? Of 24? Of 28? Of 36 ? Of 40? 
 
 10. If a ton of coal is worth 10 dollars, what is 
 1 fifth of a ton worth ? 
 
 11. What is 1 fifth of 15 dollars ? Of 20 dollars ? 
 Of 80? Of 25? Of 40? Of 50? i 
 
 12. What is one seventh of 7 ? Of 14 ? Of 28 ? 
 Of 49? Of 70? I 
 
 18. What is one eighth of 16 ? Of 24 ? Of 40 ? i 
 Of 80? Of 72? i 
 
 14. VVhatisl ninthof9? Of 27 ? Of 18 ? Of 3b ? ! 
 Of 45? Of 72? Of 90? 1 
 
 15. What is one tenth of l() ? Of 8U ? Of 20? Of! 
 ,60? Of 50 ? Of 100? i 
 
FRACTIONS. 89 
 
 LESSON V. 
 
 1. llov much will 2 apples cost, at 1 half a ceni 
 apiece ? 
 
 Solution. — Since 1 apple costs 1 half a cent, 2 ap- 
 ples will cost 2 times as much : and 2 times 1 half 
 are 2 halves, or a whole cent. Ans. 1 cent. 
 
 2. What cost 3 apples, at 1 half a cent apiece ? 
 So/uiion. — II' 1 apj)le costs 1 half a cent, 3 apples 
 
 will cost three times as much, or 3 halves : and 3 
 halves are e(\uh to 1 whole cent and 1 half. Ans. 1 
 cent and 1 half. 
 
 3. At 1 third of a dollar a bushel, how much will 
 6 bushels of oats cost ? 
 
 4. What cost 2 pounds of tea, at 3 fourths of a 
 I dollar a pound ? How much is 2 times 3 fourths ? 
 
 •'^. In 8 fourths, how many whole ones ? In 9 
 fourths, how many whole ones, and how many 
 fourths over? In 13 fourths? In 15 fourths? 
 I 6. What cost 3 yards of flannel, at 2 fifths of a 
 dollar a yard ? How much is 3 times 2 fifths ? 
 
 7. In 10 fifths, how many whole ones? In 12 
 fifths ? In 15 fifths? In 2(» fifths ? In 32 fifths? 
 
 8. At 3 eighths of a dollar a bushel, how much 
 will 4 bushels of apples come to ? i 
 
 9. In 24 eighths, how many whole ones? In 19 ! 
 eighths ? In 33 eighths ? In 40 eighths ? I 
 
 10. At 7 tenths of a dollar a pair, how much will 
 3 pair of gloves come to ? 
 
 11. How much is 3 times 4 fifths ? 
 
 12. How much is 4 times 6 eighths ? 
 
 13. How much is 7 times 4 tenths? 
 
 14. How much is 5 timfs 7 ninths? 
 
90 FRACTIONS. 
 
 LESSON Vi . 
 
 ' 1. Wha. ^art of 2 cents is 1 cent? Ans. 1 half. 
 ' Why? 
 
 Ans. Hocause, if we divide 2 cents into ttm) equal 
 
 parts, one of these parts is 1 cent ; and when aay 
 ; thing is divided into two equal parts, one of these 
 
 parts is called 1 lia/f. 
 
 I 2. What part of 3 cents is 1 cent ? Why ? 
 I 3. What part of 3 cents is 2 cents ? 
 i Solution. — Since 1 is 1 third part of 3, 2 is 2 times 
 ■ as much : and 2 linuis 1 third are 2 thirds. Aiis. 2 
 
 thirds, 
 i 4. What part of 3 is 4 ? 
 
 Ans. 4 thirds of 3, which are equal to 1 and I 
 
 third. 
 
 5. What part of 4 pears is 1 pear? What part 
 of 4 is 2 ? Is 3 ? Is 5 ? is 8 ? Is 9 ? Is 12 ? 
 
 6. What j>art of 5 dollars is I dollar? What part 
 of 5 is 2 ? Is 3 ? Is 4 ? Is 6 ? Is 8 ? Is 10 ? Is 12 ? 
 
 , Is 15 ? Is 20? 
 
 j 7. What part of 6 pins is 1 pin ? What part of i 
 
 6 is 2 ? Is 3 ? Is 5 ? Is 7 ? Is 8 ? Is 12 ? Is 18 ? 
 
 I 8. What part of 8 apples is 1 apple? What part 
 of 8 is 2 ? Is 3 ? Is 5 ? Is 7 ? Is 16 ? Is 20 ? 
 I 9. What part of 7 days is 1 day? What part of 
 
 7 is 2 ? Is 3 ? Is 6 ? Is 8 ? Is 14 ? Is 18 ? 
 
 10. What part of 10 nuts is 1 nut ? What part of 
 10 is 2 = Is 5? Is 3? Is 25? Is 30 ? Is 35? 
 
 11. What part of 12 ponce is 1 penny ? What 
 part of 12 is 2 ? Is 3 ? Is 6 ? Is 18? Is 24 ? Is 28 ? 
 Is 30? Is 47? 
 
 12. U'hat part of 16 ounces is 1 ounce? What 
 part of 16 is 2? Is 5 ? Is 10? Is 12 ? Is 16? Is 18? 
 Is 25 ? 
 
FRACTIONS. 91 
 
 13. What part of 20 sliillings is 1 shilling ? What 
 pan of 20 is 3 ? Is 7 ? Is 10 ? Is 40 ? 
 
 14. What part of 30 is 1 ? Is 2 ? Is 5 ? Is 26 ? Is 
 36 ? Is 48 ? I 
 
 15. What part of 100 is U Is 3 ! Is 10? la 60? 
 Is 73? Is 85? 
 
 LESSON VII. 
 
 1. If you buy an orange for 4 cents, what part of 
 an orange can you buy for 1 cent ? 
 
 Analysis. — 1 cent is 1 fourth part of 4 cents ; 
 therefore 1 cent will buy 1 fourth as much as 4 cents. 
 But 4 cents will buy a whole orange ; consequently i 
 1 cent will buy 1 fourth |>art of an orange. 
 
 2. At 6 shillings a pound, what part of a pound of | 
 tea can be bought for 1 shilling ? Foe 2 shillings ? 
 For 3 shillings ? For 6 shillings ? 
 
 3. At 8 cents a pound, what part of a pound of 
 saleratus can you buy for 1 cent I For 2 cent** ? For ! 
 3 cents ? For 5 cents ? For 7 cents ? For 6 cents ? 
 For 8 cents ? 
 
 4. Seven days make a week : what part of a week 
 is 1 day ? What part of a week is 2 days ? 3 days ? 
 6 days? 5 days? 
 
 5. At 8 cents a yard, what part of a yard of calico 
 can you buy for 1 ceirt ? For 5 cents? For 6 cents ? 
 For 7 cents ? 
 
 6. At 6 cents a ya? d, how much calico can you buy 
 for 7 cents ? 
 
 Analysis. — Since 6 cents will buy 1 yard, 1 cent 
 will buy 1 sixth of a yard; and 7 cents will buy 7 
 times as much : now 7 times 1 sixth Is 7 sixths, equal 
 to 1 whole one and 1 sixth. Therefore 7 cents will 
 buy 1 and 1 sixth yard of calico, at 6 :ents a yard. 
 
92 FRACTIONS. 
 
 Y. At 5 cents a yard, what part of a yard of silk 
 braid can you buy fur 1 cent ? How much can you 
 buy ^Jr d cejjts ? For 6 cents ? For 10 cents ? 
 
 8. At 10 dollars an acre, what part of an acre of 
 land can vou buy fur 1 dollar ? For 3 dollars ? Foi 
 12 dollars? For 1 5 dollars ? For 20 dollars ? , 
 
 9. Vv nat part of a pound of buiter, at 12 cents a 
 pound, can be bought for 1 cent ? For 5 cents I F^or , 
 15 cents f I 
 
 10. At 15 cents a pound, what part of a pound ot [ 
 figs can you buy for 1 cent ? For 16 cents? 
 
 1 1. Twenty shilling make a pound : what part of a 
 pound is 1 shilling? 2 shillings? 15 shillings ? 20 
 shiiUngs? 22 shillings? 30 shillings ? j 
 
 LESSON VIII. I 
 
 1. What will 2 oranges cost, at 3 and 1 half cents i 
 apiece ? | 
 
 Analysis. — If 1 orange costs 3 and 1 half cents, 2 
 oranges will cost twico as much. Now 2 times 3 
 cents are 6 cents, and 2 times 1 half are 2 halves, 
 equal to 1 cent, which added to 6 cents, makes 7 cents. 
 Therefore 2 oranges, at 3 and I half cents apiece, will : 
 cost 7 cents. 
 
 2. What will 5 yards of tape cost, at 2 and 1 third 
 cents a yard ? j 
 
 Analysis. — Since 1 yard of tape costs 2 and 1 third | 
 cents, 5 yards will cost 5 times as much : now 6 times 
 2 ctm^s a-e 1 cents ; and 5 times 1 third are 5 thirds, 
 equal to 1 cent and 2 thirds, which addec to 10 ■ 
 cents, make 1 1 and 2 thirds cents. TLorefore 5 
 yards of tape, at 2 and 1 third cents a yard, will cost | 
 1 1 and two thirds cents. i 
 
FRACTIONS. 93 
 
 4. What cost 6 yards of cloth, at 2 and 1 half 
 dollars per yard ? How much is 6 times 2 and 1 
 half? 
 
 5. At 3 shillings a yard, what will 4 and 2 thirds 
 yards of ribbon come to 1 
 
 6. Sarah bought 8 and 3 fourths yards of cash- 
 mere, at 4 shillings a yard : how much did it come to 1 
 
 7. A farmer bought 10 sheep, at 2 and 1 third 
 dollars a head : how much did they come to ? 
 
 8. In 1 rod there are 5 and 1 half yards : how 
 many yards are there in 8 rods ? 
 
 9. How much is 5 times 4 and 3 fourths ? 
 
 10. How much is 7 times 6 and 4 sevenths ? 
 
 1 1 . How much is 6 times 4 and 3 ninths ? 
 
 1 2. How much is 8 times 5 and 5 sixths ? 
 
 LESSON IX. 
 
 1. If 1 Narrel of flour costs 9 dollars, how much 
 will 2 thirds of a barrel cost ? 
 
 Suggestion. — Fii-st find the cost of 1 third, then of 2 
 thirds. (See Observation, p. 88.) 
 
 If one barrel costs 9 dollars,! third of a barren! 
 will cost 1 third of 9 dollars. Now 1 third of 9 
 dollars is 3 dollars, and 2 thirds will be twice 
 as much ; and 2 times 3 dollars are 6 dollars. 
 
 Ans. 6 dollars. 
 
 2. If 1 yard of cloth costs 6 dollars, how much 
 will 2 thirds of a vard cost ? 
 
 I 3. How much i's 2 thirds of ? Of 9 ? Of 12 ? ! 
 i 4. If a pie costs 12 cents, what will 3 fourths of ' 
 i a pie cost ? Hcv much is 3 fourths of 12? 
 
 5. How n uch will 2 fifths of a ton of coal coet, i 
 
 at 10 dollars a ton '? How much will 4 fifths ot a 
 
 ton cost 1 
 
94 FRACTIONS. 
 
 6. How much will 3 sevenths of an acre of lar d 
 cost, at 21 dollars per acre ? 
 
 7. If a ton of hay costs 16 dollars, what will 
 5 eighths of a ton cost 1 
 
 8. If a drum of figs costs 18 shillings, how much 
 will 2 ninths of a drum cost ? 4 ninths ? 
 
 9. At 20 shillings a barrel, how much will 
 4 fifths of a barrel of cider cost ? 
 
 10. How much is 3 fourths of 4 ? Of 8? Of 16 ? 
 
 11. How much is 5 sevenths of 14? Of 21 ? 
 
 LESSON X. 
 
 1 . Q. When a number or thing is divided into equal 
 parts f as halves, thirds, fourths, &c., what are those 
 |)artj4 called ? 
 
 Ajis. They are called Fractions. 
 
 2. Q. How are fractions commonly written? 
 Ans. By two numbers, one above the other, with 
 
 a line between them. For example ; 
 
 One half is written 
 
 thus 
 
 
 One third 
 
 M 
 
 (( 
 
 
 One fourth 
 
 (( 
 
 n 
 
 
 One fifth 
 
 u 
 
 n 
 
 
 Three fifths 
 
 u 
 
 n 
 
 
 One sixth 
 
 ii 
 
 « 
 
 
 Five sixths 
 
 « 
 
 (( 
 
 1, <fec. 
 
 3. Q. When we express one half by fi^gures, t'lus 
 ^, what does the figure 2, whicii is placed below the 
 line, show ? 
 
 Ans. The 2 shows that the number or thing is 
 divided into tvo equal parts; 
 
 4. Q. Wha does the 1 placed above the line, show ? 
 
FRACTIOPJS. 95 
 
 Alls. It shows that one of those parts is denoted 
 by the fraction. 
 
 5. Q. In the expression f , what dcs3 the 5, which 
 is placed below the line, show ? 
 
 Ans, It shows that the number or thing is divided 
 iintojive equal parts. 
 
 6. Q. What does the 3 above the line show ? 
 Ans. It shows that three of those parts are denoted 
 
 by the fraction. 
 
 7. Q. What is the number below the line called? 
 Ans. It is called the denomlnator. 
 
 8. Q. What does it show ? 
 
 Ans. It shows into hcia many equal parts the 
 number or thing /* divided. 
 
 9. Q. What is the number abc'>e the line called ? 
 Ans. It is called the Numerator. 
 
 10. Q. What does it show ? 
 
 Ans. It shows how many parts are expressed by 
 the fraction. 
 
 N. B. The number below the line is called the denomiria- 
 tor^ because it gives the name, as halves, thirds, fifths, &c., 
 to the fraction. The number above the line is cilled the 
 numeral or, because it numbers the parts, or shows how many I 
 parts are expressed by the fraction. 
 
 Note. — Particular jDains should here be taken to explain to the 
 young pupil, by sorae xisible illustration, what the denominator 
 and numerator signify. (See Note, p. 84.) 
 
 j 11. Q. When a whole number and a fraction are 
 written together, as "Z^, 4|, &;c., what is the express- 
 ion called ? 
 
 Ans. It is called a mixed number. 
 
 12. Q. What then is a mixed number? 
 
 13. llow are the expressions 2^, and 4f, read ? 
 Ans. 2i is read, Two and a half; and 4f, Four 
 
 and two thirds. 
 
 14 Read the following : 3^; 4f ; Sf- ; 7| ; lOf 
 
96 FRACTIONS. 
 
 MISCELLANEOUS EXAMPLES. 
 
 1. Henry had f of a dollar, and his father gave 
 him -J-, and his mother f of a dollar more : how 
 much money had he then ? 
 
 Solution. — 3 fourths and 1 fourth are 4 fourths, 
 and 3 fourths make 7 founhs. Ans. f of a dollar. 
 
 Nue. — When the numerator is e^uoi to, or greater than the de- 
 1 nominator, the fraction is called an improper fraction. Thus f 
 is an improper fraction, and is equal to if* So ^ is an improper 
 fraction, and is equal to 1. 
 
 2. If you have -^ of a dollar, and earn |^, and 
 find f of a dollar more, how much money will you 
 have? 
 
 3. A merchant sold a bushel of corn for -^ of a 
 dollar, a gallon of molasses for t^j of a dollar, and a 
 pound of tea for -i*^ of a dollar : how much did he 
 receive for all ? 
 
 4. How much are f , and f , and f , and \ ? 
 
 5. How much are ^, and -f) ^^^^ i» a^^d f ? 
 
 6. How much are t^, and i^, and t^, and \^^1 
 
 7. If you have -f of & dollar, and lose i of a dol- 
 lar, how much will you have left ? 
 
 Solution. — 5 eighths from 7 eighths leave 2 eighths. 
 Ans. I of a dollar. 
 
 8. If you have f of an orange, and give away f , 
 how much will you have left? 
 
 9. If you have a whole orange and give awav « 
 of it, how much will you have left ? 
 
 10. Take | from |. 11. Take f from ^ 
 12. Take A from H- 13- ^^^^ H ^^o^" H- 
 14. Take -H from H. 15. Take A from ij. 
 
FRACTIONS. 
 
 97 
 
 " Scents, how much wiU ^ of a 
 
 16. If a pear costs 2 cents, 
 
 near cost *? u i« n^ar costs 2 certs, 1 half 
 
 1'^ irWhafwi" V"a barrel of flour cos, at 6 
 I'lr matTviU i of a pound of starch cost, at 9 
 
 I '^t 'what'cL i of a pound of sugar, at 8 cents a 
 r,;^Wtcostiofapounaofhoney,at.^ 
 
 .''r^^^dtl:tTc^^-i:a'dof.oUsses,at30 
 
 dollars a hogshead 1 ^^i,^ ^ of a barrel 
 
 .2-2. At 6 doU«s ■! taf of 1 ^ost ? 
 
 r^r/r8u:i-;ounrwhatwiiuofapoundof 
 
 lard cost? i°f \P°""tard how much will ^ of a 
 
 24. At 12 cents a y"™' ™ ^ , ^ of a yard i 
 I yard of cambric cost 14 of a yard .^ ^.,^ , „f 
 
 |y 25. At Ifi cents a pound, h ^^f^pou„d? 
 
 pound of ra.sms 0°^^ ?*«>»? ^m ^ ^ water- 
 
 -26. At IB cents apiece, ho^^^^^^ ^ ^^ , „,«r. 
 melon cost i -^ oi ^ 
 
 «^«^«^ • . . ^ lUr, an acre, how much will i of an 
 j:;f^^*c:"rAan'acre?iofanacreM 
 
 ^ of an acre ? ^osts 30 shillings, how 
 
 '^'hwIlA^'awSiofaboxMotabox? 
 
 ^t. Mfo'f'atnt'^'Vara >>- --'"'"' ' '''"' 
 
98 FRACTIONS. 
 
 Solution. — If 1 yard costs f of a cent, 9 yards will 
 cost 9 times as much ; and 9 times f are 27 fourths, 
 which are equal .o 6 and 3 fourths. .Ans, 6f cents. 
 
 j 30. At f of a penny apiece, how much will 10 
 
 ' apples cost ? 
 
 31. At f of a dollar a basket, how much will 8 
 baskets of peaches cost ? 
 
 32. What will seven pounds of cinnamon cost, at 
 i"o of a dollar a pound ? 
 
 33. What cost 10 pounds of wool at | of a dollar 
 a pound ? 
 
 34. What cost 7 pounds of lard, at 8^ cents a 
 pound ? 
 
 Solution. — If 1 pound costs 8^ cents, 7 pounds 
 will cost 7 times as much : now 7 times 8 are 56, 
 and 7 times 1 half are 7 l»alves, which are equal to 
 3 and 1 half; and 3^ added to 56 make 59^. Ans, 
 59i cents. 
 
 35. What cost 6 yards of cloth, at 5^ dollars per 
 yard ? " 
 
 36. If I ride 7f miles an hour, how far can I 
 ride in 7 hours ? 
 
 37. A man bought 6 pounds of beef^ at 8f cents a 
 pound: how much did he pay for his beef? 
 
 38. How much is 5 times 6f ? 
 
 39. Hotv much is 6 times 4| ? 
 
 40. How much is 4 times 9f ? i 
 
 41. How much is 8 times 6| ? 
 
 42. How much is 7 times lOf? ^ 
 
 43. How much is 9 times B^iyl 
 
 44. If 1 yard of cloth costs 2 dollars, how riuch 
 will -J^ of a yard cost ? 
 
 Sohiiion. — Since 1 yard costs 2 dollars, 1 third 
 of a yard will cost 1 third of 2 dollars. Now 1 tliird 
 
99 
 
 ' " 1 .^ o thirds of 1 dollar ; for, 1 
 
 of 2 dollars is f ^f ^^^// ^ d of 2 must be 2 tin.es 
 third of 1 is 1 linrd, and 1 Uir ^^^^^_ 
 
 l^r How much Willi of a barrel of pork cos, at 
 
 8 dollars a barrel ? , 
 
 47. What IS 1 ha'f "'/;;, 
 Is. What is 1 tl-i^d of 14 ? 
 
 49. What is 1 half of H! 
 
 50. What is! third of Ih? 
 
 51. What is I fourth of il? 
 
 ^%T"Vharc:'t \ of a barrel of beer, at U dollars 
 ^trlvhat Willi of a ton of hay cost, which. 
 
 ^'irWh:f wilf/rJcord of wocKi c»st, at .3 
 
 shillings per cord ? .^^^ ;„ ^ day, how 
 
 57 If a man can wa^"" "", 
 far can he walk in i o( a day^ ^^ ^,,„^ fo, 
 
 59. What is 1 sixth of 40 _ 
 
 60. What is 1 seventh of .« • 
 
 61. What is 1 tenth otb.5? 
 
 62. Whatble..hthof74^ 
 
 63. What is 1 nu-th ol 85 . 
 
100 FRACTIONS. 
 
 64. If 1 ton of hay is worth 15 dollars, how much 
 is f or" a ton worth ? 
 
 Suggestion. — First find the worth of | of a ton, 
 then off. Ans. 9 dollars. 
 
 65. If one acre of h id costs 24 dollars, what will 
 "5 of an acre cost ? 
 
 66. What will f of h bushel of corn cost, at 36 
 cents a bushel ? 
 
 67. What will -| of a pound of tea cost, at 64 
 cents a pound ? 
 
 68. In one bushel there are 32 quarts : how nnany 
 quarts are there in -^ of a bushel ? 
 
 69. In one day there are 24 hours : how many 
 hours are there in f of a day ? 
 
 70. In one hour there are 60 minutes : how many 
 minutes are there in -^ of an hour ? 
 
 71. A hogshead contains 63 gallons : bow many 
 gallons are there in ^ of a hogshead ? 
 
 72. How much is -f of 27 T 
 
 73. Hfiy much is f of 45 ? 
 
 74. How much is f of 40 ? 
 
 75. How much is f of 54 ? 
 
 76. How much is f of 42 ? 
 
 77. How much is f of 72 '? 
 
 78. What will f of a yard of muslin cost, at 35 
 cents a yard ? 
 
 Analysis. — Since 1 yard costs 35 cents, 1 fourth of 
 a yard will cost 1 fourth of 35 cents ; and 1 fourth 
 of 35 is 8 and 3 fourths. Now, if 1 fourth of a 
 yard costs 8| cents, 3 fourths of a yard will cost 3 
 times 8J cents; and 3 times 8 are 24; 3 times 3 
 fourtus are 9 fourths, equal to 2 and 4 fourth, which 
 ad<led to 24 mabj 26 and 1 fourth. Therefore J of 
 a yard of mushn, at 35 cents a yard, will coet 20J 
 cents. 
 
\ 
 
 FRACTIONS. 101 
 
 79. What cost f of an acre of land, at 20 dt liars 
 per acre ? , 
 
 80. What cost f of a gallon of molasses, at 42 ! 
 cents per gallon ? | 
 
 81 . Wliat cost f of a bushel of pears, at 54 cents 
 a bushel ? 
 
 82. In 1 pound there are 20 shillings : Ijow many 
 shillings are there in -^ of a pound ? 
 
 88. In 1 furlong there are 40 rods : how many 
 rods are there in f of a furlong ? 
 
 84. If a man can travel 40 miles in a day, how 
 far can_he travel in 4- of a day ? 
 
 85. If a laborer can earn 75 cents in a day, bow 
 much can he earn in | of a day ? 
 
 86. If a bushel of wheat is worth 87 cents. Low 
 much is T^ Df a bushel worth ? 
 
 87. How much is f of 50 ? 
 
 88. How much is i of 42 ? 
 
 89. How much is | of 56 ? 
 
 90. How much is A of 95 1 
 
 91. How much is f of 76 ? 
 
 92. How much is i^j^ of 106 ? 
 
 93. A man sold a hat for 2 dollars, which was 
 1 half of what it cost him : how much did he pay for 
 the hat ? 
 
 Solution. — Since 1 half the cost was 2 dollars, 2 
 halves or the whole cost is 2 times as much ; and 2 
 times 2 are 4. Ans. 4 dollars. 
 
 94. 8 is 1 half of what number? 
 
 95. 4 is 1 half of what number? 
 
 96. 7 is 1 half of what number ? 
 
 97. 9 is 1 half of what number ? 
 
 98. Horace gave away 2 of his marbles, which 
 
102 FRACTIONS. 
 
 I 
 
 was 1 third of all he had : how many marbles had 
 he? 
 
 Solution.- -it 2 was 1 third, 3 thirds or the whole 
 number must je 3 times 2, which is 6. Ans. 6 
 raarbles. 
 
 99. 4 is 1 third of what number ? 
 I 100. 6 is 1 third of what number? 
 1 101. 10 is 1 third of what number ? 
 102. 3 is 1 fourth of what number? 
 I 103. 4 is 1 fifth of what number ? 
 
 104. 9 is 1 seventh of what number? 
 
 105. A man bought a cow and paid 6 dollars 
 down, wliich was ■}■ of the cost : what was the price 
 of the cow ? 
 
 106. A man bought a cask of molasses, and part 
 of it having leaked out, he found he had 7 gallons 
 letl, which was just -J- of all he bought : how many 
 gallons did he buy ? 
 
 107. If one man can do a piece of work in 30 
 days, how long will it take 6 men to do it ? 
 
 SuggestioH.—S men can do 6 times as much 
 work as 1 man ; therefore it will take 6 men only I 
 sixth part as long as it will take 1 man : that is, as 
 many days as 6 is contained times in 30 ; and 6 is 
 contained in 30, 5 times. Ans. 5 days. 
 
 108. If a ton of hay will last 1 horse 40 days, 
 how long will it last 10 horses ? 
 
 109. If a barrel of flour will last 1 peJ-son 63 
 days, how long will it last a family of 7 persons? 
 
 110. If 2 yards of calico cost W cents, how much 
 will .5 yards cost ? 
 
 So/ution. — First find the cost of 1 yard, then of 5 
 yards. If 2 yards cost 20 cents, 1 yard will cost 
 1 half of 20, which is 10 cents. Now if 1 yard costs 
 
FRACTIONS. 103 
 
 10 cents, 5 yards will cost 5 times 10 cents, which 
 are 50 cents, Ans. 50 cents. 
 
 111. If 4 cl*ickens are worth 8 shillings, how 
 much are 1 chickens worth ? 
 
 112. If 6 clmirs cost 12 dollars, how much will 4 
 chairs cost? 
 
 113. If 4 lambs are worth 20 shillings, how much 
 aie 10 lambs wcj^th? 
 
 114. If 5 pounds of butter cost 42 cents, what 
 will 3 pounds cost ? 
 
 115. If 6 pounds of cheese cost 32 cents, what 
 will 4 pounds cost ? 
 
 116. If 4 yards of calico cost 37 cents, what will 
 10 yards cost ? 
 
 117. If 4 boys can saw a cord of wood in 3 hours, 
 how long will it take 6 boys to saw a cord ? 
 
 118. If 6 teams can plough a field in 8 howrs, 
 how long will it take 8 teams to plough it ? 
 
 119. If 10 men can doti job of work in 6 days, 
 how long will it take ' 2 men to do it ? " 
 
 120. If J a yard of cloth costs 6 dollars, what 
 will 1 yards cost ? 
 
 121. If I of 3 barrel of flour costs 12 shillings, 
 what will 9 barrels cost ? 
 
 122. If f of a ton of hay costs 9 dollars, What 
 will 6 tons cost ? 
 
 123. If 9 yards of ribbon cost 72 cents, what wiil 
 i of a yard cost ? 
 
 12 4. If 12 bushels of salt cost 48 shillings, what 
 will f of a bushel cost ? 
 
 125. If i of a firkin of butter costs 4 dollars, what 
 will I of a firkin cost ? 
 
 126. If I of an acre of land costs 19 dollars, how 
 much will f of an acre cost ? I 
 
UBLtS OP MONEY, WEIGHTS, AND MK^SUKES. 
 
 FEDERAL MONEY. 
 
 I. Federal Money is the TJurrency of the United 
 States. The denominations are, Eagles, dollars, 
 dimes, cents and mills. 
 
 10 mills (m.) make 1 cent, marked ct. 
 
 10 cents " 1 dime, " d. 
 
 10 dimes " 1 dollar, " doU. or $. 
 
 10 dollars " 1 eagle. " E. 
 
 II. The national coins of the United States are 
 of three kinds, viz : gold, silver, and copper. 
 
 1. The gold coins are the eagle, half eagle, and 
 quarter eagle, tlie double eagle, and gold dollar, 
 
 2. The silver coins are the dollar, Jialf dollar, 
 quarter dollar^ the dime^ half dime, and three-cent-piece. 
 
 3. The copper coins are the cent and half cent. 
 Mills are not coined. 
 
 Note. — Federal money was established by Congress, August i 
 8th, 1786. Previous to this, English or Sterling money was j 
 the principal currency of the country. 
 
 STERLING MONEY. | 
 
 1£I. Sterling or English Money, is the national I 
 currency of Great Britrtin. I 
 
 4 farthings {qr. or far.) make 1 penny, marked d, 
 
 12 pence " 1 shilling, " s. 
 
 20 shillings " 1 pound, or savereign, j6. 
 
 *il shillings " 1 guinea. 
 
 ar«8T.— 1. What is Federal Money? Recite the Table. 2 Of how 
 many kinds are the coins of the United States ? What are the gold 
 coins ? What are the silver coins ? The copper coins 1 When and 
 by whom was Federal Money esiiiblished 1 3. What U Sterling Mon- 
 ey 1 R«peat the TaWe. n<m many farihintrs iii 2 j>eace 7 in :<[*«»<■* ^ 
 In 5 pence Jtc ? How many pence in 2 shillings T In 4 shii'iniiB, «.' . > 
 In S farthings how many ^.ence T In \1 far T lu 14 far 1 
 
 ^ft}t« — -Uuestiooa like the precedinf n.ay be a^sked, with adva&tage, 
 opon eAch of the subsequent 'I'ableB. 
 
WEIGHTS AND MEASURES. 10*6 
 
 Obs. The Pound Sterling is represented by a gold coia, 
 called a Sftver^'mn. Its IcfiaL value, according to ArA of Cmi- 
 :^resi, IS452, is S4.84 ; its in{rm$ic value, according to assays 
 at the U. S. mint, is S4.86i. The legal value of an Engiiah 
 shilling ia '24^ cents. 
 
 TROY WEIGHT. 
 
 IV. Troy Weight is used in weighing gold, sil- 
 ver, jewels, liquors, tfec, and is generally adopt(?d in 
 philosophical experiments. 
 
 24 grains {i(r.) make 1 pennyweight, markud jnt^t, 
 20 pennyweights " 1 ounce, " oz. 
 
 12 ounces " 1 pound, " lb. 
 
 Note. — Most children have very erroneous or indistinct ideas 
 of the weiirhts and measures in common use. It is, therefore, 
 strongly recommended for teachers to illustrate them practi- 
 cally, by referring to some visible object of equal magnitude, 
 or by exhibiting the ounce, the pound ; the linear inch, foot, 
 yard, and rod ; also a sqitare and cubic inch, foot, Slc. 
 
 AVOIRDUPOIS WEIGHT. 
 
 V. Avoirdupois Weight is used in weighing gro- 
 ceries and all coarse articles ; as sugar, tea, coffee, 
 butter, cheese, liour, hay, «fec., and all metals except 
 gold and silver. 
 
 If) drams (<^.) make 1 ounce, marked oz. 
 
 16 ounces " 1 pound, " lb. 
 
 I 25 pounds j "1 quarter, " qr. 
 
 I 4 quarters, or lot* lbs. " I hundred weight, cwl. 
 
 j *20 hnn.!.. or 'XK'O Hw " 1 t„n, marked T 
 
 \ 0b8. 1. CrToai weight is the weight of good.9 with the boxes, 
 , casks, or bags, which contain them, and allows 112 lbs. for a 
 ' hundred weight. 
 
 j Net weight is the weight of the goods only. 
 i 2 Formerly it was customary to allow 112 poands for a hun- 
 i dred weight ; but the laws of most of the states, as well as gene- 
 ' ral usage, now call 100 lbs. a hundred weight. 
 
 j Qn^T.— 0*«. By what i.-s tho Pound Sterling represented V \^ l>r.t *f 
 its lesral v»<lue in dofars and ccula 1 What is the valua of an Biuillsii 
 ehilliiiv?? 4. In what is Tn.y Weiuht used? Recite the Table. 5. In 
 what ia Avolrdur)oiB Weiglit ubo«1 1 Recite the Table. Ob$. What is 
 irross weip'bl 1 What is not weiglitY How many pi>u"ilR were formerly 
 
 ■ nl !•>*«.( l-r n htuilred weight '? 
 
106 WEIGHTS AND MEASURES. 
 
 APOTHECARIES' WEIGHT. 
 
 VI. Apotliecaries' Weight is used by apothec&« 
 ries and physicians in mixing medicines. 
 
 20 grains (gr.) make 1 scruple, meOrked sc. or 3 . 
 
 3 scruples «' I dram, " dr. or 3 . 
 
 8 drams " I ounce, " oz. or I . 
 
 12 ounces " 1 pound, V, ft. 
 
 Obs. 1. The pound and ounce in tliis weight are the same 
 
 as the TVv)t/ pound and ounce; the sicddnnsums of the O'unce 
 
 are different. 
 
 2. Drugs and medicines are bought and sold by avoir dup&is 
 weight. 
 
 LONG MEASURE. 
 
 VII. Long Meaaure is used in measuring length or 
 distances only, without regard to breadth or depth. 
 
 12 inches {in.) make 1 foot, marked ft. 
 
 3 feet " 1 yard, " yd. 
 
 5^ yards, or 16j feet " 1 rod. perch, or pole, r.orj>. 
 
 40 rods " 1 furlong, marked fur. 
 
 8 furlongs, or 320 rods " 1 mile. *' w. 
 
 3 miJes "^ 1 league, " I. 
 
 3H0 dcii. make a great circle, or the circumference of the earth 
 
 Obs. 1. 4 inches make 1 hand ; 9 inches, 1 span; 18 inche*, 
 1 cubit ; 6 feet, 1 fathom ; 4 rods or 100 links, 1 chain ; 25 links, 
 1 red ; 7tVo inches 1 link, 
 
 2. Long measure is frequently called litiear or lineal meas- 
 ure. Formerly the inch was divided into 3 barleycorns ; bul • 
 the* barleycorn! as a measure, has become obsfiletc. The inch j 
 is commonly divided either into eighths or ten'-hs; sometimes, 
 it is divideti into fioelfths, which are called linus. 
 
 attEBT.— T). [n what is Ajiothecaries' Weight used ? Tepeat the 
 Table. To what are the apothecaries' pound and ounce eqi al 1 How 
 are drugs and medicines bought and sold ? 7. In what is Long Meas- 
 ure used J Repeat the 'I'uble Draw a hne an inch lone up< « your 
 slate or b acit-hoard. I»ravv one two inches long. Draw another a foot 
 long. J -raw one a yard long. n«w long is your teacher's desk ? llnw ! 
 Ions is the schoolroom 1 How wide ? Obs. W hat is long laeasure fre- ! 
 qnently called 1 How la the inch comnioniy divided at the present day 7 | 
 
WEIGHTS AND MEASURES. 
 
 107 
 
 CLOTH MEASURE. 
 
 VIII. Cloth Measure is used in measuring cloth, 
 lace, and all kinds of goods which are bought or 
 sold by the yard. 
 
 '2\ inches (m.) make 1 nail, marked tm. 
 
 4 nails, or 9 in " 1 quarter of a yard, *' qr, 
 
 4 quarters " 1 yard, " yd. 
 
 3 quarters " 1 Flemish ell, " Fl. e. 
 
 5 quarters " 1 English ell, " E.e. 
 
 6 quarters " 1 French ell, " F. e. 
 Obs. Cloth measure i? a species of hnig measure. The yard 
 
 is the same in both. Cloths, laces, &c., are Iwught and sold 
 by the linear yard, without regard to their width. 
 
 SQUARE MEASURE. 
 
 IX. Square Measure is used in measuring sur- 
 faces, or things whose length and breadth are con- 
 sidered without regard to heighth or depth ; as land, 
 flooring, plastering, &c. 
 
 144 square in. (s//. in.) make 1 square foot, marked 5r/. ft. 
 
 9 square feet " 1 square yard, " sq.yd 
 
 20\ square yards, or ) ,, ( 1 sq. rod, perch, ^^ 
 
 '2Ti\ square feet \ (or pole, 
 
 40 square rods " 1 rood, " 
 
 4 rootls, or 160 sq. rods " 1 acre, " 
 " 1 square mile, *' 
 
 640 acres 
 
 Obs 1. A square is a figure which 
 has faur equal sides, and all its angles 
 ri'^ht-aniilcs, as seen in the adjoining 
 figure. Hence, 
 
 "2. A Square Inch is a square, whose 
 •ides are each a linear inch in length. 
 
 3. A Squav. Fon/ is a square, whose 
 hides are each a linear foot in length. 
 
 4. A Square V^ri-/ is a square, whose 
 sides arc each a linear yard or three 
 linear feet in lentrth, and contains 9 
 square feet, as reprcsenteil by the adjacent figure. 
 
 CirKST.— 8. In whfit is Cloth Measure used 1 Repeat the Table 
 9. 1.1 what is Square Measure u.^ed 1 Repeat the Table. 
 
108 WKIGHTS AND MEASURES 
 
 CUBIC MEASURE. 
 
 X. Cubic Measure is used in measuring solid 
 bodies, or things which have length, breadth, and 
 thickness, such as timber, stone, boxes of goods, the 
 capacity of rooms, <fec. 
 
 1728 cubic inches (ctt.iu.) make 1 cubic foot, marked cu. ft 
 '27 cubic feet " I cubic yard, " cu. yd 
 
 40 feet of round, or 
 50 ft. of hewn timber 
 
 1 ton « T. 
 
 42 cubic feet " I ton of shipping, " T. 
 
 16 cubic foe. "VZi:Z'Z^\" c.fi. 
 
 8 cord feet, or 
 128 cubic feet 
 
 I cord, " C. 
 
 Obs. 1. A pile of wood 8 feel lon^, 4 feet wide, and 4 feet 
 high, contains 1 cord. For 8 into 4 into 4=128. 
 2. A CvJba is a solid body bound- y y ^ 
 
 
 / 
 
 j e«l by s.ix equal squares. It is often y^ / y^ 
 
 j called a kexaedron Hence, 
 
 j A Cvbic Itich is a cube, each of 
 
 I whose sides is a sqiuirr. inch, as rep- 
 
 I resented by the adjoining figure. 
 
 ' A Cubic Foot is a cube, each of 
 
 i whose sides is a square foot. 
 
 j 3. The Cubic l^m is chiefly used 
 in estimating the cartage and trans- 1=- _1- 
 
 i portation of timber. By a tmi of round tiiiibei is meant, such 
 
 ! a quantity of timber in its rough or natural state, a*' when 
 
 I hewn, will make 40 cubic feet, and is tiup[»o8ed t.o l»e equal ib 
 
 I weight to 50 feet of hewn timber. 
 
 ! 4. The cvbic Um or had, is by no means an o/xurate or unu- 
 
 \ form standard of estimating weight; for, different kinds of 
 timbtr, are of very different degrees of density. But it is per- 
 haps sufficiently accurate for the pur]»ose8 to which it is ap- 
 
 j plied. 
 
 i Upest. — Ohs. What Is a square ? What Is a squsjr itch ? What 
 I is a square foox ? A square yard 1 Can you draw a square Inch ? Can 
 
 you draw « sqiiare foot ? A square yard *? 10 In what is C\>bic Mea*- 
 I lire used 1 Recite the Table. How long, wide, and hifh, ninst a pile 
 ! of wood be to makf a r.<»r( 1 What is a cube ? What is a cable inch 1 
 
 '^'hai )- u ci-itic f'tot "? Can you draw a <'u><c inch on your slate 1 
 
WEIGHTS AND MEASUKBS. 109 
 
 WINE MEASURE. 
 
 XI. Wine Measure is used in measuring wine, 
 I aloohol, molasses, oil, and all other liquids except 
 ; beer, ale, and milk. 
 
 4 gills (gi.) make 1 pint, marked pi. 
 
 2 pintg." '* 1 quart. «* qt 
 
 4 quarts " 1 gallon, " gal 
 
 Sl^gaPiOns *» 1 barrel, " bar.otbbl 
 
 4'2 gaFions " 1 tierce, " tier 
 
 63 gallons, or 2 bbis, " 1 hogshead, " hAd 
 
 2 hogsheads " 1 pipe or butt, " pi 
 
 2 pipes " 1 tun, " tun 
 
 Obs. The wine gallon contains 931 cubic inches. 
 
 BEER MEASURE. 
 
 XII. Beer Measure is used in measuring beer, 
 ale, and milk. 
 
 2 pints (pts.) make 1 quart, marked qt. 
 
 4 quarts ** 1 gallon, " gai. 
 
 36 gallons " 1 barrel, " bar. or bbl. 
 
 54 gals, or IJ bbls. " 1 hogshead, '« hhd. 
 
 Obs, The beer gallon contains 282 cubic inches. In many 
 
 places milk is measured by wine measure. 
 
 DRY MEASURE. 
 
 XIII. Dry Measure is used in measuring gn\\n 
 •ruit, salt. &c. 
 
 2 pints {pts.) make 1 quart, marked qt. 
 
 8 quarts " 1 peck, " pk. 
 
 4 pecks, or 32 qts. " 1 bushel, " ^t, 
 
 8 bushels '• I quarter, " qr. 
 
 32 bushels ** 1 chaldror, " ck. 
 
 Note. — In England, 36 bushels of coal nake a chaldron. 
 
 QrK«T. — II. In what Is Wine Measure used? Recite the Tahln. 
 Obif. Mow many cubic inches in a wine gallon? 12. In what Is Beer 
 Measiire used T Repeat the Tai>ie. Obs. How many cubic inches In a 
 beer gallon ? 13. In what is ii/y Measure used ? Recite the Table. 
 
"■"i-«VU- -jppw 
 
 M il 
 
 110 
 
 make 1 minute, 
 
 marked min 
 
 " 1 hour, 
 
 '« hr. 
 
 " 1 day, 
 
 " d. 
 
 " 1 week. 
 
 '• wk. 
 
 " 1 lunar month, 
 
 " mo. 
 
 " 1 civil year, 
 
 «• yr. 
 
 TIME. 
 
 XIV. Time is naturally divided into days end 
 years ; tiie former are caused by the revolution of the 
 Earth on ite axis, the latter by its revolution round the 
 
 Sun. 
 
 60 seconds {see.) 
 60 minutes 
 24 hours 
 
 7 days 
 
 1 weeks 
 
 12 calendar months, or / 
 365 days, 6 hrs., (nearly,) ) 
 
 13 lunar months, 1 day, and 6 hours (nearly), make 1 year. 
 
 Obs. 1. Time is measured by clocks, watches, chronometers, 
 dials, hour-glasses, Ac. 
 
 2. A civil year is a legal or common year , a period of time es- 
 tablished by government for civil or common purposes. 
 
 3. A solar year is the exact time in which the earth revolves 
 round the sun, and contains 365 days, 5 hrs. 48 min., and 48 sec. 
 
 4. A Bissextile, or Leap year, is a year which contaixis 366 
 days, and occurs once in, /our years. 
 
 It is caused by the excosa of 6 hours, which the civil year con- 
 tains above 365 days, and is so called because it leaps or runs 
 over one day more than a common year. 
 
 The odd day is added to February, because it is the shortest 
 month. Every leap year, therefore, February has 29 days. 
 
 XV. The names of the days of the week are the 
 following : Sunday, (first day,) Monday, (csecond,) 
 Tuesday, (third,) Wednesday, (fourth,) Thursday, 
 (fifth,) Friday, (sixth,) Saturday, (seventh.) 
 
 Obs. The names of the days of the week are derived from the 
 names of certain Saxon deities or objects of worship. Thus, 
 
 Sunday is named from the sun, because this day was dedicated ! 
 to its worship. I 
 
 Q,CK8T. — 14. Hi3w is Time naturally divided ? How are tJ^o \>nnor i 
 caused 1 How the latter 7 Repeat the Tabic. Obs. How is Tim< meas- 
 ured ? What is a civil year 1 A solar > ear ? A leap year ? 
 
Ill 
 
 Mond^iy « named from the moon, to whose worship it was 
 dedicated. 
 
 "^rvesdny is ikrived from 'Piiisco, the Saxon god of war. 
 
 Wediiestluy i» derived from Woden, a deity of northern 
 Euroj>e. 
 
 T/mrsday if from T/w/r, the Danish god of thunder, 
 storms, &c. 
 
 Friday is from Fri^a, the Saxon godiless of beauty. 
 
 Saturday is from the planet Saturn, to which it wae dedicated. 
 
 XVI. The 
 
 following are the names of the 
 
 12 cal- 
 
 endar months into which the 
 
 civil 
 
 year 
 
 is divided ; 
 
 with the number of days in each : 
 
 
 
 
 January, 
 
 (Jan.) 
 
 {Feb.^ 
 
 Mar.) 
 
 (Apr.) 
 
 Jirst month, 
 
 has 
 
 31 
 
 dajs. 
 
 F"ebruary, 
 
 ■second 
 
 t( 
 
 (1 
 
 28 
 
 (1 
 
 March, 
 
 third 
 
 (1 
 
 (( 
 
 31 
 
 (1 
 
 April, 
 
 fourth 
 
 
 
 3e 
 
 (i 
 
 May, 
 
 (May) 
 
 M'^ 
 
 
 
 31 
 
 (( 
 
 June, 
 
 (June) 
 (July) 
 
 sixth 
 
 
 
 30 
 
 « 
 
 July, 
 
 seventh 
 
 
 
 31 
 
 <i 
 
 August, 
 
 (Aug.) 
 
 ei^Uh 
 
 
 
 31 
 
 « 
 
 September, 
 
 rScpt.) 
 
 ninth 
 
 
 
 3t 
 
 (( 
 
 October, 
 
 (Oct.) 
 
 tenth 
 
 
 
 3! 
 
 « 
 
 November, 
 
 (Nov.) 
 
 eleventh 
 
 
 
 3(1 
 
 « 
 
 December, 
 
 (Dec.) 
 
 twelfth 
 
 
 
 3i 
 
 t( 
 
 Obs. The number of days in each month may b« •^idy re- 
 membered from the following lines : 
 
 " Thirty days hath September, 
 April. June, and November; 
 February, twenty-eight alone, 
 All the rest have thirty-one; 
 Except in Leap Year, then is the time, 
 When February has twenty-nine." 
 
 Obs. Tlie names of the calendar months were borrowed from 
 the Kouiaus, and most of them liad a fanciful orijrin. Thus, 
 
 January, was nsimed after Janu^, a Roman deity, who was 
 supposed to preside over the year and the conimencemeiit of all 
 undertakings. 
 
 February, was derived from feoruo, a Latin word which siarni- 
 fies to purify by sacrifice^ and was so called because this month 
 was devoted to the purihcation of the people. 
 
March was named after Mara, the Roman god of war ; and 
 was originally the first month of the Roman year. 
 
 April, from the Latin aperio, to open, was so called from ths 
 opening of buds, blossoms, Ac, at this season. 
 
 May was named after the goddess Maia, the mother of Mer- 
 cury, to whom the ancients used to offer sacrifices on the_^rfi/ day 
 of this month. 
 
 1 June was named after the goddess Juno, the wife of Jupiter. 
 July was so called in honor of Julius Ccesar, who was born in 
 this month. 
 
 i August waa so called in honor of Augustus Caesar, a Roman 
 I Emperor, who entered upon his first consulate in this month. 
 
 SeptcTuber, from the Latin numeral sepfem, seven, was so 
 I called, because it wa* originally the seventh month of the Roman 
 year. It is the ninth month in our year. 
 
 I October, from the Latin octo, eight, was so called because it 
 I was the eighth month of the Roman year. 
 
 j November, i -om the Latin novem, nine, was so called because 
 ■ it was the ninth month of the Roman year. 
 I December, from the Latin decern, ten, was so called because it 
 was the tenth month of the Roman year. 
 
 XVII. Tue year is also divided into /our seasons, 
 of three months each, viz : Spring, Summer, Autumn 
 or Fall, and Winter. 
 
 Spring comprises March, April, and May ; 
 Summer, June, July, and Aus^ust ; 
 Autumn or Fall, September, October, and November; 
 Winter, December, January, and Februaiy. 
 
 CIRCULAR MEASURE. 
 
 XVIII. Circular Measure is applied to the divisions 
 of the circle, and is used in reckoning latitude and lon- 
 gitude, and the motion of the heavenly bodies. 
 
 60 seconds (") make 1 minute, marked '. 
 
 60 minutes " 1 degree, " °. 
 
 30 degrees " 1 sign, " ». 
 
 12 signs, or 360° " 1 circle, " c. 
 
 Que ST.— 17. Name the seasons. 18. To what is Circular Measure ap- 
 plied ? Repeat the Table. 
 
"^^^^^^HTS AND MEASURES. 
 
 o The circumference of 
 every circle is ^^'^'^f '. ^^ 
 
 3G0 equal parts, calleV^- 
 ; ^rce5, as in the subjoined ^ 
 
 ' figuf^- . I 1 
 
 3 Since a degree is ^ 6^ 
 
 part of the circumference of 
 I a circle, it is obvious that U8 
 
 length must depend on the 
 
 siie of the circle. 
 
 MISCELLANEOUS TABLE. 
 
 12 units 
 
 1-2 dozen, or 144 
 
 1-2 gross, or 1T2» 
 
 20 units 
 56 pounds 
 
 100 pounds 
 
 196 pounds 
 
 •200 pounds ^, ip„d 
 
 14 pounds 01 iron, or lead 
 
 21 i stone 
 Spigs 
 
 make I dozen, id4>z.) 
 1 gross. 
 1 great gro8». 
 I score. 
 
 I arkin of butter. 
 1 quintal of fi-^h. 
 Ibar.offishmMaae^ 
 Ibar. inN.Y. andCt. 
 
 I bar. of flour. 
 
 I bar. of pork. 
 
 1 gtone. 
 
 I fothcr. 
 
 
114 STATE CURRENCIKS. 
 
 PAPER AND BOOKS. 
 
 X\. The terms, folio, quarto, octavo, <fec., applied 
 to books, denote the number of leaves into which a 
 sheet of paper is folded. 
 
 24 sheets of paper 
 
 make 
 
 1 quire. 
 
 20 quires 
 
 (( 
 
 1 ream. 
 
 2 reams 
 
 (( 
 
 1 bundle 
 
 5 bundles 
 
 « 
 
 1 bale. 
 
 A sheet folded in two leaves, is called a folw. 
 A sheet fohled in four leaves, is caJIed a quarto^ or 4/o. 
 A sheet folded in eight leaves, is called an octavo^ or 8tJo. 
 A .:*ieet folded in twelve leaves, is called a dtuidecinw. 
 A sheet folded in sixteen leaves, is called a \^mo. 
 A sheet folded in eighteen leaves, is called an I8md. 
 A sheet folded in thirty-two leaves, is culled a 'i-2mn. 
 A sheet folded in thirty-six leaves, is called a 'ifjvw. 
 A sheet folded in forty-eight leaves, is called a 48wm>. 
 
 XXI. Previous to the adoption of Federal money 
 in 1786, accounts in the United States were kept in 
 pounds, shillings, pence, and farthings. 
 
 In New England currency, Virginia, ) 
 
 Kentucky, Tennessee, Indiana, II- > 6 shil. make SL 
 
 linois, Missouri, and Mississippi, ) 
 In New York currency, North Caro- j g ^^ ^ 
 
 Una, Ohio, and Michigan, j •««»«> « 
 
 In Pennsylvania currency, New Jer- ) - /. , . jm 
 
 scy, Delaware, and Maryland, \ ^*' ^' "^^^^ ^^• 
 
 In Georgia currency, and South Car- ^ j - uj __u »• 
 
 In Canada currency, and Nova Scotia, 5 shil. sake $1. 
 
 Obs. At the time Federal money was adopted, the colwiial 
 i CKrreTicy or bills of credit issued by the colonies, had more or 
 
 Q.UK8T. — 20. When a sheet of paper is folded into two leaves, what 
 is it called 1 When into four leaves, what 7 When into eight? Into 
 twelve 1 Into sixteen 1 Into eij?ht«'en 1 Into thirty six "? 21. Previoo* 
 to the adoption of Fedeml Money, in what wei< accounts ke^t in ih« 
 U. 8. ■» How many shillings malce a dollar in N. E. currency 1 In N Y. 
 currency 7 la Penn. currency 1 In Georgia car. 1 In Caniid& cur. 1 
 
ALIQUOT PAETS. 115 
 
 less depreciated in value: that is, a colonial pound was worth 
 less than a pound Sterling; a colonial shillinsr, than a shil- 
 ling Sterling, &c. This depreciation being greater in some 
 colonies than in others, gave rise to the difer(dnt values of the | 
 /State currenciea. 
 
 ALIQUOT PAETS OF $1 IN FEDEBAL MONEY. 
 
 60 cents = %\ 
 831- cents = $i 
 25 cents = $i 
 20 cents = $1- 
 16f cents = %l 
 
 12^ cents = $g- 
 
 10 cents = $,\f 
 
 8i cents = %^ 
 
 6i- cents = $i 
 
 5 cents = $7 
 
 2'U 
 
 « 
 
 PARTS OF $1 IN NEW YORK CURRKNCV. 
 
 4 shillings =$i 
 
 2 shil 8 pence —^\ 
 2 shillings ~^\ 
 
 1 shilling 4 pence = $1 
 1 shilling =$i 
 
 6 pence =^tV 
 
 Obs. 1. In New York currency, it will Se seen, (Art. 21,) that 
 A 8ix-i>ence, written M. = 6} cents. 
 
 A shilling, " l«. = l-2i » 
 
 One (shil.) and 6 pence " 1/G. = \hi " 
 
 Two ehillings, " 2s. = 25 " 
 
 PARTS OF $1 IN NKW ENGLAND CURRENCY. 
 
 1 shilling = 
 
 9 pence = 
 
 3 shillings =8^ 
 
 2 shillings =Si 
 
 1 shil. and 6fl. =$i 
 
 6 pence =$t^ 
 
 Oba. 2, In New En^^land currency, it will be seen, that 
 
 A four-y>ence-half-[)cnny, written 4id. = 6^ cents. 
 
 A flix-pence, " 6d. = 8^ «« 
 
 A nine-pence, " i*d. = 12^ " 
 
 A sKdhnj;, " Is. = ir)| " 
 
 One (ahil.) and six- pence " 1/6. = 25 '' 
 
 Two 8hiIUng«, " 2s. = 33^ " 
 
 QuBST.— What are the aliquot parts of $1 in Federal Money 1 In 
 New Yiirk currency? In New England currency ] What are the ali- 
 quot parts of a i>ound Sterling 1 Of a shilling "? 
 
116 ALIQUOT PARTS. | 
 
 ALIQUOT PARTS OF 
 
 STERLINa MONET. | 
 
 Parts ef £\. 
 
 Paris of Is. 
 
 10 shil. = £\ 
 
 6 pence —^ shil 
 
 6s. 8d. =^ £\ 
 
 4 pence =i shil. 
 
 5 shil. = £} 
 
 3 pence =i shil. i 
 
 4 shil. = £i 
 
 2 pence =f shil. | 
 
 ' 3s. 4d. = £| 
 
 1^ pence =\ shil. 1 
 
 ^ 2s. 6d. = JCi 
 
 1 penny =^4 shil. 
 
 i 2 shil. = £tV 
 
 1 far.=-J- penny. 
 
 Is. 8d. = £t^ 
 
 2 far.=i^ penny. 
 
 1 shil. = £^ 
 
 3 far.=f penny. 
 
 ALIQUOT PARI 
 
 '8 OF A TON. - 
 
 10 hund. Ibs.=i ton. 
 
 2 hund. 2 qrs. = i ton. | 
 
 6 hund. lbs.=-}- ton. 
 
 2 hund. lbs. =t^ ton. 
 
 4 hund. lbs.=i ton. 
 
 1 hund. lbs. =t^ ton. ' 
 
 ALIQUOT PARTS OF A 
 
 POUND AVOIRDUPOIS. j 
 
 8 ounces=^ pound. 
 
 2 ounces =i pound. 
 
 4 ounces =-}^ pound. 
 
 1 ounce =tV pound. j 
 
 ALIQUOT PAl 
 
 ITS OF TIME. 
 
 Parts of 1 year. 
 
 Part^ of 1 month. 
 
 6 months = -J- year. 
 
 15 days=i month. 
 
 4 months =■} year. 
 
 10 days=-i^ month. 
 
 ' 3 months =1 year. 
 
 6 days=j month. { 
 
 2 months = -J- year. 
 
 6 days=3J month ' 
 
 1 \ month = 1 year. 
 
 3 days=T^ month, i 
 
 ij month =1 year. 
 
 2 days = T*j month. 
 
 1 month =T^ year. 
 
 1 day =f^ mcnth. j 
 
EXERCISES IN COMPOUND NUMBERS. 
 
 1. In 4 cents, how many mills? In 6 cents? 
 
 2. In 5 dimes, how many cents ? In 7 dimes ? 
 
 3. In $2, how many cents ? In $3 ? In 84 ? 
 
 4. How many dollars in 5 eagles ? In 6 E. ? 
 
 5. How many eagles m *40 ? In $55 ? In |!67 ? 
 
 6. How many dollars in 60 dimes ? In 76 dimes ? 
 
 7. How many mills in ^ cent ? In ^ cent ? In 
 i ct. ? In I ct. ? 
 
 8. How many cents in ^ dollar ? In ^ doll. ? 
 In I doll. ? 
 
 9. In 4 pence, how many farthings? In 6 d. ? 
 
 10. In 2 shillings, how many pence? In 4 s. ? 
 
 11. In 2 pounds, how many shillings? In £4? 
 
 12. In 5 farthings, how many pence? In 6 far. ? 
 
 13. How many shillings in 18 ponce ? In 24 d. ? 
 
 14. How many pounds in 40 shiUings ? In 60 s. ? 
 
 15. How many farthings in i penny ? In -J^ d. ? 
 In i d. ? In H d. ? In 2i d. ? In 4^ d. ? 
 
 16. How many pence in t^ shilling? In -J s. ? 
 In is.? In is.? In Is.? In H s. ? In 2i s. ? 
 
 17. How many shillings in -^ pound? In £| ? 
 In £i ? In X| ? In £f ? In £H ? In £2j ? 
 
 I 18. How many ounces in 2 lbs., Troy weight? 
 
 I Ixx 3 lbs. ? In 4 lbs. ? 
 
 I 19. How many ounces in ^ lb., Troy ? In -J lb. ? 
 
 1 In i lb. ? In i lb. ? In li lb. ? In 2i lbs. ? 
 
 I 20. How many pwts. in -J- oz., Troy ? In -J- oz. ? 
 
 j Inioz.? In I oz.? 
 
 ! 21. How many grains in j[ pwt. ? In ^ pwt. ? 
 
 I In -f pwt. ? In I pwt. ? 
 
 ! 22. In 2 tons, how many hundred weight ? In 3 
 
 1 tons ? In 4 tons ? 
 
118 COMPOUND 
 
 23. In ^ lb. Avoir., how many ounces ?» In ^ lb. ? 
 In I lb. ? In H lb. ? In 2i lbs. ? 
 
 24. In ^ oz., Avoir., how many drams ? In } oz ? 
 
 25. In i ton, Avoir., how many cwt. ? In -J- ton ? 
 In ^ ton ? 
 
 26. In 2 feet, how many inches ? In 4 ft. ? 
 
 27. In 2 yards, how many feet ? In 3 yds. ? In 
 4 yds. ? In 5 yds. ? In 10 yds. ? 
 
 28. In 2 rods, how many yards ? In 3 rods ? In 
 4 rods ? In 5 rods ? 
 
 29. In 2 furlongs, how many rods ? In 3 furlongs ? 
 
 30. In 2 miles, how many furlongs ? In 3 miles ? 
 In 4 miles ? 
 
 31. In 3 leagues, how many miles ? In 5 1.? 
 
 32. How many feet in 18 inches? In 24 in.? 
 
 33. How many yards m 6 ft.? In 10 ft.? 
 In 11 ft.? 
 
 34. How many leagues in 6 miles? In 13 m. ? 
 
 35. How many inches in ^ foot? In -^ foot? 
 In li ft. ? In 2i ft. ? In 3i ft. ? In 4i ft. ? 
 In 5^ ft. ? 
 
 36. How many feet in i yard ? In 1 yd. ? In f 
 yd. ? In 11 yd. ? In 2i yds.? In 5f yds. ? 
 
 I 37. How many furlongs in i mile? In ^ m. ? 
 In { m. ? In f m.? In 1^ m. ? In 2\ m. ? 
 I lu 3f m.? 
 
 I 38. How many miles in ^ league? In i league? 
 I In I league? In 2\ leagues ? In 4i- leagues ? 
 I 39. In 2 nails, how many inches? In 3 na.? 
 ! In 4 na. ? 
 
 I 40. In 2 yds., how many quarters ? In 3 yds.? 
 I In 4 yds. ? 
 
 I 41. In 8 qrs., how many yards? In 10 qrs. ? 
 I In 12 qrs.? 
 
NUMBERS. 110 
 
 4*2. In 8 nails, how many quarters? In 12 na. ? 
 Iul7na.? 
 
 43 riow many quarters in ^ yard ? In 2j^ yds. ? 
 
 44. How many inches m i yd. ? In li yd. ? In 
 If yd.? 
 
 45. How many square feet in ^ square yard ? In 
 2i square yds. ? In 3^ square yards ? 
 
 46. In 2 pints, how many gills ? In 3 pts. ? In 
 6 pts. ? 
 
 47. In 3 quarts, how many pints ? In 4 qts. ? 
 
 48. In 2 gallons, how many quarts ? In 5 gals. ? 
 In 6 gals.? In 7 gals.? 
 
 49. in 2 barrels,* how many gallons ? 
 
 50. In 2 hogsheads,* how many barrels ? 
 
 51. In 3 pipes, how many hogsheads? In 4 
 pipes ? In 5 pipes ? 
 
 52. How many pints in 8 gills ? In 13 gills ? In 
 16 gills? In 20 gills? 
 
 53. How many quarts in 4 pts. ? In 6 pts. ? In 
 11 pts.? 
 
 54. How many gallons in 8 qts. ? In 12 qts. ? In 
 14 qts. ? 
 
 55. How many gills in ^ pint ? In ^ pint ? In 
 \ pint ? In 2i pints ? In 31 pints.? 
 
 ,'^6. How many pints in \ quart ? In 2^^ quarts ? 
 In 3^ quarts ? 
 
 57. How many quarts in ^ gallon ? In ■}■ gal. ? 
 Infgal. ? In2igals. ? In 31 gals.? In 5i gals.? 
 
 58. How many gallons in ^ hlid. ? In -^ hhd. ? 
 
 59. In 2 pecks, how many quarts ? In 4 pks. ? 
 In 6 pecks ? 
 
 60. In 2 bushels, how many pecks ? In 4 bu. ? 
 
 * Wine measure. 
 
120 COMPOUND NXJMBERS. 
 
 61. In 12 q,uarts, how many pecks? In 24 qts. ? 
 In 17 qts. ? In 28 qts. ? In 35 qts. ? 
 
 62. In 6 pecks, how many bushels ? In 8 pks. ? 
 In 12 pks.? 
 
 63. How many quarts in i peck? In ^ pk. ? 
 In i pk. ? In 2i pks. ? In 3i pks. ? In 5i pks. ? 
 
 64. How many quarts in ^ bushel ? In -^ bushel ? 
 In i bu. ? In i bu. ? In li bu. ? In 2i bu. ? 
 
 65. How many days in 2 weeks ? In 3 weeks ? 
 In 6 weeks ? 
 
 66. How many hours in 2 days ? In 3 days ? 
 
 67. How many minutes in 2 hom's ? In 3 hrs. ? 
 
 68. How many seconds in 2 min. ? In 3 min. ? 
 
 69. How many seconds in ^ minute ? In ^ min. ? 
 In -fV inin. ? In -f- min. ? In 1^ min. ? 
 
 70. How many minutes in ^ horn* ? In ^ hour ? 
 In I hour ? In ^ hour ? In 1 i hour ? In 2i hours ? 
 
 71. How many hours in -^ day? In ^ day ? In 
 I day? In i day? In f day ? In f day ? In i 
 day ? In t^ day ? In 1^ day ? In 2i days ? 
 
 72. How many calendar months in -^ year ? In ^ 
 year ? In f year ? In -J- year ? In f year ? In i 
 year? In ^ year? In 1^ year? In 3i years? 
 
 73. How many degrees in 2 signs ? In 3 signs ? 
 
 74. How many degrees in ^ sign? In ^ sign? 
 [n ^ sign ? In li sign ? 
 
 75. How many units in 2 dozen ? In 3 doz. ? 
 In 4 doz. ? In 5 doz. ? In 6 doz. ? 
 
 76. How many units in ^ dozea ? In ^ doz. ? In -J 
 doa. ? In 1 i doz. ? In 2i doz. ? 
 
 THE END. 
 
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