A ei i apt ae é rahe ad % * 5s mA — Je 3 C2 lS ee . + 2; PIERS okt THE UNIVERSITY OF ILLINOIS LIBRARY % The Frank Hall collection of arithmetics, presented by Professor H. L. Rietz of the University of Iowa. , LACT 5/3. DZEpr IMARY ae enid Pi Yi Yi Y O~ Q LL.D. b, By CHARLES DAVIE oak COURSE OF MATHEMATICS. FULL AUTHOR OF A SUGGESTIONS. | }. Sensible objects should be used in all the elementary opera- tions of numbers. | 2, The unié of a number, and the number of units taken, should be dwelt upon in every example. 3. The idea of number is purely abstract, and can only be appre- hended by the contemplation of sensible objects—individually, and collectively. 4, The eight units of science, arranged into classes in the Tables, | | should be carefully distinguished from each other. | §. The idea of the abstract unit, 1, comes from contemplating the | | denominate unit, 1 apple. The unit of currency, 1 dollar, is easily apprehended; and the foot-rule, or the yard-stick, will fix per- inanently in the mind the unit of length. | | 6. The unit of surface, is the square constructed on the unit of | length; and « paper cube, constructed on this square, as a base, exhibits to the mind one of the units of volume. The gallon measure, and the half-bushel, are two other units of volume in common use. | | i ! | 7. The pound, is the most familiar unit of weight, and should be exhibited to every class of beginners. The day, is the familiar unit of time, and the degree, of angular measure. af PREFACE. Tue present work is designed for beginners, being adapted to the capacities and wants “of very young children. M It commences with counting, by means of sensible | objects, and these are employed through the entire work i to illustrate and render familiar the elementary com- binations of numbers, The work is constructed on the plan of object teach- | ing. The object is first presented to the mind, and then its number, in connection with other objects of the same kind. From these, the child readily passes to the idea of number in the abstract, derived as it is, directly, from. sensible objects. Each Lesson is Bt to illustrate a sing fe rinciple 31m7T oOmD ti Ae is A} the 1 ssons 1g are hr a com OI ; ew r s & +} Ala = ’ lar pare to be Py sae prrere sto t we analysis; afte which, the Table eca. pitula been illustra Leal cc <% J a » - s. PREFACE. The subject of Division has been introduced by naming the quotients of numbers divisible by 2, 3, 4, &c.; and these quotients are not treated as fractions—the term. fraction being applied, in abstract nuumbers, only to the equal parts of 1, and in denominate numbers, to the equal parts of an entire thing, numerically denoted by 1. This principle of classification and naming, has not, to my knowledge, been used before, and as it forms the basis | of a system, is deemed important. nn RE ASD | The plan of this work requires the beginner to search out his way, by short and easy steps, to what lies before him. He is to use his faculties to discover principles, and not rely on his memory for rules to guide him. Hience, the Table is placed at the end of cach Lesson, -as the result of what has preceded; and not at the be- ginning, as heretofore, in all similar works. The combination of the pictorial representation, the practical example, and the abstract table, in the order in which they are placed, and on pages facing each other, has not, I believe, been made before; and I hope it may prove a valuable aid in elementary instruction. _» The reading of figures is one of the most useful exer- , ee in object- De a The Lessons on that subject. p-Bnrey toe. te, notie and meet the appre oval ; Ne 5 Rs 5 het . — x, vs 1862, . hs 7 See ‘y a Pe \ PRIMARY ARITHMETIC. LESSON I. ‘ Cranes, can you count? “Vl try, Sister.” | Which is your right hand? Which your left? Tow many hands Hees you? How many thumbs have you on your right hand? How many on our left? _ How man, on pele o tetie *, ae , 2 3 ; ave YC re i eR F eS othe mar Ly "4 a y ony a ang y thumb with't fingers, ho : ent han ae many on | both? _~ How many ears "ai the dog, Carlo? Ho | many eyes has How many legs’ | 6 COUNTING. LESSON II. | \ y Need Dare. en eg Jane has a few pet rabbits. She is very fond of them, and plays with them~*often. They are pretty little animals. See how tame and gentle _ 24 they are. How many rabbits are there? || Jane feeds them with apples. See how they eat. Here are pictures of some apples. | ” How many apples are th af? mm \ ah val ‘ ae) this row? ~~. * a COUNTING. 7 LESSON ITt. | \s 1. What isa unit? Ans. A single thin = ‘Bs 2. What is a number? Ans: AS unit, or a col- lection of units. 3. How may numbers be oxprtsondl Bis, By words, by figures, and by letters. 4, What is counting? Ans. Counting is ex- pressing consecutive numbers by words. %| 5. How many figures are there? Ans. Ten. Name them. RS ~¥ : : \ Naught, One, Two, Three, Four, Five, Six, Seven, Eight, Nine. Pees) 4 8 ABR eG Count the hats in each of these rows. rie renga Nine ) Mh A OL to den. “| Fifteen 8 COUNTING. LESSON IV. The ten figures of Arithmetic were first used in Arabia. The Arabs are a wandering people, live in tents have fine horses and camels. This pic- ture will remind you of the country from which we got our ten figures. __ ‘Ten \ _ Eleven elve Nineteen ! Sixteen = * ; Twenty-five Seventeen | Twenty-six Eighteen a8: . 7 % COUNTING. LESSON V. Si AV H Sey Sy . a HENS 4 ‘ Sy AN aN SS = S NS SN PRN SD = WS Wy =. LS VE S A? <> OO H Or bo aT bo Or CS H= CO Sd LO AT CO Gs LO ADDITION. LESSON REViEW and 4 are how many ?| 5 and 2 and 3 and 2 and 5 and-3 and 6 and 7 and 4 and 2 and 3 and 5 and 7 and 4 and 9 and 5 and 8 and 5 and 4 and 5 and 6 and 3 and 2 and 8 and 7 and 4 and 7 mv I: LESSON. and 6 are how many ¢ 3 and 8 and 4 ef and 9 re and 3 Me and 8 + and 4 re and 6 vf and 7 4 H= ~T bO St CH S Or C LO = 09 So aT OD SO OC LC Or > Oo H ATCO DO OO and 7 are how many ? and 6 < : and 3 “ and 5 rs and 8 bie and 6 y and 4 : and 7% * and 2 a and 6 are how many? and 7 . | and.d ee and 7 he ee and 8 ¥ and 9 Ke and 8 © * and 3 xs ander 5, 8 ADDITION. LESSON XVII. READING FIGURES. Twenty-one Twenty-nine . Thirty-seven . + Forty | Sixty-seven Seventy va Ninety-five . «-. One hundred . er. One hundred andten. . . . One-hundred and seventy-five . One hundred and ninety-five Two hundred and sixty-seven . Three hundred and twenty-seven . Three hundred and ninety-five . Four hundred and fifty ‘Your hundred and sixty-seven . Five hundred Six hundred and seventy-tu oe Seven hundred . . . “s ; Seven hundred and fiftee “2 os. LESSON XVIII. _ 82 ADDITION. | | PROMISCUOUS EXAMPLES. 1. John bought a top for 6 cents, and some eandy for 5 cents; how many cents did he pay for both ? Awatysis.—He pad yor both as many cents as there are in the sum of 6 cents and 5 cents: the ei. of 6 and 5 is 11: Therefore, he paid for both, 11 cents, | 2. In a school-room there are 5 boys on one bench, and 9 boys on another; how many boys | are there on both benches? _ 3. A farmer sold a pig for 10 dollars, and a | ¢ calf for 9 dollars; how many dollars did he get | for both? | 4, James paid 5 cents for an inkstand, and 8 _cents for pens; how many cents did he pay for | both? | 5. A tailor sold a coat for 7 dollars, and a pair |. inte pantaloons for 3 dollars; how many dollars | | did he get for both? ee 6. A man gave ‘ dollars for 2 harness, and 8 dollars for a sag@le; how many dollars did he pay for both? ta 7. A lady b | nt a shawl for’ 10. de 85 | pay for both? ~~ t NE Sina pea A yee ADDITION. 33 8. There are 3 red roses on one bush, 8 yellow roses on another, and 2 white roses on another; how many roses are there in all? 9. John gave 6 apples to Mary, 5 to George, and kept 3 himself; how many apples had he at first ? g 10. low many boys are 4 boys, 10 boys, and 7 }. boys? | , 11. James has 4 rabbits in one pen, 7 in an- other, and 8 in a third pen; how many rabbits has he in all? | , 12. Nancy had 8 yellow-birds in one cage, 5 in another, and 9 flying about the room; how many birds had she in all? _ 18. Lucy bought sealing-wax for § cents, paper for 7 cents, and a pencil for 2 cents; how many cents did she pay for all? _ 14. James bought three rose-bushes: one had 8 buds, one 5 buds, and the other 6 buds; how many buds were there on all of them ? 15. Charles had 8 cents in one pocket, 4 cents in another, and 5 cents in his hand; how many } cents had he in all? 16. James has 8 marbles, and wins 2; then John gives him 4: how many marbles will he then have? | | 17. Jane bought a pineushion for 6 cents, some icedles for 4 cents, and a pencil for 8 cents; how Hany cents did she pay for all ? CR yl ae 7 Se - St siatelapmlee 3 bc eames Mad hs cal a a ne UE ENN NEESER! LESSON I. Suprracrion is the operation of finding the | difference between two numbers. \ 1. One duck gin from 2 dueks, leaves how many ducks? One from 2 leaves how many ¢ 2. One duck taken from 3 3 drake, leaves how many ducks? One from 3 leaves how many @ . One duck taken from 4 Sioks. leaves how |} es ducks? One from 4 leaves how many ? 4, One acorn taken from 6 acorns, ‘eaves how | many acorns? One from 6 leaves how many? = | Set a tea acorns? ‘One ae 8 He o eat ss: : pee eee eae carter ee ene ee EE SUBTRACTION. 35 1. A boy had 4 plums, and gave 1 to his sister ; how many had he left? Ans. 3. Why? Because 3 and 1 more make 4: ey la af we take 1 from 4, 3 will be left. 2. Rollin found 3 ripe peaches under a tree, and ate 1 of them; how many had he left? 38. A hen haded chickens, and 1 died; how many had she left? 4. John has 6 acorns, and gives 1 to William ; how many has he left ? 5. A tailor had 7 yards of cloth in a piece, he cut off 1 yard; how many yards had he left? 6. Jane has 6 ducks, and 1 died; how many hwere left ? | 7. Julia had 10 cents, and gave 1 cent for a pencil; how many cents had she left? 1 from 10, leaves how many ! 8. There were in a class 6 boys and 1 girl; how ‘many more boys than girls in the class | _ 9. If I have § pears, and eat 1, how many are left? 1 from 1 leaves 0/1 from 6 leaves 5 1 from 2 leaves 1 | 1 from 7 leaves 6 1 from 3 leaves 2 | 1 from 8 leaves 7 1 from 4 leaves -3 |°1 from 9 leaves 8 1 from 5 leaves 4 | 1 from 10 leaves 9 Norz.—A small line is placed under what is taken away. Let the “obila. put its finger over what is taken away, and count what is left. i le ee RR RRC Bac ir te : SUBTRACTION. LESSON II. 1. Two turkeys taken from 2 turkeys, leaves how many turkeys? 2 from 2 leaves how many? 2. Two turkeys taken from 3 turkeys, leaves how many turkeys? 2 from 3 leaves how many? 3. Two turkeys taken from 4 turkeys, leaves how many turkeys? 2 from 4 leaves how many? 4, Two oranges taken from 6 oranges, leaves how many oranges? 2 from 6 leaves how many? 5. Two oranges taken from 7 oranges, leaves | how many oranges? 2 from 7 leaves how many ? | car eS rll nen nr i a pnt tn mo me . a ee SUBTRACTION. ST 1. Eliza picked 5 roses, and gave 2 to her eacher ; how many had she left? Ans. 3. anys Because 3 and 2 more make 5: therefore, 2 From 5 leaves 3. 9. Andrew had 6 chickens, and the cat caught 2 of them;-how TARDY had he left? 3. Aman gave 5 dollars for a hat, and 2 dollars for a vest; how much more did he give for the hat than fo the vest ¢ 4. A farmer had 7 horses, and sold 2 of them; a. many had he left? _ A teacher asked a scholar 9 questions, mt he tae 2 of them; how many did he answe 6. Jacob had 4 ge and lost 2; how1 Shae AWert rode 10 inn, 5 aa walked 2 miles; yw many m e miles did he ride than walk? A drover had 8 cows, and sold 2 of them; OW many had he left ? 9. Caroline had 11 books, and gave away 2; how many had she left ? 10. Mary had 7 birds, and 2 died; how many were left? , 2 from 2 leaves 0 | 2 from 7 leaves 5 2 from 3 leaves 1 | 2 from 8 leaves 6 2 from 4 leaves 2 | 2 from 9 leaves 7 & from 5 leaves 8 | 2 from 10 leaves 8 2 from 6 leaves 4 | 2 from 11 leaves , 38 SUBTRACTION. LESSON III. 1. Three hives taken from 4 hives, leaves how | many hives? 9. Three hives taken from 5 hives, leaves how | smany_hives? Bi sa had 7 seen and gave 3 to Ann; how | _had she ear i ) a. “Te a. pastiii ~are-9 sheep, 3 black, and i 7 rest are white 5 how many are white? os 5. Sold some butter for 10 dollars, and receiv 3 dollars; how much more is due? ale 6. Samuel borrowed 12 cents, and paid 3; how | many did he then owe 2 . 7. A merchant bought 11 barrels of flour; after | selling some, he Poand he had 3 barrels left; how many hiirels had he sold ¢ 3 from 8 leaves 0 | 8 from 8 leaves 5 3 from 4 leaves 1 | 3 from 9 leaves 6 3 from 5 leaves 2 | 3 from 10 leaves 7 8 from 6 leaves 3 | 3 from 11 leaves 8 3 from 7 leaves 4 | 3 from 12 leaves 9 1. Four cars taken from 5 cars, leaves how nany cars ! 2. Four cars from 6, leumes id many cars ? a chem; how many re sell? - * 7 “9: a A mat ‘ La 12, sola ave — DU nat 6. Rufus j is 18 years old, and Betsey is 4 years 7 ; what is the difference in their ages / _ 7. A lady having 5 dollars in her purse, gave 1 follax to a beggar; how much had she left ? 8. A boy ale fishes, and threw 4 of them back into the pond; how many had he left? : 4 from 4 leaves 0 | 4 from 9 leaves 5 4 from 5 leaves 1 | 4 from 10 leaves 6 4 from 6 leaves 2 | 4 from 11 leaves 7 4 from 7 leaves 3 | 4 from 12 leaves: 8 4 from 8 leaves 4 | 4 from 13 leaves 9 3. A farmer Raving 10 cows, sold all but 4 of | | 40 SUBTRACTION. | LESSON V. | oe | i Tan = 1: Five lemons from 7 lemons, leaves how | many lemons ? . | 2. Vive lemons from 9 lemons, leaves how | any lemons ? i _ 8. There are 6 boys and 5. girls in a class ; how | i -e boys than girls? Dt So | -| 4. Reuben ‘has 5 pi te John; how many has he left ? 5. Carlos fires into a flock of 14 pigeons kills 5 of them; how many are left? 6. If you eat your supper at 5 o'clock, and go} ‘to bed at 9, how many hours have you to read } and play ¢ 7. Nathan had 13 cents, and gave 5 cents for three pens; how many cents had he left ? | from 5 leaves 5 0 | 5 from 10 leaves 5 5’ from 6 leaves 1 | 5 from 11 leaves 6 5 from % leaves 2 | 5 from 12 leaves 7 | 5 from 8 leaves 3 | 5 from 13: leaves 8 | 5 from 9 leaves 4 | 5 from 14 leaves 9 ~ eer aa nin pion = A i Se SUBTRACTION. 41 ~ 1. Six oranges from. i oranges, leaves how lany oranges ¢ é iy or Taos — 3. A bo i 8 cents for a top, and so ‘cents ny many cents did he lose? = her; how many did he keep for himself? | al there are 16 boys and 6 girls; _ ow many more boys than girls are there? 6. There are 14 sheep in a fold, and a wolf kills of them; how many are left alive? | 7. A grocer bought 8 cheeses; after selling me, he found he had 6 left: how many were from 11 leaves from 6 leaves 7 from 12 leaves leaves 8 leaves from. 9 leaves 0 leaves from 14 leaves from 15 leaves m= WOOD Fr © . a aa 49, SUBTRACTION. — ee ee se re ee 2. Seven cherries from nine cherries, leaves row many cherries ? , 3 Theres»were 7 chairs in a room, and Mary | took Tout; au a, any doh ; | 4, There were 10 doveson the roof of the barn | and 7 flew away; how many were left ? | 5. Frank having 15 cents, spent 7 eents fd toys; how many cents had he left? 7: 6. A farmer having 16 pigs, sold them all but 6; how many did he sell? | 7. Julia, finding 14 roses in bloom, picked them » all but 7; how many did she pick ? | 8. Twelve cents, less 11 cents, are how many ¢ 7 from 7 leaves 0! 7 from 12 leaves 5% 7 from 8 leaves 1 | 7 from 13 leaves 6 7 from 9 leaves 2 |-7 from 14 leaves 7 7 from 10 leaves 3 | 7 from 15 leaves 8° 7 from 11 leaves 4 | 7 from 16 leaves 9. ah ; eee SUBTRACTION. 43 ————$—_—___— —— LESSON VIII. bbbbddde i. Eight bottles from 8 bottles, leaves how many bottles ¢ bhddbddada 2. Eight bottles from nine bottles, leaves how many bottles? 3. Mr. Jones bought 12 firkins of butter, and sold 8 of them; how many had he left? 4. James is 11 years old, and John 10 years ld; what is the difference of their ages? 5. A boy carried 9 quarts of berries to market, and sold 8 quarts; how many had he left? 6. From a class of 17 boys, 8 are taken and put into a higher class; how many are left? 7. There are 14 shade-trees in arow; 8 of them die: how many are left? | 8. Ten dollars less 8 dollars, are how many ? 8 from 8 leaves 0 | 8 from 18 leaves 5 8 from 9 leaves 1 | 8 from 14 leaves 6 8 from 10 leaves 2 | 8 from 15 leaves 7 8 from 11 leaves 3 | 8 from 16 leaves 8 & 4 | 8 from 17 leaves 9 from 12 leaves La | 44 SUBTRACTION. a na an i LESSON IX. (868886 8008680 1. Nine balls taken from twelve balls, leaves how many balls? @@ 8&6 06686 8860 2. Nine balls from 13 balls, leaves how many? 3. A lady having 15 dollars, gave 9 dollars for a bonnet; how many dollars had she left? - 4. Harriet has a writing-book of 12 pages; she | has written 9 pages: how many pages are left? 5. The school-term is 14 weeks long; 9 weeks have passed: how many weeks remain ? 6. A boy had 18 peaches, and sold 9 of them ; Sh many had he left? . Ina certain school, there are 17 boys and 9 | | paw how many more boys than girls? 8. In an orchard are 13 pear-trees, and 9 of them die; how many are still alive? 9. Ghavles bought a knife for 11 cents, and gold | it for 9 cents; how many cents did he lose? 9 from 9 leaves 0 | 9 from 14 leaves 5 9 from 10 leaves 1 | 9 from 15 leaves 6 9 from 11 leaves'2 | 9 from 16 leaves 7 | 9 from 12 leaves 3 | 9 from 17 leaves 8 | 9 from 13 leaves 4 | 9 from 18 leaves 9 i SUBTRACTION. 45 LESSON X. 0260000000606 80 1. Ten balls from 14 balls, leaves how many balls @86 80008608 8 6 4 0086 2. Ten balls from fifteen balls, leaves how many balls? 8. Horace put 14 dollars in the savings bank, and drew out 10 dollars; how many dollars were left in ? 4. A boy earned 18 cents, and received 10 cents; how much was still due him / 5. William shot 16 pigeons, and gave 10 away ; how many were left ? 6. Mary had 19 pins, and lost them all but 10; how many did she lose? 7. Harry borrowed 11 cents, and paid 10 cents; how many cents did he still owe? 8. Edgar had 12 marbles, and lost 10; how | many had he left? 10 from 10 leaves 0 | 10 from 15 leaves 5 10 from 11 leaves 1 | 10 from 16 leaves 6 10-from 12 leaves 2 | 10 from 17 leaves 7 10 from 13 leaves 3 | 10 from 18 leaves 8 10 from 14 leaves 4 | 10 from 19 leaves 9 a ne OS, 46 SUBTRACTION. LESSON XI. REVIEW LESSON. : 6 from 11, how many? | 8 from 10, how many? 5 from 10, “ 6 from 12, 3: | 4 from 8, ie 9 from 11, “ 9 from 12, x 8 from 13, % 7 from 12, ms 3 from 8, . 6 from 7, f 7 from 10, ‘ 9 from 10, Ms 5 from 11, 5 from 9, us 8 from 15, re 2 from 8, . 4 from 7, ti 2 from 10, how many? | 4 from 12, how many? 7 from 9, $6 § frome. a Setrom alo | 96 6 from 13, s 9 from 14, 4 from .< (85 5 from’ 8, 9 from 16, . 3 from 7, S 8 from 12, 1" 2 from 11, T from 13, i Gafrom’” 9, ca 5 from 12, s 7 from 16, Hf 3 from 10, aS! 8 from 14, how many? | 4 from 13, how many? 9 from 17, * 6 from 10, A 5 from 18, 8 from 11, “ 3 from 11, ‘g 9 from 18, % 7 from 14, * 6 from 15, if 2 from 9, 2 3 from 12, 4 from 10, v¢ 4 from 9, ae 8 from 17, rf 7 from 11, ni | 7 trom 15, $e 9. fron 15,” wai es SUBTRACTION. 47 LESSON XII. PROMISCUOUS EXAMPLES. 1; Ifenry had 18 cents; he gave 4 cents for an orange, and 6 cents for a pencil; how many cents had he left ? Awnatysis.—He had left the difference between’ (18 cents and the sum of & cents and 6 cents: the sum of 4 and 6 is 10: Therefore, he had left 18 cents less 10 cents, which vs 8 cents. Ce eS Se ee 2. A boy gave 20 cents for a sled, and 5 cents to have it painted; he then sold it for 15 cents: ‘how many cents did he lose? 3. A farmer bought a sleigh for 19 dollars, and paid a ten dollar bill, and a five dollar bill; how much did he still owe? 4. A drover bought 4 pigs of one man, and 8 of another; he sold five: how many had he left ? 5. Eli’s father gave him 15 cents on Christmas; he bought a book for 7 cents, and gave 6 cents to a beggar; how many cents had he left? 6. John earned 10 cents, and found 6 cents; he then bought a slate for 9 cents; how many cents had he left? | 7. A farmer had 9 sheep in one lot, and 9 in another; he sold 7 of them: how many were left / 8. There were 18 scholars in a school, of which 9 were boys; how many girls were there? . e 5 yy ay oe wr ( LE S'S ONST. MULTIPEICATION. Mouttiprication is the operation of taking one number as many times as there are units in | another. 1. One orange, taken once, is one orange. 5. Five oranges, taken once, is 5 oranges. once once once ~ ONCE once Orv He Oo bD me 18 is is is is once once Once once once SCO Ot SD MULTIPLICATION. 49 LESSON II. 1. James has 1 apple in each hand; how many has he in both hands? Two times one, are how many ? 2. Charles has two apples in each hand; how many has he in both hands? Two times two, are how many ? 3. John has 3 apples in one basket, and 3 in another; how many apples in both baskets? Two times three, are how many ¢ 4. Here are four pears in one row, and 4 in another; how many pears in both rows? Two times four, are how many 5. Here are five cherries in one row, and 5 in another; how many cherries in both rows? Two times five, are how many ¢ 3 Fn : { | | 50 MULTIPLICATION. 6. Here are six bottles in one row, and 6 in | another; how many bottles in both rows? bddbdd Two times six, are how many ? 7. Here are seven soldiers in one row, and seven how many soldiers in both rows? adda do in another ; “RAAB ARE Two times seven, are how many ? 8. John has two piles of apples, and 8 apples in how many apples has he? 9. Charles has 2 piles of apples, and 9 apples in each pile; how many apples has Charles? 10. James has 2 piles of apples, and 10 apples | in each pile; how many apples has James? 11. Lucey has 6 roses on one bush, and 6 roses each pile ; ‘on another; how many roses has she? 12. James has 5 birds in one cage, and 5 in another cage; how many birds has he? 13. Nancy shes two pieces of tape, each 4 yards long; how many yards of tape has she? _times times times times times ee 1 bs) ou pe are are are are are pomsy =) CO o> He bo bo bo bo bo bo times 6 are times 7 are times 8 are times 9 are > times 10 are TTT) ty 20 ee Or ee ee enna! MULTIPLICATION. 51 LESSON III. 1. Here are 3 turkeys. Now, if each turkey costs 4 shillings, what will the 3 turkeys cost ? Awnatrysis.—TZhree turkeys will cost 3 times as much as 1 turkey: 1 turkey costs 4 shillings: Therefore, 3 turkeys will cost 3 times 4 shillings, which are 12 shellings. | 2. What will 8 axes cost, at 2 dollars apiece? . If one sheep costs 3 dollars, what will be the sk of 3 sheep ¢ 4. Joseph gave 3 apples apiece to 3 of his com- panions; how many apples did he give to all? 5. If a farmer gives 7 bushels of corn for one yard of cloth, how much must he give for 3 yards ¢ 6. If Sarah reads 9 pages a day, how many pages will she read in 3 days? 7. What will be the cost of 5 yards of ribbon, at 3 shillings a yard? a times 6 are 18 8 times 1 are 8} 3 8 times 2 are 6 | 38. times are 21 3 times 3 are 9 8 times S$. are 24 8. times 4 are 12 | 8 times 9 are 27 3 times 5 are 15 | 3 times 10 are 30 59 MULTIPLICATION. LESSON IV. 1. Here are 4 hives: If 1 hive costs 3 dollars, what will 4 hives cost? 2. If John rides 7 miles an hour, how far will he ride in 4 hours ? 8. A drover bought 6 calves, at 4 dollars apiece; how much did he pay for them ? 4, If there are 9 gallons of cider in 1 keg, how many gallons would there be in 4 kegs? 5. If there are 4 weeks in one ‘month, how many weeks are there in 4 months? 6. If there are 9 panes of glass in one window, how many panes of glass are faced in 4 windows ? 7. At 10 shillings a day, what will 4 days’ work come to? 8. If 4 boys have 8 marbles apiece, how many will they all have? _. 9. What will 9 hats cost, at 4 dollars apiece? 4 times 1 are 4{|4 times 6 are 24 4 times 2 are 8} 4 times 7 are 28 4 times’ 3 are’ 12 |} 4. times 8 - are 32 4 times 4 are 16 | 4 times 9 are 8 4 times 5 are 20 |4 times 10 are 40 MULTIPLICATION. 53 LESSON V. 1. If 1 car has 4 wheels, how many wheels have 5 cars? 2. What will 5 quarts of berries cost, at 8 cents a quart ? 3: If there are 7 trees in a row, how many trees are there in 5 rows? 4. What will 5 yards of ribbon cost, at 6 cents a yard ? 5. If a boat sails 3 miles an hour, how far will it sail in 5 hours? 6. George bought 5 books, at 10 cents apiece; what did they all cost him? 7. What will 5 pounds of sugar cost, at 9 cents a pound ? 8. If a boy goes to school 5 days in a week, how many days would he go to school in 5 weeks? 9. What will 5 melons cost, at 10 cents apiece? iB} times 1 are 571 5 times “6. .are,730 5 times 2 ‘are 10'| 5 times -7 are 85 5 times 38 are 15.| 5 times 8. are 40 5 times 4 are 20! 5 times 9 are 45 5 5 are 25 | 5 times 10° are 50 times Sap SV: REE PERERRRAARRIRDN | 54 MULTLILPLPROATION. LESSON VI. 1. Here are 6 sheep: A farmer paid 3 dollars for each sheep; how much did he pay for the 6 sheep ¢ 2. If aman eats 8 ounces of meat in a day, how many ounces would he eat in 6 days? 3. In an orchard are 6 rows of trees, and 10 trees in a row; how many trees in the orchard ? 4. If-an apple is worth 4 cherries, how many cherries are 6 apples worth ? 5. Charles gave 6 beggars 6 cents apiece; how | many cents did he give to them all? 6. What will be the cost of 6 watches, at 9 dollars apiece ? 7. If a scholar works 7 examples in one hour, show many can he work in 6 hours ? 8. If 1 pencil costs 2 cents, what will be the cost of 9 pencils ? 6 times 1 are 6 | 6 times 6 are 36 6 times 2 are 12 | 6 times 7 are 42 6 times 3 are 18 | 6 times 8 are 48 6 times 4 are 24 | 6 times 9 are 54 6 times 5 are 30: 6 times 10 are 60 MULTIPLICATION. LESSON VII. 1. Here are 7 bells: If 1 bell costs 2 dollars, 4 what will be the cost of 7 bells? . If 1 hat costs 4 dollars, what will be the cost: of 7 7 sabi 3. What will 7 pounds of rice cost, at 5 cents a [> | pound ¢ 7 4, James has 7 brothers, and gives to each 9 marbles; how many does he give to them: all ? 5. William gives 7 apples to each of 9 school- mates; how many apples does he give away ? | 6, At 10 cents apiece, what will be the cost of | 7 pineapples / ' 7. How much will 7 yards of calico cost, at 9 a a yard / . What will 7 tops cost, at 9 cents for each | ve 9. At 5 cents each, what will 7 tops cost ? | 7 times 1 are 7|7 times 6 are 42 | 7 times 2 are 14 | 7 times 7 are 49 | J times 3 are 21 !|7 times 8 are 56 7 times 4 are 28 | 7 times 9 are 63 7 times 5 are 35 | 7 times 10 are 70 56 MULTIPLIOATION. LESSON VIII. 1. Here are 8 mugs: If 1 mug costs 3 shillings, } what will be the cost ef 8 mugs? . What is the cost of 8 pounds of rice, at 5 al a pound ¢ : . 8. If a horse travels 7 miles in an hour, how far | will he travei in 8 hours? 4, At 9 cents a dozen, what will 8 dozen of egos cost ? » 5. William bought 8 pens, at 2 cents apiece; | what did the pens cost ? | _ 6. If William sells 8 quarts of cherries, at 4 cents a quart, how much will they come to? ‘ 7. If a man earns 9 dollars in one month, how ae will he earn in 8 months? _ If 1 plate costs 10 cents, what will 8 plete | ae : a 9. At 3 cents each, what will 8 wih gaa cost ! 8 times 1 ‘are 8 /| 8 times 6 are 48 8 times 2 are 16) 8 times 7 are 56 8 times 3 are 24 | 8 times 8 are 64 8 times 4 are 32 | 8 times 9 are 72 ~ 8 times 5 are 40; 8 times 10 are 80 ee MULTIPLICATION. 57 - at the same rate? LESSON IX. 1. If 1 pear costs 2 cents, what will 9 pears cost, _ 2. If one cord of wood costs 3 dollars, what _ will 9 cords cost ¢ a pound ? 8. What will 9 pounds, of lard cost, at 7 cents 4, If one week’s board costs me 5 dollars, what will 9 weeks’ board cost me? 5. If a family consumes 8 pounds of butter in a week, how many pounds will they consume in 9 } i ! weeks ¢ 6. At 9 ee aa cost ¢ cents a pound, what will 9 pounds of . What will be the cost of 9 sheep, at 2 dol- . bia apiece ¢ c 8. If Jane writes 6 lines a day, how many lines : will slye write in 9 days? | 0 times . 9 times | 9 times _ 9 times 9 times are are are 9 18 27 56 45 9 times 6 are 54 9 times 7 are 63 9 times 8 are 72 9 times 9 are 8l 9 times 10 are 90 | 3% Sa TS PP TP Ome LONs 1 or Obhe. LESSON X. 1. If 1 chair costs 2 dollars, what will 10 chairs cost, at the same rate ¢ FoR Pah Ph ah aa | . If James gave 4 apples for one orange, how ay apples must he give for 10 oranges ? 3. At 6 cents a quart, what will 10 quarts of strawberries cost ? 4. If a man travels by stage, at the rate of 3 miles an hour, how far will he travel in 10 hours? 5. There are 4 quarts in one gallon, how many quarts are there in 10 gallons ? 6. What will 10 paras of broadcloth cost, at 5 pal ayard? — . If a barrel of potatoes costs 7 shillings, how | meh will 10 barrels cost? — . Ten cents make one dime; how many cents are hes: in 10 dimes? 9. At 4 cents each, what will 10 ats qgst? 2 gsacemeeiea la epi d Sous Mia aa 10 times 10 times 10 times 10 times 1@ times are 10 | 10 times 6 are 60 are 20 10 times 7 are 70 are 30 | 10 times 8 are 80 are 40 10 times 9 are 90 0 are 100 Sou HR £9 bo He are 50 | 10 times 1 MULTIPLICATION. 59 LESSON XI. REVIEW LESSON. me — . ond © is 9 ‘ or 2 times 9 are how many?/8 times 3 are how many? Tt “ 6 times 4: ve | 5 times 9 a 9 times 5 7 | 8 times 4 se 5 times 8 cl | 4 times 9 2 times 8 i." | 6 times 3 a 5 times 7 “ | 9 times 4 ; 9 times 3 + | 7 times 5 Be 4 times 7 o 3 times 9 7 '6 times 5 Seer 7 | 64 DIVISION. { 5. When a number is divided into 6 equal | parts, each of the parts is called, one-sewth. | Here are six axes: What is one-sixth of 6 axes? What is one-sixth of 6? Here are 12 axes: What is one-sixth of 12 axes? What is one-sixth of 12? 6. When a number is divided into 7 equal parts, each of the parts is called, one-seventh. Here are 7 acorns: What is one-seventh of 7 acorns? What is one-seventh of 7 ? What is one-seventh of 14 oranges? What is one-seventh of 14? 7. When a number is divided into 8 eqital | parts, each of the parts is called, one-eeghth. AKAD AAI Here are 8 boots: What is one-eighth of 8 boots? What is one-eighth of 8? DIVISION. 65 What is one-eighth of 16 boots? What is one- | eighth of 16% 8. When a number is divided into 9 equal parts, each of the parts is called, one-ninth. @@228288288 Here are 9 trees: What is one-ninth of 9 trees ! What is one-ninth of 9? | What is one-ninth of 18 trees? What is one ninth of 18 ? 9. When a number is divided into 10 equal parts, each of the parts is called, one-tenth. Here are 10 hats: What is one-tenth of 10 hats? What is one-tenth of 10? What is one-tenth of 20 hats? One-tenth of 20% 10. How do you find one-half of a number? Ans. By dividing the number by 2. What is one-half of 22 Of 4? Of 10? 11. How do you find one-third of a number? Ans. By dividing the number by 3. What is one-third of 8%. Of 6? Of 12? 12. How do you find one-fourth of a number 4 Ans. By dividing the number by 4. What is one-fourth of 44 Of 8? Of 12% Put similar questions to include the one-tenth. ‘ 66 DIVISION. LESSON II. Drvision is the operation of finding how many times one number is contained in another. 1. Which is the greater, 1 apple or 2 apples? 2 apples are how many times as great as | apple? is contained in 2 apples, 1 in 2, how many times? 2. 2 apples are contained in 2 apples, how many times? 2 in 2, how many times? )) eal L, 8. 2 apples are contained in 4 apples, how many times? 2 in 4, how many times? how many times? 2 in 6, how many times? 5. 2 cherries are contained in 8 cherries, | 4. 2 pears are contained in 6 pears, | how many times? 2 in 8, how many times? | ie | c | DIVISION. 67 Se . Four apples are how many times as great as 2 apples? Awatysis.—Lour apples are as many times as great as 2 apples, as 278 contained times in 43 2 is contained in 4,2 times: Therefore, 4 apples are 2 times as great as 2 apples. 7. How many times are 8 pears as great as 2 pears? 2 in 8, how many times? bs S. How many times are 12 marbles as great as 8 marbles? 38 in 12, how many times? 9. par aa sticks of candy are how many times as great as 2 sticks of candy? 2 in 18? 10. Sixteen are how many times 2? 2 in 16, how many times? 11. Ten are how many times 57 5 in 10} how many times ? 12. Fourteen are how many times 7? 7 in 14, how many times / | 13. Twelve are how many times 2? 2 in 12, how many times ¢ 14. Two apples are contained how many times in 16 apples? 2 in 16, how many times ? Satin. 2, once. | 2 in 12, 6. times. 2 in 4, 2 times. | 2 in 14, 7 times. 2 in 6, 38 times. | 2 in 16, 8 times. 2 in 8, 4 times. 2 in 18, 9 times. 2? in 10, 5 times. | 2 in 20, 10. times. Se EE 6s DIVISION. t i | LESSON III. / 1. John divided 9 acorns, equally, among his _ three brothers; how many did he give to each ? Awatysis.—l7e gavg to each brother one-third of 9 acorns: one-third of 9 is 8: Therefore, he gave each brother, 3 acorns. , 2. Twelve scholars, in a school, are distributed | _ equally on 3 benches; how many sit on cach bench? 38. James buys 15 oranges, and divides them equally among 3 boys; how many has each boy ? _ 4, William divided 21 plums, equally, among 3 _of his companions; how many did he give to each ? _ 5. A farmer put 30 sheep into 3 pens; how | many did he put in each pen? ' 6 Charles earned 27 cents in 3 days; how _many cents did he earn each day ? 7. If 24 marbles are divided, equally, among 3 boys, how many will each boy have? Paine. 8, once. | 38 in 18, 6. times. Pore se OD temer 8 in woh, timesn: | dein 9, 8 times. | 3 in 24,. 8 times. | 8 in 12,. 4 times. | 3 in 27, 9 times. | 3 aie 16.) 5) times 1/3. in #30; 10) times, DIVISION. 69 LESSON IV. 1. If 4 barrels of apples cost 12 dollars, how mapy dollars will 1 barrel cost ? Anatysis.—One barrel of apples will cost one- | fourth as much as 4 barrels: 4 barrels vost 12 dollars, one-fourth of which ts 3 dollars: There- | Sore, 1 barrel of apples will cost 3 dollars. 2. If 4 yards of cloth cost 8 dollars, what will 1 yard cost ? 3. If 4 oranges cost 20 cents, how much will 1 | or ange cost ? 4, Te 4 pineapples cost 36 cents, how much is that apiece ? 5. If 40 dollars will buy 4 coats, how much does each coat cost ? | 6. If 28 cents will buy 4 melons, what is the _ cost of 1 melon ? | 7. If James pays 32 cents for 4 tops, how much | does each top cost him? — _ 8. Jane paid 36 cénts for 4 yards of ribbon; how much did she pay for 1 yard # fa ES), ae once. | 4 in 24, 6 times. | 4 in 8, 2 times. | 4 in 28, 7° times. | 4 in 12, 8 times. | 4 in 82, 8 times. | 4 in 16, 4 times. 4 in. 36, 9 times. | 4 in 20, 5 times. ! 4 in 40, 10 times 70 DIVISION. LESSON V. 1. If 20 dollars will buy 5 yards of broadcloth, how much is that a yard ? 2, At 5 dollars a week, how many weeks’ board | pee I obtain for 35 dollars ? . If 5 men pay a bill of 15 dollars, how much ae each man pay ? 4. If 5 scholars can sit on 1 bench, how many | benches will accommodate 50 scholars ? 5. How many barrels of flour can be bought for 40 dollars, at 5 dollars a barrel ? 6. low many hours will it take a man to travel 10 miles, if he travels 5 miles an hour? A man paid 45 dollars for building 5 rods of | fence; how much did he pay for 1 rod? 8. If I put 25 bushels of apples into 5 boxes, how many do I put in each box? 9. A person received 50 dollars for 5 weeks’ labor; how many dollars did he receive in one week ? | 10. If | receive 5 dollars for 5 bushels of wheat, how much is that a bushel? Rican B, once. atnaciulte) aut By an ces?) “Gey time Pain 10, -2.times: | 5. inic3h, ‘7. times, 5 in 15, 38 times. te 5 in 40, 8 times. jean .20, 4 times. | 5 in 45, 9. times. 5” in 25, 5 times. 7 5 ma) 50, - 10% times, DIVISION. 711 LESSON VI. 1. If 6 sheets of paper make a copy-book, how | many books will 18 sheets make? 2. If 24 peaches be equally divided among 6 | boys, how many will each have? ‘ 3. At 6 cents a yard, how many yards of ribbon | can te bought for 42 cents? : . At 6 shillings 2 day, how many days’ board | can is obtained for 36 shillings ? 5. A butcher paid 30 dollars for 6 calves; how | much did he pay apiece 4 6. If Mary reads 6 pages a day, how many days will it take her to read 48 pages % 7. [fa ship sails 6 miles an hour, how long will | it take her to sail 54 miles # 8. I gave 12 dollars for 6 bushels of wheat; bin did I pay a bushel? | . A mason finds that he can build 60 rods of Bris fence in 6 days; how many rods can he build in one day ? 10. If 6 men can build 6 rods of wall in one day, how much can one man so age dessa OH. « JG) once. | 6 Be vom, Be 36, 6 times. 6 in 12, 2 times. | 6 in 42, 7 times. 6 in 18, 3 times. |.6 in 48, 8. times. | 6 in 24, 4 times. | 6 in 54, 9 times. 6 in 30, 5 times. | 6 in 60, 10 times. 2 DIVISION. LESSON VII. 1. How many pounds of sugar, at 7 cents a ‘pound, can be bought for 28 cents ? 2. Susan gave 21 cents for 7 pencils; how : /many cents did she give for one pencil? 3. A boy sold 7 baskets of strawberries for 56 cents; how much did he get a basket? 4, A farmer received 14 dollars for 7 pigs; what did he receive for 1 pig? 5. A farmer has 35 dollars, which he wishes to expend in plows; he finds that they are 7 dollars | apiece: how many can he buy? 6. If a stage runs 49 miles in 7 hours, how far does it run in one hour? 7. If 7 dozen of eggs are worth 63 cents, what is one dozen worth ? 8. There are 7 days in one week; how many weeks are there in 56 days? 9. I paid 70 cents for 7 yards of calico; how much did I pay for one yard ? 10. George bought 7 apples, for which he gave 7 cents ; eae bith did he give apiece? Fran 8, once. | 7 in 42, 6 times. 7 in 14, 2 times. | 7 in 49, 7 times. fan? 21, Be times: | Fane o6, 8s dimes: 7 in 28, 4 times. | 7 in 638, 9 times. 7 in’ 35, 5 times. | 7 in 70, 10 times. DIVISION (3 LESS ONGV EIT. tl. A lady purchased 8 yards of ribbon for 48 cents; what did one yard cost? 2. A gentleman bought 8 yards of broadcloth for 32 dollars; what was the cost of one yard? 3. At 8 cents a pound, how many pounds of ginger can be bought for 40 cents? 4. I paid 16 dollars for 8 barrels of apples; what did I pay for one barrel ? 5. There are 8 quarts in one peck; how many pecks are there in 24 quarts? 6. When 80 dollars are paid for 8 acres of land, what is paid for one acre? 7. At 8 dollars a month, how long must a per- son work to earn 64 dollars? 8. If one tree bears 8 bushels of apples, how many trees will yield 56 bushels? 9. Josevh so!d 8 melons for 72 cents; what was the price of one melon? 10. if a tailor requires 8 yards of cloth to make 1 suit of clothes, how many suits of clothes will 32 yards of cloth make? 8 in 8, once. | 8 in 48, 6 times. 8 in 16, 2 times. | 8 in 56, 7 times. 8 in 24, 8 times. | 8 in 64, 8 times. 8 in 32, 4 times. | 8 in 72, 9 times. 8 in 40, 5 times. | 8 in 80, 10 times. 74 DIVISION. LESSON IX. 1. At 9 cents apiece, how many melons can be bought for 27 cents? | 2. How many yards of calico, at 9 cents a yard, can be bought for 54 cents? 3. If a horse eats 9. bushels of oats in a month, how long will 36 bushels last him ? 4. If a horse travels 9 miles an hour, in what time will he travel 90 miles? 5. If 9 sewing girls received 45 shillings for a day’s work, how much did each receive? — 6. In an orchard there are 81 trees, and 9 trees in a row; how many rows in the orchard ? 7%. A farmer divided 18 bushels of potatoes, equally, among 9 persons; how many bushels to each person ? 8. How many yards of silk, at 9 shillings a yard, can be bought for 63 shillings? 9. A workman received 9 dollars fer 9 days’ work; what were his daily wages ? 10. If a man spends 9 cents a day for cigars, how long will 72 cents last him? On <9, once. | 9 in 54, 6 times. 9 in 18, 2 times. | 9 in 68, ‘7 times. 9 in 27, 3 times. |.9-m 72, 8 times. 9 in 36, 4 times. | 9 in 81, 9 times. 9 in 45, 5 times. | 9 in 90, 10 times. DIVIBION. LESSON X. 1. At 10 cents a quart, how many quarts of molasses can be bought for 50 cents? 2. At 10 cents apiece, how many melons can be bought for 70 cents ? 3. A farmer had 40 sheep, and put 10 in a flock; how many flocks had he? 4, Thats are 10 cents in one dime; how many dimes are there in 80 cents ? 5. How many calves will 60 dollars buy, at 10 | | | dollars each ? 6. At 10 cents a yard, how many yards of | calico can be bought for 90 cents ¢ Y 7. Paid 20 dollars for 2 colts; what was the | bo of one colt ¢ | . If a boy earns 10 cents a day, how long will it say him to earn 70 cents? 9. A grocer finds that he can buy cider for 10 dollars 2 barrel; how many barrels of cider can he buy for 30 dollars 2 10. How many pineapples, at 10 cents apiece, ean I buy for 100 cents? 10 10 10 10 10 10, 20, 30, 40, 50, 10 10 10 10 10 in 60, 70, 80, 90, 100, oOo ON SD times. times. times. times. times. a “16 DIVISION. LESSON XI. REVIEW LESSON. 6 in 54, how many times/ 8 in 40, how pay times? | 3 in 18, 4 in 36, | 4in 20, oak Tin 49, 6 | 9 in 27, oe 4 in 16, as 8 in 72, 7 in 28, st 5 in BD; ff 8 in 64, 6 9 in 81, rh 6 in 12, My 6 in 18, i 9 in 63, e 7 in 42, ss 5 in 2d, é | 8 in 16, how many times? 9 in 54, how many times? 7 in 21, “6 3 i in 21, ps6 | 3in 27, eS ra in 56, . 7 in 63, « 8 in 48, “ 5 in 40, 9 in 45, * 9 in 18, Y 2 in 14, ms Bevaoe 5 gS '6 in 48, FF 6 in 42, « 8 in 82, os yan £5, 277, 7°88 4 in bi = 6 in 30, how many times ‘3 in 24, how many times? 66 9 in 36,: 2 in 16, 5 in 380, cs 4 in 32, ¢ 4 in 24, e 6 in 24, 2in 6, . Tip uh 5 7 in 14, a: 2 in 10, $$ 5 in 10, A 5 in 20, A, 7 in 35, pee 4in 8, S 4 in 12, -yO1in 10, . o DIVISION. T% -—————$—$ eens LESSON XII. PROMISCUOUS QUESTIONS. r 1. Sarah learned 32 lessons in 8 days; how _many lessons did she learn each day ? | . If a horse travels 68 miles in 7 hours, how | many miles does he travel in one hour? | 3. If 9 men consume 81 pounds of bread in a week, how much would one man consume? 4. How long will it take 6 men to do a piece of work, that one man can do in 48 days? 5. If 90 bushels of apples will make 10 barrels of cider, how many bushels will make one barrel of cider? | 6. How long will it take a man to build 72 feet of wall, if he builds 9 feet a day ? | %. How long would it take a steamboat to go 70 miles, at the rate of 10 miles an hour? 8. How many sheep, at 3 dollars a head, can be | bought for 27 dollars? | 9. How long will 45 dollars pay for keeping a , horse, at the rate of 5 dollats a month? 10. A boy divided 36 cents, equally, among 4 beggars; how many cents did he give to each? 11. At 6 cents a pound, how many pounds of rice can I buy for 42 cents? 12. At 7 dollars a rod, how many rods of fence can be built for 49 dollars ? | | : | | } / 18 DIVISION. Se 13. There are 7 days in a week; how many | weeks are there in 56 days? 14. If 5 men can build a wall in 8 days, how long will it take 1 man to build it? 15. If I pay 4 dollars for a ton of coal, how many tons can I buy for 382 dollars? 16. If you have 72 pounds of butter, which you | wish to put in 9 sh ein how much must you put in each box? 17. A farmer sold 8 cords of wood for 48 dol- | lars; how much did he receive a cord ? 18. If a cabinet-maker sells 6 chairs for 54 dol- | lars, what would be the cost of 9 chairs ? 19. If ten pounds of tea cost 60 shillings, what | will 5 pounds cost? 20. If'4 men can hoe a field of corn in 3 days, | how long will it take 1 man to hoe it. 21. Ifa boy travels 64 miles in 8 days, how far | will he travel in 5 days? 22. Ifa piece of cloth containing 22 yards will make 11 coats, how many yards will it take to make 9 coats ? 23. How many pounds of honey, at 9 cents a pound, can you buy for 108 cents ? 24. What will 15 pounds of cheese cost, if 8 pounds cost 40 cents? 25. A grocer has 64 pounds of tea, which he wishes to put into parcels of 8 pounds each; how | many parcels will he have? | DIVISION. 79 LESSON XIII. 1. How many melons, at 6 cents apiece, will | pay for 9 oranges, at 4 cents apiece ? Awatysis.—WVine oranges, at 4 cents apiece, cost 36 cents: As many melons can be bought for 36 cents as 6 is contained times in 36: 6 in 36, 6 times: Therefore, 6 melons, at 6 cents aprece, will pay for 9 oranges, at 4 cents aprece. 2. Tow many yards of cloth, at 3 dollars a yard, can be bought for 4 barrels of flour, at 6 | dollars a barrel? 3. A grocer sold 9 pounds of tea, at 7 cents a pound, and took his pay in eggs, at 9 cents a dozen; how many dozen did he receive? | 4. Harry has lemons worth 4 cents apiece; how many must he give John for 2 quarts of cherries, | worth 8 cents a quart? | 5. William worked 6 days, at 10 cents a day, _ and took his pay in oranges, worth 3 cents apiece; how many did he receive? _ 6. If a family of 6 persons have provisions for | 8 weeks, how long will it last 1 person ? 7. A butcher sold a baker 9 pounds of beef, at 5 cents a pound, and took his pay in bread, at 12 | cents a loaf; how many loaves did he receive ? 8. If 3 weeks’ board costs 18 dollars, what will | 9 weeks’ board cost, at the same rate? —_——— ——- 80 DIVISION. 9. How much sugar, at 9 cents a pound, must be given for 9 dozen of eggs, at 10 cents a dozen ¢ 10. How many barrels of flour, at 8 dollars a | barrel, must be given for 10 sheep, at 4 dollars | apiece ¢ | 11. How many yards of cloth, at 3 dollars a | yard, must be given for 6 calves, at 9 dollars | apiece ? | 12. How many bushels of wheat, at 2 dollars a | bushel, must be given for 2 barrels of sugar, worth | 16 dollars a barrel ? | 13. A man wishes to exchange 20 sheep, worth | 3 dollars apiece, for calves worth 5 dollars apiece; | how many calves should he receive? | 14. If 2 apples are worth 10 chestnuts, bow | | | | { | | many chestnuts will 20 apples buy ? 15. Six lemons are worth 24 apples; how many lemons will 16 apples buy ? | 16. How many yards of cloth, at 4 dollars a yard, can be bought for 12 calves, at 3 dollars apiece ¢ 17. John wishes to exchange hens, worth 2 shil- | lings apiece, for 12 ducks, worth 3 shillings apiece; | how many hens must he give for the ducks ? | 18. How many sheep, worth 4 dollars apiece, must be given for 6 calves, worth 6 dollars apiece ¢ 19. A grocer sold 12 pounds of tea, at 6 shillings | a pound, vane took his pay in wheat,’at 9 shillings | a bushel; how many bushels did he receive? | FRACTIONS. LESSON I. _ 1. Ifanorange _ be divided into equal parts, each of the parts is called, one-half. 2. Ifan orange be divided into equal parts, each of the parts is called, one-third. 3. Ifan orange __ be divided into equal parts, each of the parts i&called, one-fourth. 4. Ifan orange be divided into equal parts, each of the parts is called, one-fifth. | 5. If an orange be divided into 6 equal parts, each of the parts is called, one-siath. 6. If an orange be divided into 7 equal parts, each of the parts is called, one-seventh. 7. If an orange be divided into 8 equal parts, each of the parts is called, one-eighth. | 8. If an drange be divided into 9 equal parts, each of the parts is called, one-ninth. 82 FRACTIONS. 9. If an orange be divided into 10 equal parts, each of the parts is called, one-tenth. These equal parts of the orange, are called Fractions. They are thus written: One-half . 4 One-seventh . } One-third . t One-eighth _ One-fourth 1 One-ninth. a One-fifth . 1 One-tenth. wi One-sixth. . . §% | One-twelfth. . ;4 The number above the line, is called the nwmer- ator; and the number below the line, is called the denominator. 10. How many halves are there in one orange? How many thirds are there in one orange? How many fourths are there in one orange? How many fifths are there? How many sixths? | How many sevenths? How many eighths? How many ninths? How many tenths ? 11. Which is the greater, one orange or one-half of an orange ? Which is the greater, one-half or one-third / Which is the greater, one-fourth or one-third ? Which is the greater, one-fourth or one-fifth ? Which is the greater, one-sixth or one-fifth ? Which is the greater, one-sixth or one-seventh ? Which is the greater, one-eighth of one-half? Which is the greater, one-third or one-tenth ? FRACTIONS. LESSON II. 1. How many halves of one orange are there in two oranges ¢ Awnatysis.—ln 2 oranges, there are two times as many halves as in 1 orange ; in 1 orange there are 2 halves: Therefore, in 2 oranges there are two times 2 halves, or 4 halves. 2. How many halves of one orange are there in 3 oranges? How many in 4 oranges? In 5? 3. How many halves of one orange are there in 7 oranges? How many in 8 oranges? In 10? The halves are thus written: Two-halves . = Ten-halves . 32 Three-halves . $ Twelve-halves - 42 Four-halves . $ Sixteen-halves . 48 Five-halves . 5 Kighteen-halves . 42 Seven-halves. 5 | Twenty-halves . 2? . How many halves of 1 are there in 2? . How many halves of 1 are there in 6? In 7? . How many halves of 1 are therein 9% In 10? How many halves of 1 are there in 8? In 8% . How many halves of 1 are there in 5? In 4? COOnr DS Ot > 84 FRACTIONS. 9. HLow many oranges are equal to 8 halves ? Awnaxysis.—Since 2 halves are equal to 1 orange, there will be as many oranges in 8 halves as 2 a8 contained times in 8: 2 im 8, 4 times: Therefore, 8 halves are equal to 4 oranges. . How many apples are equal to 2 halves? . How many apples are equal to 4 halves? . How many pears are equal to 8 halves? . How many melons are equal to 20 halves? . How many peaches are equal to 16 halves? . How many plums are equal to 18 halves? . How many plums are equal to 14 halves? . How many lemons are equal to 12 halves? - . How many lemons are equal to 18 halves? . How many pears are equal to 10 halves? . How many plums are equal to 8 halves? . How many units 1 are there in 6 halves? . How many units 1 are there in 12 halves? . How many units 1 are there in 14 halves? . How many units 1 are there in 18 halves? . How many units 1 are there in 20 halves? . How many units 1 are there in 16 halves? . How many units 1 are there in 18 halves? . How many units 1 are there in 6 halves? . How many units 1 are there in 2 halves? FRACTIONS. LESSON III. 1. How many thirds of an orange are there in 4 oranges ? | Anatysis.—ln 4 oranges there are 4 times as many thirds as in 1 orange: in 1 orange there sare 3 thirds: Therefore, in 4 oranges there are 4 | times 8 thirds, which are 12 thords. 2. How many thirds of an orange are there in 2 oranges ? How many thirds are therein 3 oranges? In 4? 'low many thirds of 1 are there in 2¢ In 6? [low many thirds of 1 are therein 4? In 5? 3. How many whole oranges are equal to 9 | thirds ¢ | Awatysis.—Since 8 thirds of an orange are | equal to 1 orange, there will be as many oranges in 9 thirds as 3 7s contained times in 9: 3 in 9, 3 times: Therefore, 9 thirds are equal to 3 oranges. 4. Flow many oranges are equal to 12 thirds? How many oranges are equal to 15 thirds? How many units 1 are equal to 21 thirds? 5. How many units 1 are equal to 27 thirds? How many units 1 are there in 3 thirds? How many units 1 are there in 9 thirds? 86 FRACTIONS. | LESSON IV. | | 1. How many fourths of a lemon are there | in 3 lemons? | | / Anatysis.—In 3 lemons there are 3 times as | many fourths as in 1 lemon: in 1 lemon there | are 4 fourths: Therefore, in 3 lemons there are 3 times 4 fourths, which are 12 fourths. 2. How many fourths of a lemon are there in | | 2 lemons ? In 3? In 4? | | How many fourths are there in 6 lemons? | | How many fourths of 1 are therein 5? In 7? | | 3. How many whole lemons are equal ‘to 8 | | fourths ? | Awnatysts.—Since 4 fourths of a lemon are equal to 1 lemon, there will be as many lemons an 8 fourths as 4 is contained times in 8: 4 m 8, 2 times: Therefore, erght fourths are equal to 2 lemons. 4. How many lemons are equal to 12 fourths ¢ How many lemons are equal to 16 fourths ? How many lemons are equal to 32 fourths? 5. How many lemons are equal to 36 fourths ! How many units 1 are equal to 4 fourths? How many units 1 are equal to 20 fourths ? FRACTIONS. LESSON V. 1. How many fifths of an orange are there in 2 oranges ¢ Anatysis.—Jn 2 oranges there are 2 times as many fifths as in 1 orange: in 1 orange there are 5 fifths: Therefore, in 2 oranges there are 2 times 5 fifths, which are 10 fifths. How many fifths of 1 are there in 3? In 4? How many fifths of 1 are therein 52 In 6? 2. How many units 1 are there in 20 fifths? Awnatysis.—ZIn 1 there are 5 fifths: in 20 fifths there are as many units 1 as 5 is contained times in 20: 5 in 20, 4 times: Therefore, there are 4 units 1 in 20 fifths. 3. How many units 1, in 45 fifths? In 60 fifths? 4, How many fifths of 1, in 6? In 7? In 8? 5. How many sixths of an orange are there in 2 oranges? In4? In 5! How many sixths of 1, in 2? How many in 3? How many. oranges are equal to 24 sixths? How many units 1, in 36 sixths? In 42 sixths? How many units 1, in 48 sixths? In 54 sixths? How many sixths of 1,in 12% In 8? In 9? How many sixths are there in 7¢ In 12% 88 - FRACTIONS. 6. How many sevenths of an orange are there in 3 oranges ? How many sevenths of 1,in3? In7? In 9? How many sevenths of 1, in 4? In 5? In 8? How many oranges are equal to 21 sevenths? ° How many units | are there in 21 sevenths? How many units 1, in 35 sevenths ? 7. How many eighths of an orange are there in 2 oranges ? How many eighths of 1 are there in 2? In 3? How many eighths of 1 are therein 4? In 5? How many oranges are equal to 24 eighths? How many units 1,in 24 eighths? In 40 eighths? 8. How many ninths of an orange are there in 3 oranges ? How many ninths of 1 are there in 3? How many ninths of 1 are there in 4? In 5? How many oranges are equal to 18 ninths ? How many oranges are equal to 27 ninths? How mé@ny units 1 are equal to 36 ninths? 9. How many tenths of an orange are there in 2 oranges? How many tenths of 1 are there in 3? In 4? How many tenths of 1 are there in 5? In 6? How many tenths of 1 are therein 7? In 8? How many oranges are equal to 30 tenths? How many units 1 are equal to 40 tenths? How many units 1 are equal to 60 tenths? How many units 1 are equal to 70 tenths? FRACTIONS. 89 LESSON VI. 1. If 1 pound of tea costs one-half of a dollar, what will 4 pounds cost? Anatysis.—four pounds of tea will eost 4 times | as much as1 pound. Since 1 pound costs one-half of a dollar, 4 pounds will cost 4 half-dollars, which are equal to 2 dollars: Therefore, if one pound of tea costs oa a dollar, 4 Bowness, will cost 2 dollars. 2. If a bushel of apples costs one-third of a dol- lar, what will 9 bushels cost é 3. If John pays one-fourth of a dollar for a pen- knife, how much must he pay for 8 penknives, at the same rate? 4. If a yard of calico costs one-fifth of a dollar, how much will 20 yards cost? 5. What will 8 barrels of flour cost, if one-sixth of a barrel costs 2 dollars ? c 6. If 1 pound of sugar costs one-eighth of a ran what will 16 pounds cost sale one-ninth of a piece of cloth contains 5 yaaa how many yards are there in the whole. pr _ If 1 bushel of wheat costs one-tenth of a dol- ms what will be the cost of 40 bushels? 9. If a bushel of corn costs one-fifth of a dollar, what will be the cost of 15 bushels? 3 Sa a ——— | 90 } FRACTIONS. 10. If half an ox is valued at 50 dollars, what is the value of the ox? 11. If one-fourth of a bushel of peaches costs 4 shillings, how many shillings will 2 bushels cost ? 12. If a man earns 3 dollars in one-fifth of a month, how much will he earn in 2 months? 13. If one-seventh of a yard of silk costs 10 cents, how much is that a yard ? 14. If one-eighth of a pound of tea costs 7 cents, how much is that a pound? yards, how many yards are there in the piece ? 16. If a man earns 8 dollars in one-tenth of a month, how much will he earn in 2 months? 17. If one-fifth of a barrel of flour lasts a family 8 days, how long will 2 barrels last them ? 18. If one-third of a cheese is worth 2 dollars, what is the value of the whole cheese ? 19. If one-eighth of a barrel of apples is worth 2 shillings, how many shillings are 3 barrels worth ¢ - 20. If in one-tenth of a month, a man earns 2 dollars, how much ean he earn in 8 months ? 21. If two cents pays for one-eighth of a melon, how many cents will buy-2 melons? 22. If 3 cents pays for one-fourth of a dozen of eggs, what will 4 dozen cost? 23. If one-ninth of a piece of cloth contains 5 yards, how many yards will 4 pieces of the same | length contain Fe ee ee ee i oe 15. If one-eighth of a piece of cloth contains 4 | | q $1 = 100 cents. 1 4 UNITS OF ARITHMETIC. 91 | Uwirs or Apstract NuMBERS. 10 units make 10 tens 10 hundreds . UNITS OF 1 ten. 1 hundred. 1 thousand. The abstract units are, 1, 10, 100, 1,000, d&e. CURRENCY. Unirep Stares Money. 10 mills make BOs cenis (.:°: 1@ dimes . 10 dollars . 20 dollars 4 of a dollar = 1 of a dollar = 1 of a dollar = 1 of a dollar = Ewauisu Srertinc Money. 5 2 e 0 2 4 farthings make . 12 pence. . 20 shillings . 21 shillings a ae 4s - i s 1 2 1 cent, . 1 dime, . 1 dollar, 1 eagle, 7 . . . 1 double eagle, D. #. The units of this currency are, 1 mill, 1 cent, 1 dime, 1 dollar, and 1 eagle. of a dollar = 122 cents, zs of adollar = 10 ys of a dollar = 61 so Ofadollar= 5 * of a cent 1 penny, . 1 shilling, 1 pound, . 1 guinea, es —- 2 2 5 mills, | -—< The units of this currency are, 1 farthing, 1 penny, shilling, 1 pound, and 1 guinea. | | 92 UNITS OF ARITHMETIC. Units or Lenornu. Linear Merasure. 12 inches, in. make 3 feet. oarie% ; 54 yards, or 164 feet . 40 rods 8 rniles . statute miles. 8 furlongs, or 820 rods. geographical, or 693 e ty k: f00t 4) Jo pene ast Yyard,.. ‘¢.aeiwie@ ated. h POG ei oth pditaecey es 1 furlong, . . . 7. far. PRONG. Uk niente ioe ae ais Pdeacud, Bosse lena ede . deg. or °. degree, . What are the units of this measure ? Crotn MErasure. 27 inches, im. make . ATONE oa iS a QuaCibTS, js.) t. le yard 7. tal @ 8. boat S quarters, . .. . 1 Ell Flemish, . £4. F7. SB UATIORS 2 eu” . 1 El) English, . #B What are the units of this measure? Univs or SURFACE. SquaRE Muasure. 144 square inches, sg.ia. make 1 square foot, . ag. ft. | 9.-square feet)... - 1 square yard, . sq. yd. 30} square yards. . « 1 squarerod; 2. P. 40."square reds i=") is 2. 2 reed, 2 set) 2 RB. A: OOS) 2 MEE OS PL are GtGrcacres eye Pr) cha eeiguare miley mere AP. What are the units of this measure ? ; Pnail 2 Se ee 1 quarter of a yard, qr. [(———-——- / UNITS OF ARITHMETIC. 93 Units oF VOLUME. Supic MEASURE. 1728 cubic inches, cv.in. make 1 cubic foot, . cu. ft. 27 cubic feet 2° i. . . 1 eubie yard, ’aicu. yd. 40 feet of round, or ) 50 feet of hewn timber § 1100; ey rate Bi 42 cubic feet . . . . . 1 tonofshipping,. 7. 16 cubic feet “SH Lore! J* cord footy err Fe fh 8 cord feet, or } 128 eubic feet J ° What are the units of this measure? be bords. tS eee Liguip MEASURE. 4 gills, gi:make . . . 1 pint, . . . pt. | 2 pints L*quart, .) . 496 4 quarts , 3 Vegallon, 9... aregars Po old pallots; 2 4... «1 barrely sr bar. | 63 gallons 1 hogshead,. . hhd. | 2 hogsheads L pipe; 2.) Ge pte 2 pipes, or 4 hogsheads 1 tun,. . «. « tum. What are the units of this measure? Dry Measure. 2 pints, pt. make. . . 1 quart, . . . gt. Sequarta... .. jyeteedy 3 2 peck. 5) jedunwt ae 4 pecks . . . . ~~ 1 bushel,. . . bu. $6) buabelé...vutsees 4. 1 chaldron, sumo eke What are the units of this measure? 94 UNITS OF ARITHMETIC. Sw Units or WerIGut. Avorrpuprors Wricurt. hGncrams, dz wmaks» ..1..%. 1] ounce... 5 aii Ome EG LOUNCES adie bo A PORN, nnd ce mo POURS fe PW eB GATE eek a ee 4 quarters . . ... . 1 hundredweight, cwt. 20 “hundipdweighh..ps. . BytODy 6 saeenten te What are the units of this weight? Troy Weieut. - 20 pennyweights . ./ 1 ounce, . . O28, E22 OUNCES s. 0! (eee Eee eae, ~~ os abe ’ APporTHoecaARins’ Wrigut. 20 “wramseor. make . ¢. ‘1 serapley .. 3 | Boecraplea”. 20ers. eng) 1 rams. MEOFOINS: i, ah ie, kee TOU DOR, 12eannees. |. 34. £2) 2 1 pound, ape. SO Units or Time. 60 seconds, sec. make . 1 minute,. . . ™. GOomimtes oe.fes/ eas ew 2) Wate . . aeaiee er, Sdohonts. praat ete 1: CY ice! ihe ern omae Ty Gage ae" a st? AMO > L oweekyg., 4, un gee. weeks +. .e Piet oo. Lomonthy .. Baca. bg eee PET Ts oad SOE, 2 og, ae eee as | 100 years... 1 @entury;. aoe | \ What are the init of time ? “s | | 24 grains, gr. make . . 1 RAnAY SineAh put. | | | | a UNITS OF ARITHMETIC. 95 | Ture YEAR. Winrek, 4 1 month, January,, 31 days. 2 “ February, 28, in leap-year, 29. | 3 “March, 31 days. } | SPRING, 4: seo gw Api), 20.;, 4 5st May, Sioa ( 6 Ayh*> vdane, BOs ae Summer, { 7 ee daly, si + / 8 . August, hme a. & ipepeamben, 30° |S Autumn, < 10 11 “ November, 30 “ Winter, 12 “ December, 31 ¢ There are, inthe year, . . 365 days. Unirs or Crrcutar Measure. 60 seconds, ’’ make . . 1 minute, « 60 minutes . .. . . 1 degree, 30 aw LESSON II. READING AS FAR 5. TWENTY. rol gs Ube nee ee Icgh pod pal) DR honey ek: 2 2 2 2 2 i. § ee Epes Sl BS et ier nD a Ceo Si: ee eee PR i ae Fis Bi, Achaea ae vi i eS a ae | 3 bie 06 6 eb Bs. gre Sh? 4 PORBG ge MR ONES OGD D tiie 6) en aa ris fe een age Pay APE Bs eee aBicee Niheee ORG. By wk. ee 10 10 10 10 10 S oo | = dO Teh. eee Miewe nay So eae et ee ee trae | ae READING FIGURES. 99 LESSON ITI. READING WITH THE LARGER NUMBERS. lg A ae ile Sl ae Ss a ae m 1 10 16 1 1 10 40 10 M a Ome. eT SA ah et 8 8 OO (/ie Wh it bb. Wk he Ie lb 12 Maa | + ta ea wie a3 | AS es Sa ts aE Se a ae Mois 12 12 12 Bb 2b Bb Ye gee he ey Ed ehitd geo ty 18 13 18 18 13 18 18 13 13 18 18 ee eee ae 4 3 Rg eta: S14 Lg se Be iy St Ss ee SS Se Boye loro 1b 1S 15. 15) SaaS o Feet, Mow oO. 4°, ee ae SiG ator etO mGomlg 1G hep lé Pao" oS YS SY FE THEM 8S tg eee Beh. 20) OPUS as RG Os PO 49° 9S SR 26. ch 14> 78s 480d | 18 18 18 18 18 18 18 18 18 18 18 ro), Gee (ah stay, a eee kee Le ae 192 TS TOD OT YQ FOP PE ge ay ——— _— —_—, ee ee ee —_—— _ — —— 100 READING FIGURES. LES SOW aby. READING BY THE EYE ABOVE TWENTY. By 9 BURT) 6 REP BA RY BES 0 20 20 20 20 20 20 20 20 20 20 20 3 ining Sai: UR 3 Wi? eS UR) MS) SO A ae ee MS ee Be 24 R494 Od Gd od Bd ok ae Pee ee a Ta Se Ss aT BE 8S APE IP 20) 088. Uy SANA SE LORS aia Qe Mare Gerrit, ia) 26 26 26 26 26 26 26 26 26 26 26 bil eM se SMies aie kei cet oe ie a Mm oe ame Py br 27° 97.907 BT OT 97.0% ATi eT oat ges Let the Teacher writé, in succession, on the | blackboard, all the numbers to 100, in sets of ten, and | exercise the class in the readings. | READING FIGURES. 101 ee LESSON V. | READING COLUMNS OF THE SAME FIGURES. Rae ae Be Gta att ER beose 8 4 EBS oT) 8 Se repose Ss (84 Se OB) TTR) gs C819 Stee Reeth 6c BS Ge Ay. - 8 oy Gem | Pesiy Sat, cb: Gy Tie Briel pene 7 84 OG Ge: Teg cere fee 8 04 oS lg 8h e 4tO fees Sua 5 BR. te Se yO arO ey SPOS Be DT 4 Bi BRIO Mee e384 Bb Be ay 8b 8 oO Ten times 1, are how many? ‘Ten times 2, are how nany? Ten times 3? Ten times 4? Ten times 5? [en times 6? Ten times 7? Ten times 8? Ten jimes 9? Ten times 10? | Read the following : 1 2 3 0 1 3 I 4 3 | > 00 Hm Fe co bo Or 9 JOR OOD We bo LAN RAR OTaRaHO i>TWOWHDH OD jer OH RH Oo H-TO OH HT |; PLL HOF, OOS |lOomorFNonwor Pe |oOoOHONWWaAS?D 102 READING FIGURES. LESSON ‘EXAMPLES IN READING 2) ie (BPP A Te) 0 5 " 3 1 1 4 HoT A u0e ” 2.0 Bu O08, 80 A dias 4 1 9 Yam .9 8 7 1 5 7 0 8 6 6-6 6 i. FAD 8 3 ie Be mac On tae Hee 3 0 1 4 Buia ob st 3 9 ae LONG (6) JR DOWArTOONO-T COLUMNS, Cid (8) Git 9 94%.58 Saket ee Tin ty 9 6 0 lia. "9 Sy ge re alt uae IS READING FIGURES. LESSON VIT. READING IN SUBTRACTION. 8 7 6 5 4 3 1 1 ] 1 1 1 9 8 7 6 5 4 2 3 yy 2 2 2 10 9 8 7 6 5 CES et oan CAC LL> iu 9 8 T 6 4 1m GC 4 4 4 LS jth lO 9 8 yf Bini ve Shing Re to bY eee i a 9 8 6 6 6 6 6 ahiincdnie a Adee: a Tt to, Lame 1. hee eo 1 AM 7 A 7 qT L600 14 -- 43. | 4 8 8 8 8 8 8 [woo jaw faa [aw [eo [om roc [eno pias oS = Bs 1038 v 1. 2. t= OO “I co Gn —" he OO Nar 6 "00 qn oF —" m™ GH pom © SS @ eat ora! the other numbers, as far as 10. READING FIGURES. LESSON VIII. COUNTING BY THE NUMBERS FROM 1 To 1QO. Count by the one’s to 50. How many 1’s are there? Count by the 2’s to 50. . Count by the 3’s to 51. . Count by the 4’s to 52. . Count by the 5’s to 50. . Count by the 6’s to 54. . Count by the 7T’s to 56. . Count by the 8’s to 56. . Count by the 9’s to 54. . Count by the 10’s to 50. . Subtract 1 from each number, from 50 to 1. . Subtract 2 from 50, and then from each remainder. . Subtract 3 from 51, and then from each remainder. . Subtract 4 from 52, and then from each remainder. . Sabtract 5 from 50, and then from each remainder. . Subtract 6 from 54, and then from each remainder. | . Subtract T from 56, and then from each remainder. . Subtract 8 from 56, and then from each remainder. . Subtract 9 from 54, and then from each remainder. . Subtract 10 from 50, and then from each remainder. . Add 1 to 50, and to the sum, as far as 100, . Add 2 to 50, and to the sum, as far as 100. . Add 3 to 50, and to the sum, as far as 100. . Subtract 1 from each number from 100 down to 50. . Subtract 2 from each number from 100 down to 50. . Subtract 3 from each number from 100 down to 50. ik How many 2’s are there? How many 3’s are there? How many 4’s are there? How many 5’s are there? How many 6’s are there? How many 7’s are there? How many 8’s are there? How many 9’s are there? How inany 10’s are there? Do the same in addition and subtraction, for each of READING FIGURES. 105 LESSON IX. MULTIPLICATION BY THE EYE. SS Bee. Sey eee ee: ee eae eee Hh aS | Si SRR: TS SS FP A AE nm ee eee ows Ce CO. ae a ae Ze me Ro Ce ee epee OO EES Read mm eee 0 0 2 0 3 a 4 0 fie 0 ite 0 ah 0 8 0 iD 0 10 106 READING FIGURES. ———— a LESSON X. DIVISTON BY THE 2k YE. Le : Se: a See ae ORR pa eee ts 8 Bee. 19 ae tee B23 OWN 12 We 18-81 4 Oy BO W)4 OB 18" 16) 20) 24 28 82) Sh cad By Googe) By 867.46 . 54 163) 128 Seee 10)10 20 30 40 50 60 70 80 90 100 Gu (ay (8) (4) (5) (6) |e 2)24 2)36 2) 1938. 2)428 2) 362 2) 486 | | Bee ety ode GD). agg GAO) ans 4)86 8) 126 8) 96 8)42 8) 25a (12) (13) (14) (15) (16) 448 4)28 4) 2484) B44) 16 f (1) 1) 61 (6) 2) 16 (iL) 5) 21 (16) 4) 124 (20) - Bah) 105 (24) 6) 216 (28) v)an7 (32) 8) 968 (36) 9) 819 READING FIGURES. LESSON XI. DIVISION BY THE EYE. (2) (3) (4) 1) 45 1) 28 1) 29 (9) 2) 86 (14) 3) 672 (7) (8) Hie (13) #) 129 (12) 3) 66 (18) (17) 5 4) 484 (22) 5) 360 (26) 6 ) 504 (30) 7) 966 __ PB. (34) 8) 728 (38) 9) 459 (5) 1) 40 (10) 2) 90 (15) 3) 201 (19) +) 368 (23) 5) 215 (27) 6) 954 ya —T) 815 (35) 8) 488 (39) 9) 648