COUNTlfcw B^>' 
 
THOMSON'S NEW MATHEMATICAL .SFRIES. 
 
 ILLUSTRATED 
 
 TABLE-BOOK, 
 
 OR 
 
 JUVENILE ARITHMETIC, 
 
 CONTAINING 
 
 ORAL AND SLATE EXERCISES 
 
 FOR 
 
 BEGINNERS. 
 
 BY JAMES B. THOMSON, LL.D., 
 
 -tW GRADED SERIES OK ARITHMETICS, PRACTICAL ALGEBRA^SETC. 
 
 NEW YORK: 
 CLARK & MAYNARD, PUBLISHE 
 
 5 BARCLAY STREET, 
 1880. 
 
THOMSON'S.- MATHEMATICAL 'SERIES. 
 
 I. A Graded Series of Arithmetics, in three Books, ; 
 
 New Illustrated Table Book, or Juvenile Arithmetic. 
 
 oral and >. :ses. (For begh. 
 
 New Rudiments of Arithmetic. < '..muihiu^ Mental with V. 
 t.-n Arithniftic. (For Iuterim-J,i:ite Classes.) 
 
 New Practical Arithmetic. Adupti-d \<> a romplete business 
 -du. ;. r Qraamuur Departments.) Ub' 
 
 II. Independent Books. 
 
 Key to New Practical Arithmetic. < ..ntainiii^ ;able 
 
 (For teac 
 
 New Mental Arithmetic. pie and ('<>iu- 
 
 il".r I'riitmry Scliools.) 144pp. 
 
 Complete Intellectual Arithmetic. Specially adapted to (.'looses 
 : ammar Schools and Academies. 168 pp. 
 
 III. Supplementary Course. 
 New Practical Algebra. Adapted to Hiirli S.hoola and Acad- 
 
 Key to New Practical Algebra. \Vitl full ! For 
 
 ! pp. 
 
 New Collegiate Algebra. 
 Complete Higher Arithn. |in-|.anu, 
 
 ' 
 
 IfO*. hy JAFJ II. 
 
PREFACE. 
 
 IN order to pursue the study of Arithmetic with pleasure and 
 success, two things are essential. First, the elementary princi- 
 ples and 7 \ilile* must be thoroughly understood; Second, their 
 application mu> perfectly familiar. 
 
 The Raised Table Book is designed to assist both the teacher 
 and the pupil in the accomplish in ent of these important ends. 
 It is constructed on the following plan : 
 
 1. As soon as a child learns a fact or principle in arithmetic, 
 he is taught it.s nintH'-ilion, and begins to practice it. In this 
 \v.iy an inter -st is awakened in the subject, and the pupil is 
 
 1 from the irks nneness of learning and repeating i t ]y- 
 stract results and principles, while i'juorant of their nature and 
 use. 
 
 2. The pupil is taught to iUuttrate and/arm the Simple Tables 
 for himself. A child g-iins a much ele.-irer idea of a thing by 
 (1 -i:iu r it himself, than by having his teacher do it for him. 
 
 3. Alternate Mental and Slate Exercises are inters-;' 
 
 iiout the book. These exercises are carefully adapted to 
 
 the capacity of beginners, and to the principles they are designed 
 
 to illustrate. They should therefore l>e made perfectly familiar 
 
 . // either at home or at school. In this 
 
 w.iy the pupil will learn how to study, how to think, and how to 
 
 4 Sp.-1-inl pnin. have been taken to correct the Tables of 
 11', i/hfH ,,<l Mi'iimirt'*, according to present Law and usage ; the 
 o!>s Y.ctr denominations sin-.l those not used in the Unitrd Stairs 
 I carefully excluded. 
 
 191 
 
k . . , ; PREFACE. 
 
 -l&ginnere in Arithmetic should be furnished 
 : irf table*. '(oob ; fl/8laui blackboards, numeral IV 
 
 .duntrng- toartfe,^ etc. , and bt > 
 
 learning to count, and in illustrating the elementary cor 
 tions and principles <>t numbers. 
 
 MT(ibU objfct*u*ed for counters, or unit marks made ! 
 pupil uj*>n a slate or blackboard, are pr.-f. Table to the fated 
 seen in pictures, or the stationary numbers r 
 
 _rht lines, or other unit marks upon charts and 
 wall maps. 
 
 Tli. a BOARD is a new and valuable acces 
 
 api>aratii8 of primary schools. Its length d< M the 
 
 the recitation r-xn!!. an.l tljenunilHT 'ntheclttfc 
 Wli'ii placed apainst the wall, its wi.l :iy fn>m i = 
 
 - ; the upj>er surface i : narks 
 <>r >r rij* of wood ; the edges are faced with a plain mou 
 raised sufficiently to prevent the counters from rolling off. If 
 placed in tin- middle of the roov 
 
 to allow pupils to stand on >r.) 
 
 NEW YORK, August, 1874. 
 
 NOT I . 
 
 THE few changes in the fore part of this 
 
 it it* use in com ' 
 ions, 
 iiibcr, 1877. 
 
COUNTING, i 
 
 LESSON I. 
 
 i. How many of these little girls an^ boys wish to 
 learn to count ? All that do may hoW up a hand. 
 
 / 
 
 2. How many hands dm-.s rach hold 
 
 3. How many are one hand and one hand ? 
 Two. 
 
 4. Hmv many hands have you ? How many feet ? 
 
 5. liu\v numy arc two pencils and one pencil? 
 Three. 
 
N T 1 V 
 
 "" 6.' h'o\v 1110 throo lingers and count thrin, 
 
 7. \\hicli is y.ur ri,L r ht hand ? \\hich your left ? 
 
 8. Ilo\\ many thumbs liavr Y..U <>n your ri-hi 1;.. 
 How many on your left hand ? 
 
 9. How many on both ? 
 
 10. How many an- t\\o liners and one 
 u. Three is how many m<m than i 
 
 LESSON II. 
 
 To TEACHERS.-.* child learns much tester by dotng or 
 thing, than by simply nptatl*g an explanation which he hears, bat does 
 not understand. Hence, the pupil at every exercise, should be called upon 
 to do as much as possible with his own hands. This is the only way to In- 
 sure rapid progress and a thorough knowledge of numbers. 
 
 1. L- t tach show me two fingers. 'I irere. 
 
 2. (Map your hand- thnr time- in 
 ^. \Y1;;;' 
 
 4. Three is how many more 
 
 with your fingers. 
 
 5. ('mint tluvr. iM-iitin.ir lime with 'it hand. 
 
 6. Count from three back 
 
 7. Each show t! .: Xow 
 the oth. 
 
 8. How many are three fingers and on< 
 Pbur. 
 
 9. How many are three pencils and .-il? 
 
 10. (Map your ha: 
 
 11. \Vh. after \\\ 
 
 12. II -\\ man\ BlOPe than three is ft.ur? Than one? 
 i; v What e >ur? Hef uv thn 
 
 14. Count from four >:ic. 
 
r T N T I N (J . 7 
 
 15. How many lingers on your left hand? '-Four." 
 
 16. Count your thumb with them; how many? 
 Fire. 
 
 17. Count five in concert, beating time. 
 
 1 8. Count from five hack to one. Twice more. 
 
 LESSON III. 
 
 1. When we say one, two, three, four, &c., what is it 
 called ? 
 
 Counting. 
 
 2. Count five in concert, beating time. 
 
 3. Rap on your slate with your pencil five times. 
 
 4. Copy the figures used to express the first five 
 numbers, as I make them upon the blackboard. 
 
 i, 2, 3, 4, 5. 
 
 one, two, three, four, five. 
 
 5. Five is how many more than four? Show it. 
 fj. Show by your fingers how many things are 
 denoted by the figure 3. By 2. By 4. By 5. 
 
 I ' & 
 
8 
 
 7. George may make live stiaiirht marks upon tlio 
 blackboard : tin- others, oil their .-!;. 
 
 8. Count thm. pointing to cadi. 
 
 9. Make another; how many have \ou now? 
 
 fffo. 
 
 10. Count six in concert, beating tinn i . 
 
 1 1. Show me six fingers. 
 
 12. Make six raps on your slate with your pencil. 
 
 13. > \ many more than five? Shov 
 
 1 4. Six is how many more than one ? 
 
 15. What co i. before si 
 
 Before four? Before thrc. re two? 
 
 1 6. Count from six back to one. 
 
 LESSON IV. 
 
 To TEACH***. The division into k^on< i- not for the pnrpo> of fixing 
 the daily task of pupils, bat to point out the pr 
 
 be tMght conw-cot ivelj. It may be nocewwry to subd 
 them into tererml recitation*. Bat however thio may be. the cUu-n should 
 not bo permitted to POM from one to the next, till the former la thoroughly 
 understood. 
 
 i. Here is a pile of six books; if I put aim; 
 
 them, how many will ii 
 
 .S >'<'H. 
 
 >unt seven in concert, beat in <r 
 
 3. Who can count srv-n alone promptly? II 
 may try. Carrie. William. Louise. 
 
 4. Let cadi j?how me ^even fin_ 
 
 5. Count from seven 
 
 6. Seven i> h>\\ many more QafB 
 
 7. Show it by I'onnti 
 
co u NT i x <;. 9 
 
 8. Seven is how many more than one V 
 
 9. Make seven unit marks upon your slates. 
 
 10. How many are seven pencils and one pencil? 
 Eight. 
 
 11. Count eight in concert, beating time. 
 
 1 2. Let each count eight alone. (The teacher names 
 individuals.) 
 
 13. Make eight raps on your slute with your pencil? 
 
 14. Eight is how many more than seven? 
 
 15. Show it by count* 
 
 16. Eight is how many more than one? 
 
 17. Count from eight back to one. 
 
 18. How many are eight counters and one counter? 
 
 19. Count nine in concert, beating time. 
 
 20. Show me nine objects. 
 
 21. What comes next before nine? Next before 
 eight? Before seven? Before six? Before live? 
 Before four ? Before three ? 
 
 22. Count from five to nine, inclusive. 
 
 23. How many are nine cents and one cent more? 
 Ten. 
 
 24. How many fingers and thumbs has each ? 
 
 25. Count ten, beating time? 
 
 26. Write the figures denoting six, seven, eight, nine, 
 ten. 
 
 6, 7, 8, 9, 10. 
 
 rix, leven, eight, nine, ten. 
 
 27. Show by marks upon your slate how many things 
 are denoted by the figure 6. By the figure 8. By the 
 figure 7. By the figure 9. 
 
10 
 
 > r N T : 
 
 LESSON V. 
 
 i. fount tlio ! a!N on tin- iipjcr wire of tin- Xni: 
 Frame, as I move them from left to right. 1 1 
 
 I 
 many will it make rnmih-il wit 
 
 ; v It'I ni.vi- two on the nc\i. h>\v many 
 
 4. If tlmr lulls nn t .u in;n: 
 
 5. If four bails on the next, h>\\ numy - 
 
 6. If fi'. >.;. h..\v many ': 
 ~. IT "ii tli- next, hiixv niair 
 
c o r x T i x G . 11 
 
 8. If seven bulls on the next, ho\v miuiy '' 
 
 9. If eight balls on the next, how many ? Eighteen. 
 
 10. If nine balls on the next, how many ? Nineteen. 
 
 11. If ten balls on the next, how many? Twenty. 
 
 LESSON VI. 
 
 1. What comes next after ten ? "Eleven." 
 
 2. Eleven is how many moiv than ten? "One." 
 
 3. How represent eleven by the Numeral Frame? 
 J//.v. By moving across ten balls on the upper 
 
 wire and one on the next. 
 
 4. What comes next after eleven ? 
 
 5. Twelve is how many more than eleven ? 
 
 6. How represent twelve by the Numeral Frame ? 
 Ans. By the ten balls on the upper wire and two 
 
 on another. 
 
 7. What comes next after twelve ? 
 
 8. Thirteen islmw manymore than twelve? Than ten? 
 
 9. How show that thirteen is three more than ten V 
 Ans. By the ten balls on the upper wire and three 
 
 on another. 
 
 10. The meaning of the word thirteen? 
 Ans. Three and ten. 
 
 11. What comes next after thirteen ? 
 
 12. The meaning of the word fourteen? 
 Ans. Four and ten. 
 
 13. How show that fourteen is four more than ten? 
 
 14. What comes next after fourteen ? 
 
 15. The meaning of the word fifteen? 
 Ann. Five and ten. 
 
1'.' n r x T i x <; . 
 
 16. How show that lii'uvn is live move than ten? 
 
 17. What conies n-xt after lift. n r 
 
 18. The meaning nf tin- \\nnl M.Meen? 
 
 . Six and i.-n. 
 
 19. How show that >i\t<vn is six in>iv than 
 
 20. Wh next a'u een? 
 
 21. Next aft- a? Afti-r n 
 
 22. Count from ten to twenty, u-atiiiLr ; 
 
 23. \\\\. 
 
 . Two tons. 
 
 24. Write i: ,vc., to fifteen. 
 
 , 12, 13, 14, 15. 
 
 eleven, Uelw, thirl**, fovtcea, fiftwa. 
 
 25. What comes next after 13? After n? After 14? 
 After 
 
 26. Wliic-h is th. ;i..\v 
 show 
 
 27. Write the figures denoting sixt 
 
 16, 17, 18, 19, 20. 
 
 liiteeo, WTfnUfn, elghteo, ninetwa, tu 
 
 28. Which is the greater, seventeen or 
 
 Sli\v it. 
 
 29. Which is the greater, nineteen or eighh 
 
 30. Write in liirurrs thin 
 
 ixti'i-n. fU'vi'ii. t\\ 
 
 ^y Haviiiir h-arncd to cf)tint ton, childron will easily l.-nrn to 
 count from U-n ler\-ing that after twd\ 
 
 names of the successive nuinlKTs arc formed by prefixing the 
 names of the numlx-rs. three, four. live, six, A;- 
 to teen or ten. They will also find great assistance 
 liendiiiir the meuniiii: f the terms from ten t> a hui.ilrcd by 
 dirertinir attention to their dcrivution. 
 
COUNTING. 13 
 
 LESSON VII. 
 
 1. What does the word twenty denote ? 
 A H*. Twenty denotes two tens. 
 
 2. How is twenty written ? 
 
 Ans. By writing 2 in the second place, with a 
 cipher on the right ; as, 20. 
 
 3. Count the marks, as I make them upon the black- 
 board; how many ? "Ten." 
 
 4. Count on, us 1 make another row. " Twenty." 
 
 5. If I make another, how many? "Twenty-one." 
 
 6. If I make another, how many ? " Twenty-two." 
 
 7. If another, how many ? "Twenty-three." 
 
 8. If another, how many? "Twenty-four." 
 
 9. If another, how many? "Twenty-live." 
 10. If another, how many ? "Twenty-six." 
 n. If another, how many? "Twenty-seven." 
 
 12. If another, how many? " Twenty-eiirht..'' 
 
 13. If another, how many? "Twenty-nine." 
 
 14. If another, how many ? "Thirty." 
 
 15. Twenty-one is how many more than twenty? 
 
 16. Twenty-two is how many more than twenty? 
 
 17. Twenty-live, than twenty? Show it. 
 
 18. Twenty-seven, than twenty? Show it. 
 
 19. Thirty is how many more ihun twenty? Show it. 
 
 20. Count from twenty to thirty in concert. 
 
 21. Write the ligures denoting twenty-one, i \\vnty- 
 two, &c., to thirty. 
 
 22. What do the figures 23 standing side by side- 
 denote? What 25? What 27? What 26? What 
 29? What 28? What 22? 
 
14 <_ u L N T 1 X r . 
 
 LESSON VIM. 
 
 i. What i> i lu- niranincr of the word thirty? 
 
 Ails. Thirty denotes ////</ /<//*. 
 \ 2. llo\v is thirty expre- 
 
 . 1'y writing 3 in the second place with a 
 cipher on the right ; as, 30. 
 
 3. Count from thirty to forty. 
 
 4. Write in tiguivs thirty-one, &a, to f 
 
 5. Count fn>m forty to fifty, in like manner. 
 
 6. Write in : i-.iin forty to lifty. 
 
 7. Wiiat do the li- iigure834? 
 
 -? 43? 48? 50? 
 
 8. Count from lifty to >i\ty. In-iti; 
 
 9. Hake tlu- iiirurc's ill-noting tifty-three? 
 seven ? Fittv-ti\-? Fifty-i-i- 
 
 10. What do the tiiim- 52, denote? 54? 56? 59? 
 
 11. Count from sixty to seventy, i:, 
 
 12. Write the figures from sixty to E 
 
 13. Count from seventy to eigh 
 
 14. Make tl 
 three. Seven ty-ti\. 
 
 15. Count from eighty to nin 
 
 16. Write the figures from eighty to ninety. 
 
 17. Count from ninety to a Innul: 
 
 18. Write tli- .roni ninety to a hundi- 
 
 19. Wliat do the iiLTii: t0Y What 
 Ans. The figures 12, denote i ten and .? I 
 
 21 denotes j tens and i unit. 
 
 jo. What do t lie figures 34 denote ? 47? 63? 
 SSi" <;;,? ioo? 
 
COU.X1ING. 15 
 
 LESSON IX. 
 
 To TEACHERS. Ae i?oon as children have learned to count and write one 
 hundred with accuracy, they will find no difficulty in counting and writing 
 larger numbers. 
 
 1. Count from one hundred to one hundred and ten. 
 
 2. Write the figures from one hundred to one hun- 
 dred and ten. 
 
 100, 101, 102, 103, 104, 105, 106, 107, io8cVOQd 
 
 3. IIow is one hundred and ten expressed t 
 
 A/i*. Hy writing i in the third place, i in the 
 second, and a cipher in the first ; as, no. 
 
 4. Count from one hundred and ten to one hun- 
 dred and twenty. 
 
 "One hundred eleven, one hundred twelve, &c." 
 
 5. Write in figures from no to one hundred twenty. 
 
 in, 112, 113, 114, 115, 116, 117, 118, 119, 120. 
 
 6. Count from one hundred twenty to one hundred 
 thirty, in like manner. 
 
 7. Count from one hundred thirty to one hundred 
 forty, and so on to two hundr-'d. 
 
 8. Write in figures one hundred thirty. One thirty- 
 seven. One thirty-nine. 
 
 9. Write in figures each decade from 140 to 200. 
 10. What do the figures 135, denote? 
 
 .I//*. One hundred, 3 tens, and 5 units. 
 
 n. What do the figures 124, denote? 136? 140? 
 159? 
 
 12. What do the figure- 160, denote? 177? 185? 
 188? 190? 199? 200? 
 
1G C O U X T 1 N G. 
 
 LESSON X. 
 
 1. I low is two hundred expressed by figure 
 Ans. By writing 2 in the third place, wit 1 
 
 ciphers on the 1 ri:rht ; as, 200. 
 
 2. How cxpr.-ss three hundred ? Four hundred, Ac., 
 t< nine hundred 'i 
 
 3. W rile in figures two hundred and ten. Two hun- 
 dred ;md twenty. &<.. to three linndred. 
 
 4. Write three linndred Mveniy-ihe. Three hn; 
 iorty-.-ix. Three hundred iit'iy-iniir. 
 
 5. Write five liundn-d t\vi'iity-sc\ 
 t'iirht. Five forty-six. Fivesixty-i 
 
 6. Write six hundred thirty-! 
 Six fifty-tun. >e\en nineM-toiir. 
 
 7. Write nine hundred iii'teen. Nine twenty-* 
 Nine torty-tli roe. Nine sixty. Nine ninety-nine. 
 
 8. What do the figures 235, denote? 
 Ann. 2 hundreds, 3 tens, and 5 units. 
 
 9. What do the figures in 346, denote ? In 378 ? 
 < . and read the following numbers: 
 
 j. 408. 10. 525. 19. 703. 
 
 2. 310. II. 405. 20. 890. 
 
 3. 101. 12. 239. tl, 875. 
 
 4. 230. 13. 350. 22. 940. 
 
 5- '75- M- 475- 23- 963- 
 
 6. 240. 15. 509. 24. 893. 
 
 7. 301. 16. 643. 
 
 17. 538. 26. 990. 
 
 9. 305. 1 8. 720. 27. 1000. 
 
 (For explanation of terms, sec p. 40.) 
 
ADDITION TABLES. 
 
 LESSON I. 
 
 To TEACHERS. The present Lesson consists in adding the unit one to the 
 
 several digits in succession. As the results correspond with the regular in- 
 
 of numbers by counting, they need no further illustration. The 
 
 object of the next ei<,'ht k-sons is to fiamiliartee the learner with the addition 
 
 of the other digits to each other. 
 
 and I are I. 5 and 
 
 1 " I " 2. 6 " 
 
 2 I 3 . 7 " 
 
 3 - i 4. 8 
 
 are 6. 
 
 " 7- 
 
 " 8. 
 
 " 9- 
 
 10. 
 
 4 l 5- 9 
 
 1. If you have three pears and I give you one pe;ir, 
 how many pears will you have r* 
 
 SOLUTION. Three pears and i pear are 4 pears. 
 
 2. How many are 4 apples and i apple ? Show it 
 with your fingers. 
 
 3. How many are 5 pencils and i pencil ? Show it. 
 
 4. George had 6 cents and earned i more : how numy 
 had he then ? 
 
 5. How many are 7 marbles and i marble? Show it. 
 
 6. Eight tops and i top are how many ? Show it. 
 
 7. If a teacher has 9 roses and a pupil gives her i 
 more, how many roses will she have ? 
 
 8. Write the following numbers in figures : Thirteen, 
 eleven, nineteen, twenty, twenty-five, thirty, and forty. 
 
 2 
 

 
 and 
 
 2 
 
 are 
 
 2. 
 
 5 
 
 I 
 
 *< 
 
 2 
 
 u 
 
 
 6 
 
 2 
 
 .. 
 
 2 
 
 
 4- 
 
 7 
 
 3 
 
 M 
 
 2 
 
 
 5- 
 
 8 
 
 1 - ADDITION. 
 
 LESSON II. 
 
 To TKAcmcB*.-Tbe Addition Table of) may be illustrated thoa: 
 
 :j: ind :: :*: an- / ; 
 : # and :*: :: 
 
 "i* ' * .|lul *4? *if 
 
 y * ^ tlllVA (r^ ** 
 
 ' .*:' :'- :: and ^ * * k *, &c. 
 
 Let the elans nniah the illwtration, writing the table out in full. 
 
 and 2 are J. 
 
 10. 
 
 4 " 2 " 6. 9 " 2 " ii. 
 
 1. If ("Jrori;.- ha- 4 ]>mcils and ln\- 2 more, hoW 
 many pencils will he h; 
 
 - 
 
 2. How many are 3 slates and 2 slates : 
 
 .;. How many are 5 hats and 2 hats? Sliou 
 
 4. How many are 6 roses and 2 roses? 
 
 How many an- S cherries and 2 chcr 
 
 6. Add 2 to itself continually, till the sum is 50. 
 
 y and add the following : 
 (7 .) (8.) (9.) (10.) u.) (12.) (. 
 
 I I I 2 2 I 2 I 
 
 2221 I 2 I 
 
 3465728 
 
 r As Mwn a* the combination* of the digite are andcrMood. they 
 fhould be PO thoroughly flxM in the memory, that when any result is re- 
 quired, it should instantly flash upon the mind. 
 
A D D 1 T I X . 19 
 
 LESSON III. 
 
 and 3 are 3. 5 and 3 are 8. 
 
 1 " 3 " 4- 6 3 " 9. 
 
 2 3 " 5- 7 " 3 " I0 - 
 
 3 3 " 6. 8 " 3 " ii. 
 
 4 " 3 " 7- 9 " 3 " 12. 
 
 1. How many are 4 boys and 3 boys? Show it. 
 
 2. How many are 5 needles and 3 needles ? Show it. 
 
 3. George has 3 flowers in one hand and 6 in the 
 other: how many has he in both hands? 
 
 4. 3 cents and 9 cents are how many cents? 
 
 5. 7 knives and 3 knives are how many ? 
 
 6. If 8 chickens are under the coop and 3 outside of 
 it. how many chickens are there in all ? 
 
 7. Harry's kite line is 9 yards long: if he ties on 
 3 yards more, how long will it then be? 
 
 8. Add 3 to itself continually, till the sum is 60. 
 
 9. What is uniting two or more numbers in one, 
 called ? 
 
 Addition* 
 
 10. What is the result or number obtained called? 
 The Suui or Amount. 
 
 11. When we say 2 and i are 3 and 2 are 5, which 
 is the sum ? 
 
 Copy and add the following : 
 (12.) (13.) (14.) (15.) (16.) (17.) (18.) (19-) 
 
 2 I 232223 
 
 3 3 3 3 3 3 ' i 
 45 346789 
 
A I) I) 1 T 10 N. 
 
 LESSON IV. 
 
 
 
 ..M.l 
 
 4 
 
 re 
 
 4- 
 
 5 
 
 and 
 
 4 
 
 rr 
 
 9- 
 
 I 
 
 .. 
 
 4 
 
 .. 
 
 5- 
 
 6 
 
 U 
 
 4 
 
 .. 
 
 10. 
 
 2 
 
 ft 
 
 4 
 
 
 
 6. 
 
 7 
 
 .. 
 
 4 
 
 * 
 
 i i. 
 
 3 
 
 flf 
 
 4 
 
 H 
 
 7- 
 
 8 
 
 
 4 
 
 
 
 4 
 
 ft 
 
 4 
 
 M 
 
 s. 
 
 9 
 
 .. 
 
 4 
 
 t( 
 
 
 i II v, many are 4 grapes and 5 grapes? 
 
 2. Charles has 4 credits: bow many U\UA \ 
 have 7 ? 
 
 3. 4 and what number are 6? 
 
 1 f you lia < I tits and buy 4 more, how many 
 
 will you thru huve? 
 
 5. How many arc 9 cents and 4 cents? 
 
 6. 7 ducks and 4 ducks are how many ? 
 
 7. Uilliain has 4 apples and (Jeorge has 4 11: 
 William: how many has Geor^: 
 
 8. How many are 8 girls and 4 gir 
 
 9. Julia has 4 peaches and 1 -iv than 
 .Tnlia : how many has Fain 
 
 10. How many are 9 tops and 4 tops? 
 
 1 1. Add 4 to i!>i'lf continually till the sum is 60. 
 
 Copy and add the following: 
 (12.) (13.) (14.) (15.) (16.) (17.) (i 
 
 I 2234323 
 21432144 
 
 3 4 3 2 l 4 i 
 43242342 
 54 6 7 Q 
 
A 1) D I T I O X . '.' I 
 
 LESSON V. 
 
 and 5 are 5' 5 au( l 5 ar * 1O ' 
 
 1 " 5 " 6. 6 " 5 " ii. 
 
 2 " 5 " 7- 7 " 5 " 12. 
 
 3 " 5 " 8. 8 " 5 " 13. 
 
 4 5 9 . 9 5 14. 
 
 1. 5 pencils and 3 pencils are how many? 
 
 2. 5 apples and 4 apples are how many ? 
 
 3. There are 5 birds on one tree and 5 on another : 
 how many birds are on both trees? 
 
 4. On one rose-bush are 6 buds, and on another 5 : 
 how many buds are on both ? 
 
 5. How many are 5 trunks and 7 trunks? 
 
 6. How many are S guns and 5 guns? 
 
 7. Moses wrote 9 lines and Margaret 5 lines: how 
 many lines did both write? 
 
 8. Add 5 to itself continually, till the sum is 60. 
 
 9. How many are ii and 5? 12 and 5? 14 and 
 5? 13 and 5? 16 and 5? 15 and 5? iSands? 
 17 and 5 ? 19 and 5? 
 
 10. Write the following in figures: Forty-nine, Fifty- 
 two, Sixty-seven, Eighty-one, Seventy-four, Eighty-six, 
 One hundred and fifteen. 
 
 Copy and add the following : 
 (n.) "(12.) (13.) (14.) (15.) (16.) (17.) (18.) 
 
 2 
 
 2 
 
 4 
 
 2 
 
 4 
 
 4 
 
 2 
 
 4 
 
 3 
 
 I 
 
 2 
 
 3 
 
 3 
 
 i 
 
 4 
 
 2 
 
 2 
 
 3 
 
 3 
 
 5 
 
 i 
 
 2 
 
 5 
 
 3 
 
 5 
 
 5 
 
 5 
 
 4 
 
 2 
 
 5 
 
 3 
 
 5 
 
 
 
 4^ 
 
 A 
 
 2 
 
 5 
 
 3_ 
 
 4 
 
 2 
 i-.- 
 
A D D 1 1 1 ' N . 
 
 LESSON VI. 
 
 and 6 are 5 and 6 are 1 I. 
 
 1 " o " 7. 6"6 - 12, 
 
 2 " 6 " 8. 7 " 6 
 
 3 " 6 8 " 6 
 
 4 6 " 10. 9 " 6 
 
 1. H.'W many are 5 dollars and 6 dolla: 
 
 2. If yon have 6 pears and buy 4 more, how many 
 will you thru ha\ 
 
 j, 11 u many are 10 melons and 6 mel 
 
 4. It' you pick 6 peaches from ODI ind 7 from 
 
 now many \\\\\ yoi, 
 
 5. If there are 8 birds on a tree, and 6 mo: 
 .1, how many arc there in all !' 
 
 6. George paid 6 cents for a ball, and 6 cents f 
 orange : how many cents did he pay for both ? 
 
 7. Add 6 to itself cjnitinually, till i Ifl 60. 
 
 8. Express Forty-four in figareh, 
 
 . Eighty-t 
 
 9. How mai 13 and 6? 1431 
 
 12 and 6? 15 and 6? 17 and 6? i6and6? 18 
 and 6? 19 and 6? 
 
 :d add the following: 
 
 (10.) (II.) (12.) (I 3 .) (I4-) (I5-) (16.) (I?-) (13.) 
 
 5 
 
 4 2 
 
 5 3 
 
 6 6 
 
 3 4 
 
 4 
 
 3 
 
 2 
 
 4 
 
 2 
 
 5 
 
 
 3 
 
 5 
 
 4 
 
 3 
 
 4 
 
 4 
 
 5 
 
 2 
 
 6 
 
 3 
 
 6 
 
 3 
 
 6 
 
 4 
 
 6 
 
 4 
 
 6 
 
 5 
 
 6 
 
 3 
 
 6 
 
 5 
 
 2 
 
 4 
 
 3 
 
 2 
 
 4 
 
 5 
 
ADDITION. 
 
 LESSON VII. 
 
 and 7 are 7. 5 and 7 are 12. 
 
 1 " 7 " 8. 6 " 7 " 13. 
 
 2 " 7 " 9. 7 " 7 " 14- 
 
 3 7 10. 8 7 "15. 
 
 4 " 7 " n. 9 " 7 " 16. 
 
 1. Sarah has 3 dolls, and Louise has 7 : how many 
 have both ? 
 
 2. 5 hats and 7 hats are how many ? 6 and 7 ? 
 
 3. George spent 4 cents for marbles, and 7 cents for 
 a sponge : how many cents did he spend in all ? 
 
 4. How many are 7 dollars and 5 dollars ? 8 and 7 ? 
 
 5. Charles obtained 12 credits in the morning, and 
 7 in the afternoon : how many had he in both ? 
 
 6. How many are 7 caps and 9 caps ? 
 
 7. George has 8 doves, and has sold 7 : how many 
 had he at first ? 
 
 8. Add 7 to itself till the sum is 70. 
 
 9. Express in figures, Fifty-nine, Seventy-eight, 
 Eighty-four, Sixty-two, Ninety-three, Ninety-seven. 
 
 10. How many are n and 7 ? 12 and 7 ? 14 and 
 7 ? 13 and 7 ? 15 and 7 ? 18 and 7 ? 19 and 7 ? 
 
 Copy and add the following : 
 
 (II.) 
 
 (12.) 
 
 (13.) 
 
 (14.) 
 
 (IS-) 
 
 (16.) 
 
 (170 
 
 (18.) 
 
 
 4 
 
 2 
 
 3 
 
 5 
 
 4 
 
 5 
 
 6 
 
 4 
 
 2 
 
 3 
 
 5 
 
 4 
 
 5 
 
 3 
 
 5 
 
 2 
 
 3 
 
 7 
 
 3 
 
 3 
 
 2 
 
 6 
 
 4 
 
 3 
 
 7 
 
 6 
 
 4 
 
 2 
 
 3 
 
 7 
 
 5 
 
 7 
 
 6 
 
 5 
 
 7 
 
 6 
 
 7 
 
 2 
 
 6 
 
 2 
 
 3 
 
 4 
 
 _3 
 
 4 
 
 _5 
 
 _4 
 
 J 
 
,'l A Ii I) I T I .. N " . 
 
 LESSON V I I I, 
 
 and 8 are 8. 5 and 8 AM 13. 
 
 1 8 " 9. 6 " 8 " 14. 
 
 2 u 8 " Jo. 7 " 8 " 15. 
 ' 3 8 " ii. 8 " 8 " 16. 
 
 4 " 8 u. 9 " 8 " 17. 
 
 1. .Tune hud 2 needles on IKT \vrk. and 8 ii; 
 needlcbook : how many had she in all 'i 
 
 2. Julia paid 8 cents for a thimMr. and 5 
 
 a spool of cotton : h<\v much did .-In- p.: M ? 
 
 3. How many are 7 yards and 8 y; and 8 ? 
 
 4. Edward bought figs for 6 cents, and cakes for 8 
 - : how much did he pay for Imih ? 
 
 manyaiv 4 IV-et and 8 : 
 
 6. One pupil gave the teacher 7 pinks, and an<>th r 
 gave 8 : how many did hot 
 
 Id 8 to itself t un is 80. 
 
 8. Write in figures, 1 
 
 ighty-eigi y-six, a IIiuu, 
 
 9. How many are 1 1 and 8 ? 13 and 8 r i2;md8? 
 14 and 8? 16 and 8? 15 and 8? 17 and S ? 19 
 
 8? 
 
 Copy and add the following : 
 
 (10.) \n.) (12.) (13.) (14.) (15.) (16.) (17.) 
 6s6245 66 
 54233375 
 3^355 47 
 438 2566 
 
 8845 7 
 
 A 5 1. - A 7 
 
ADDITION. :> 
 
 LESSON IX, 
 
 and 9 are 9. 5 ami 9 are 14. 
 
 1 9 10. 6 " 9 " 15. 
 
 2 " 9 " ii. 7 " 9 " 16. 
 
 3 " 9 " 12. 8 " 9 " 17. 
 
 4 " 9 " 13. 9 " 9 " 1 8. 
 
 NOTE. The first five numbers are easily added. The re- 
 sults of adding 9, being i less than if 10 were added, are also 
 easily remembered. The ethers, 6, 7, 8, are more difficult, and 
 therefore should receive *pc<'i<il < it tendon. 
 
 1. Charlotte solved 4 examples in Addition, and 9 
 in Subtraction : how many did she solve in all ? 
 
 2. James has 3 pears, and gave away 9 : how many 
 had he at first ? 
 
 3. How many are 6 books and 9 books ? 9 and 7 ? 
 
 4. 9 dollars and 5 dollars are how many dollars ? 
 
 5. Joseph played 5 games of checkers, and 9 games 
 of dominoes : how many games did he play in all ? 
 
 6. William is 8 years old : how old will he be 9 year* 
 hence ? 
 
 7. Helen has given away 9 apples, and has 6 left : 
 how many had she at first ? 
 
 8. Add 9 to itself, till the sum is 90. 
 Copy and add the following : 
 
 (9-) 
 
 (10.) 
 
 (n.) 
 
 (12.) 
 
 ( T 3-) 
 
 (140 
 
 (I5-) 
 
 (16. 
 
 8 
 
 5 
 
 8 
 
 5 
 
 6 
 
 8 
 
 7 
 
 9 
 
 7 
 
 9 
 
 5 
 
 6 
 
 5 
 
 7 
 
 8 
 
 6 
 
 7 
 
 5 
 
 4 
 
 7 
 
 7 
 
 5 
 
 7 
 
 8 
 
 5 
 
 8 
 
 6 
 
 9 
 
 3 
 
 9 
 
 6 
 
 7 
 
 9 
 
 7 
 
 9 
 
 4 
 
 9 
 
 7 
 
 8 
 
 9 
 
 4 
 
 6 
 
 3 
 
 7 
 
 8 
 
 6 
 
 7 
 
 <S 
 
;i; A Dli IT IK 
 
 LESSON X. 
 
 Oral l)i ill. 
 
 To TEACHERS. The object of this and other Oral Drill*, i to 
 accurate and rapid combinations. Each example should be continued 
 through the ti-n decades, and be dwelt upon till perfectly familiar. 
 
 1. How many arc 2 and 10? 12 and 10 ? 22 ami 
 10 ? 32 and 10 ? 42 and lo ? etc., to 92. 
 
 2. 2 and 2 ? 12 and 2 ? 22 and 2 ? etc., to 92. 
 .V i and 3 't ii and 3 !r 21 and 3, etc., to 
 
 4. 2 and 3 'i 12 and 3 '' 22 and 3, etc., to < 
 
 5. 3 and 3 ? 13 and ;, etc., to 96 ? 
 
 6. i and 4 ? 1 1 and 4 ? 21 and 4 ? 31 and 4 ? 
 
 7. 2 and 4 ? 12 and 4 ? 22 and 4 ? 32 and 
 
 8. 3 and 4 ? 13 and 4 ? 23 and 4 ? 33 . 
 
 9. 4 and 4 ? 14 and 4 ? 24 and 4 !" 34 and 4 ? 
 10. 3 and 10 ? 13 and 10 ? 23 and 10 ? etc, 
 
 1 1. 4 and 10 ? 14 and 10 ? 24 and 10 ? etc. 
 
 12. 5 and 10 ? 15 and 10 ? 25 and 10 ? . 
 
 13. f and 10 ? 16 and 10 ? 26 and 10 ? 
 
 14. 7 and 10 ? 17 and 10 ? 27 and 10 ? etc. 
 
 15. 8 and 10 ? 18 and 10 ? 28 and 10 ? etc. 
 
 16. 2 and 5 ? 12 and 5 ? 22 and 5 ? 32 and 5 '.' 
 
 1 7. 3 and 5 ? 13 and 5 ? 23 and 5 ? 33 and 5 ? etc. 
 18.4 and 5? 14 and 5 ? 24 and 5 ? 34 and 5 ? etc. 
 19. 5 and 5 ? 15 and 5 ? 25 and 5 ? 35 and 5 ? etc. 
 
 The Irnrwr will observe that the right hand figure <>f 
 flu- sinn *>f tw dibits in < \. ry decade, is always the same. 
 Thu*. 3 and 4 are 7 ; 13 and 4 are 17 ; 23 and 4 are 27, etc., the 
 ri^rht hand figure being ahv 
 
A D 1) 1 T I O N . Zi 
 
 LESSON XI. 
 
 1. How many are 2 and 6 ? 12 and 6 ? 22 and 6 ? 
 32 and 6? 42 and 6V 52 and 6? 62 and 6? 72 
 and 6? 82 and 6 ? 92 and 6 ? 
 
 2. 3 and 6 ? 13 and 6 ? 23 and 6 ? 33 and 6 ? etc. 
 
 3. 4 and 6 ? 14 and 6 ? 24 and 6 ? 34 and 6 ? etc. 
 
 4. 5 and 6 ? 15 and 6 ? 25 and 6 ? 35 and 6 ? etc. 
 
 5. 6 and 6 ? 16 and 6 ? 26 and 6 ? 36 and 6 ?'etc. 
 
 6. i and 5 ? n and 7 ? 21 and 7 ? 31 and 7 ? etc. 
 
 7. 2 and 7 ? 12 and 7 ? 22 and 7 ? 32 and 7 ? etc. 
 
 8. 3 and 7 ? 13 and 7 ? 23 and 7 ? 33 and 7 ? etc. 
 
 9. 4 and 7 ? 14 and 7 ? 24 and 7 ? 34 and 7 ? etc. 
 
 10. 5 and 7 ? 15 and 7 ? 25 and 7 ? 35 and 7 V i-lc. 
 
 1 1. 6 and 7 ? 16 and 7 ? 26 and 7 ? 36 and 7 ? etc. 
 
 12. 7 and 7 ? 17 and 7 ? 27 and 7 ? 47 and 7 ? etc. 
 
 13. nandS? 21 and 8? 31 and 8? 41 and 8 ? etc. 
 
 14. 2 and 8 ? 12 and 8 ? 22 and 8 ? 32 and 8 ? etc. 
 
 15. 3 and 8 ? 13 and 8 ? 23 and 8 ? 33 and 8 ? etc. 
 
 1 6. 4 and 8 ? 14 and 8 ? 24 and 8 ? 34 and 8 ? etc. 
 
 17. 5 and 8 ? 15 and 8 ? 25 and 8 ? 35 and 8? etc. 
 
 18. 6 and 8 ? 16 and 8 ? 26 and 8 ? 36 and 8 ? etc. 
 
 19. 7 and 8? 17 and 8? 27 and 8 ? 37 and 8? etc. 
 
 20. 8 and 8 ? 18 and 8 ? 28 and 8 ? 38 and 8 ? etc. 
 Write the following numbers in figures : 
 
 21. Fifty-seven, Sixty-eight, Eighty, Ninety-three, 
 One hundred and one, One hundred and ten. 
 
 Copy and read the following : 
 
 22. no 25. 139 28. 205 31. 480 
 
 23. 125 26. 203 29. 250 32. 308 
 
 24. 108 27. 230 30. 319 33. 500 
 
A 1) 1. 1 T I o N . 
 
 LESSON XII. 
 
 1. How many arc i and 9? n and 9 .- 19? 
 31 and 9? 41 and 9? 51 and 9? 61 and 9? 71 
 and 9 ? 81 and 9 ? 91 and 9 ? 
 
 2. 2 and 9? 12 and 9? 22 and 9? 32 anc 
 42 and 9 ? 52 and 9 ? 62 and 9 ? 72 and 
 
 3. 3 and 9 ? 13 and 9 ? 23 and 9 ? 33 and 9 ': 
 and 9? etc. 
 
 4. 4 and 9 ? 14 and 9 ? 24 and 9 ? 34 and 9? etc. 
 
 5. 5 and 9? 15 and 9? 25 and 9? 35 and 9? etc. 
 
 6. 6 and 9? 16 and 9 ? 26 and 9 ? 36 and 
 
 7. 7 and 9 ? 17 and 9? 27 I 
 
 8. 8 and 9 ? 18 and 9 ? 28 and 9 ? 3 - 
 
 9. 9 and 9 ? 19 and 9 ? 29 and 9 ? 3 
 
 10. Count by twtt till you reach 60. 
 four, six, eight, ten, t\\ 
 
 1 1. Count by 33 till you reach 60. 
 
 12. Count l>y 43 till you reach 60. 
 
 13. Count by 53 till you reach 60. 
 
 14. Count by 6s till you reach 60. 
 
 15. Count by 73 till you reach 70. 
 
 1 6. Count by 8s till you reach 80. 
 
 17. Count by 95 till you reach 90. 
 
 1 8. Count by los till you reach 100. 
 
 Copy and read the following : 
 
 19. 506 22. 883 25. 1,007 28. 32,368 
 
 20. 610 23. 915 26. 2,100 29. 
 
 21. 740 24. 999 27. 3,075 30. 568,073 
 r <^xplauation of terms iu Addition, see p. 48.) 
 
SUBTRACTION TABLES. 
 
 LESSON I. 
 
 To TEACHERS. The object of this Lesson i* to familiarize the learner 
 with the natural decrease of \hc first ten numbers. 
 
 from I leaves O. 
 
 I from 6 leaves 5* 
 
 " 2 I. 
 
 i " 7 " 6. 
 
 " 3 " 2. 
 
 i 8 " 7. 
 
 " 4 " 3- 
 
 i " 9 ' 8. 
 
 " 5 " 4- 
 
 I " 10 " 9. 
 
 1. Here arc 4 books: if I take i away, how many 
 will be left ? 
 
 SOLUTION. i book from 4 books leaves 3 books. 
 
 2. If George has 3 apples, and gives i to his sister, 
 how many will he have left ? 
 
 3. If Henry has 5 cents, and pays i cent for a pen- 
 cil, how many cents will he have left ? 
 
 4. James being asked how many marbles he had, 
 'vplied he had 6, lacking i : how many had he ? 
 
 5. If you have 8 pears, and eat i, how many will 
 you have left ? 
 
 6. One pen from 9 pens, leaves how many ? 
 
 7. James caught * butterflies, and i of them IU i \v 
 away : how many did he have left ? 
 
 8. i from 10 leaves how many ? i from 9 ? i from 
 6 ? i from 5 ? i from 4 ? i from 3 ? 
 
30 9 I IITK ACT [OH. 
 
 LESSON II. 
 
 To TEACHKRS. The class can readily iUn-innr ih- Snbtrnr ti<m Table of 
 2, in the following main 
 
 Make 2 marks (i i) ; cancel 2, none arc- Vk 
 
 " 3 " (in); cancel 2, one is l<Tf. 1% i. 
 
 " 4 " (i in); cancel 2, two are left, 1! 
 " 5 " (inn); cancel 2, three are lit. H. ii i. 
 
 Let the class continue the illustration, and write oat the Table, as below. 
 
 from 7 leave* 5. 
 
 " 8 " 6. 
 
 2 from 2 l at 
 
 0. 
 
 4 
 
 2 
 
 2 " 3 " 
 
 M 
 
 2 
 
 t " 4 " 
 
 z - 
 
 2 
 
 - " 5 " 
 
 iv 
 
 2 
 
 2 " 6 
 
 4- 
 
 2 
 
 10 " 
 
 11- 
 
 i. William had I, and pave 2 t his hi 
 
 many did he then hu\ 
 SOUJTION. 2 oranges from 5 oranges leave 3 oranges. 
 
 If you pay 3 cents I'm- -\ sponge, and sell i 1 
 2 cents, how m n c!i will you lose? 
 
 3. Two and what number aiv 7 ? 2 from 7 ? 
 
 4. Eight less 2 are how many ? 2 and 
 
 5. What nnmher is 2 less than 10? 2 more than 10? 
 
 6. Nine peaches less 2 peaches are how many ? 
 
 7. Two and what numhrr make 1 1 ' J . 
 
 8. "What is taking one number from another culled ? 
 Suhtrttction. 
 
 9. What is the result, or nuniher obtained, called ? 
 
 T/tf l>tff<'reif<-<' />/ Ift'iHfiiiiflci: 
 
 10. When we say 2 from 5 leaves 3, which is the re- 
 mainder? 
 
> I' BIB ACTION. 31 
 
 LESSON III. 
 
 3 from 3 leave* O. 3 from 8 leaves 5* 
 
 3 " 4 " i. 3 " 9 u 6. 
 
 3 " 5 " * 3 10 7. 
 
 3 " 6 " 3. 3 ii 8. 
 
 3*7*4- 3 " 12 9. 
 
 1. John started with 5 pencils, but on his way to 
 school lost 2 of them : how many did he then have ? 
 
 2. If you have 6 cents, and spend 3 cents, how many 
 cents will you have left ? 3 plus 6 ? 
 
 3. How many are 8 less 3 ? 8 plus 3 ? 
 
 4. Show each with your fingers. 
 
 5. How many more than 3 is 5 ? 
 
 6. Show each with your fingers. 
 
 7. If you obtain 3 credits in the morning, how many 
 must you get in the afternoon to make 10? 
 
 8. Surah lias 9 dollars, and her sister has only 3 : 
 how many more has one than the other ? 
 
 9. Susan having 9 cents, gave 3 of them to a pool- 
 child: ho\v many cents did she have then ? 
 
 10. Twelve marbles less 3 marbles are how many ? 
 
 11. Write in figures, One hundred and five, One 
 hundred and ten, One hundred and thirty, One hun- 
 dred and forty-one. 
 
 Copy and subtract the following : 
 
 (12.) (13.) (MO (-SO (us.) (?.) (i&) (19.) 
 
 12 13 14 13 16 17 18 19 
 33333333 
 
9VB T K A < 11' 
 
 LESSON IV. 
 
 -1 
 
 from 
 
 4 
 
 travel 
 
 0. 
 
 4 
 
 from 
 
 9 Irnvei 
 
 5- 
 
 4 
 
 tt 
 
 5 
 
 .. 
 
 I. 
 
 4 
 
 .. 
 
 10 
 
 6. 
 
 4 
 
 tt 
 
 6 
 
 tt 
 
 2. 
 
 4 
 
 U 
 
 II 
 
 ;. 
 
 4 
 
 (( 
 
 7 
 
 tt 
 
 3- 
 
 4 
 
 .. 
 
 12 
 
 K 
 
 4 
 
 tt 
 
 8 
 
 M 
 
 4- 
 
 4 
 
 tt 
 
 13 
 
 9- 
 
 1. If you have 7 plums, and give away 4 of tl 
 how many will remain ? Show it 
 
 2. If 4 pinks are taken from 6 pinks, how many will 
 remain ? Show it. 
 
 3. If Henry has 8 pin-wheels, and sells 4, how many 
 will he then have ? Show it 
 
 4. There are 10 balls on a wire of the nunu-nil t'i 
 if I move across 4, how many will remain ? 
 
 5. If there are 12 pupils in a class, and all are pci 
 I. ut 4, how many arc pi-rU-ct? 
 
 6. Charles had 9 chickens, but a hawk killed 4 : 
 many has he 1 
 
 7. How many are 7 pens less 4 pens? 
 
 8. How many are 10 boys less 4 bo 
 
 9. Amelia is 13 years old, and IK is 4 years 
 younger: how old is her sister? 
 
 10. Copy and read the following: 147, 175, 183, 196, 
 101, 105, 210, 213, 248, 260. 
 
 Copy and subtract the following: 
 (11.) (12.) (13.) (14.) (15.) (16.) (17.) (18.) 
 12 13 14 15 16 17 18 19 
 44444444 
 
SUBTRACTION. 
 
 33 
 
 LESSO N V, 
 
 fro i 
 
 5 Irnvc* O. 
 
 6 i. 
 
 7 " 2. 
 
 8 " 3- 
 
 9 " 4- 
 
 5 from IO lea-re* 5. 
 
 "n " 6. 
 
 " 12 " 7. 
 
 " 13 " 8. 
 
 (( 
 
 13 
 M 
 
 1. Homer had 8 rabbits, and has sold 5 : how many 
 has he now remaining ? 
 
 2. If you have 5 pins, how many more will make 10 ? 
 
 3. Five and what number make 7? Show it 
 
 4. Ten less 5 are how many ? 10 plus 5 ? 
 
 5. George caught n fish, which was 5 more than 
 his brother caught: how many did his brother catch? 
 
 6. How many are 1 1 less 5 ? 12 less 5 ? 
 
 7. What number taken from 9 leaves 5 ? 
 
 8. How many are 13 chestnuts less 5 chestnuts ? 
 
 9. The price of a slate is 12 cents, and an inkstand 
 5 cents : what is the difference in their prices ? 
 
 10. If you take 5 pears from a basket of 13 pears, 
 how many will remain ? 
 
 11. On a tree there were n pigeons, and a hunter 
 shot 5 of them : how many were left ? 
 
 12. Express in figures, Two hundred forty-five, Two 
 hundred sixty, One hundred eighty-three. 
 
 Copy and subtract the following : 
 
 (, 3 .) (14.) (15-) ('6.) (i?-) (18.) (19.) (^o.) 
 12 13 14 15 16 17 18 19 
 
 55555555 
 
34 -^ f U T H A i T I o N . 
 
 LESSON VI. 
 
 6 from 6 leaves O. < from 1 I leaves 5. 
 
 6 " 7 i. 6 " ;_ - 6. 
 
 6 S _. 6 " 13 
 
 6 " ij 6 " 14 
 
 * 10 " 4. " 15 
 
 1. A party of 12 1 ova were skating, and 6 
 i>roke through the ice: how many c&capi 
 
 2. A waiter dropped a pile of 9 plau-s, and ! 
 but 6 : how many did he bruik ? 
 
 3. If you pay 8 cents for a slate and sell it for 6 
 B, how much will you lose? 6 and 2 ? 
 
 4. IIow many are 10 quarts less 6 quar 
 
 5. Nine bananas less 6 bananas an- how many? 
 
 6. Eleven birds less 6 birds are how ma: 
 
 ;. The price of a hat is 6 dollars, and t u 
 
 dollars: what is the difference in their prif 
 
 8. Helen is 13 years old, and is 6 yearg o; 
 her brothor : how old is her brother ? 
 
 9. A certain class contained 15 pupils, 6 - 
 were girls : how many boys were th 
 
 10. George is now 15 years old: how old was he 6 
 ago ? 9 and 6 are how many ? 
 
 1 1. Copy and n-ad : 175, 290, 105, 210, 245, 209. 
 Copy and subtract the following : 
 
 12.) (13.) (14.) (I5-) (16.) (17.) (18.) (19.) 
 
 12 13 14 15 16 17 19 
 
 66 66666 
 
7 from 7 leaves O. 
 
 7 from 12 
 
 7 8 " i. 
 
 7 " 13 
 
 7 9 2. 
 
 7 " 14 
 
 7 " 10 " 3- 
 
 7 " 15 
 
 7 ii " 4. 
 
 7 " 16 
 
 SUBTRACTION. 35 
 
 LESSON VII. 
 
 leaves 5* 
 
 " 6. 
 
 " 7- 
 
 8. 
 
 " 9- 
 
 1. Edward bought a slate for 10 cents, and paiu 7 
 cents down : how much does he owe for it? 
 
 2. A lad having 12 eggs took them to marker, and 
 on his way broke all but 7 : how many did he break '{ 
 
 3. How many are n less 7 ? 12 plus 7 ? 
 
 4. If from a dish of 13 oranges, 7 are taken out, how 
 many will remain ? 7 and 6 are how many ? 
 
 5. Six from n leaves how many ? 6 from 13 ? 7 
 from 13? 7 from i o ? 7 from 1 1 V 
 
 6. Charles had 15 young doves, and a cat killed 7 of 
 them: how many did he then have ? 7 plus 8? 
 
 7. During the last 14 school days Julia has been 
 tardy 7 days: how many days has she been punctual ? 
 
 8. Twelve is how many more than 7 ? What num- 
 ber must be added to 7 to make 12 ? 
 
 9. If you have 16 cents and spend 7 of them for a 
 lunch, how many will remain? 
 
 ic. Seven tops from 16 tops leave how many ? 
 IT. K\|>ivs in figures. Five hundred, One thousand 
 six hundred, Four hundred thousand. 
 Copy and subtract the following: 
 
 (12.) (13.) (14.) (15.) (16.) (17.) (i 8.) (19.) 
 
 13 12 16 14 15 18 19 17 
 
 777777 7 7 
 
36 SUBTRACTION. 
 
 LESSON VIM. 
 
 8 from 8 leaves O. 8 from IJ Imvrs 5. 
 
 8 " 9 u i. 8 " 14 " 6. 
 
 8 " 10 " 2. 8 " 15 7. 
 
 8 " ii " 3. 8 " 16 
 
 8 " 12 4. 8 " 17 " 9. 
 
 1. James picked 13 quarts of chestnuts, and John 8 
 quarts: how many mmv did one pick than the other? 
 How many quarts did k ? 
 
 2. A father Lrave each of his two sons a garden s; 
 Ider sold his vegetahles for 12 dollars, the 
 
 sold his for 8 dollars: what was the dill 
 sums eacli received ? 
 
 3. If the older of two sisters is 16 years, and 
 younger 8 years, what is the difference in their ages? 
 
 4. Fourteen peaches less 3 peaches are how mat 
 
 5. Eight from 13 l-av.-s how nnnv ? s pin 
 
 6. A market woman bought 15 turkeys and sold 8 
 of thorn : how many had she on hah 
 
 7. If you walk 8 miles in the morning, how far must 
 you walk in the afternoon to make 15 miles? 
 
 8. Eight from 14, how many? 6 from 14 ? 
 
 9. George saved 8 yards of his kite line, which was 
 1 7 yards long : how many yards did he lose ? 
 
 10. Copy and read the following: 1510, 2620, 3 
 6659, 1870, 10,807, 25,977* 85,999, 100,000. 
 
 Copy and subtract the fallowing: 
 (n.) (12.) (13.) (14.) (15.) (16.) (17.) 
 12 13 15 16 14 17 
 88888888 
 
SUBTRACTION. 37 
 
 LESSON IX. 
 
 9 
 
 from 
 
 9 
 
 leaves 
 
 0. 
 
 9 
 
 from 
 
 14 
 
 leaves 
 
 5- 
 
 9 
 
 a 
 
 10 
 
 a 
 
 I. 
 
 9 
 
 a 
 
 15 
 
 (( 
 
 6. 
 
 9 
 
 a 
 
 ii 
 
 a 
 
 2. 
 
 9 
 
 ft 
 
 16 
 
 tt 
 
 7- 
 
 9 
 
 a 
 
 12 
 
 a 
 
 3- 
 
 9 
 
 H 
 
 i7 
 
 (t 
 
 8. 
 
 9 
 
 a 
 
 13 
 
 M 
 
 4- 
 
 9 
 
 (( 
 
 18 
 
 (t 
 
 9- 
 
 1. If you have 12 peanuts, how many cau you eat 
 and have 9 left ? 
 
 2. Fourteen pencils less 9 pencils are how many ? 
 14 slates less 8, are how many ? 8 plus 6 ? 
 
 3. If you have 15 cents, how many can you spend 
 and have 9 left ? 
 
 4. William had 16 cherries upon his tree, and the 
 birds took all but 9 : how many did they take? 
 
 5. Sarah bought 15 pink roots, 9 of which died: how 
 many lived ? 
 
 6. A farmer had 14 cows in a pasture, 9 of which 
 broke out : how many remained in the pasture ? 
 
 7. What is the difference between 9 and 13? How 
 many must be added to 9 to make 13 ? 
 
 8. James saw 18 butterflies upon a bed of flowers, 
 and caught 9 of them : how many flew away ? 
 
 9. There are 15 sheep in a pasture: 9 of which are 
 white and the rest black : how many were black ? 
 
 10. Express the following in figures: Two thousand 
 and ten, Forty-five thousand six hundred. 
 
 Copy and subtract the following : 
 
 (ii.) (12.) (13.) (14.) (IS-) (16.) (I7-) (18.) 
 
 12 13 15 16 14 17 18 19 
 
 99999999 
 
3S l T It A i T I 1 1 s . 
 
 LESSON X . 
 
 Oral Drill. 
 
 1. Ten from u leaves how many? 10 from 
 
 10 from 31 ? 10 from 41 ? 10 from 51 ? 10 from 61 ? 
 10 from 71 ? 10 from 81 ? 10 I'mm 
 
 2. Ten from 12 leaves how many:' 10 from 
 
 10 from 32? 10 from 42? 10 from 52? 10 from 
 i 72 ? 10 from 82 ? 10 from <, 
 
 3. Ho\v many are 13 less 10? 23 less io ? 33 less 
 10 ? 53 less 10 ? . 
 
 4. How many ore 24 less 10? 44 less 10? 64 less 
 10 'i 34 less 10 ? 54 less 10 ? 
 
 5. How many are 15 less 10? 45 less 10? 25 less 
 10? 55 less 10? 35 less 10 ? < 
 
 6. How many are 16 less 10? 36 less 10? 5'- 
 10 ? 46 less 10? 66 less 10 ? 
 
 7. How m:my an- 17 less io? 37 less 10? 27 
 10? 47 less io? 67 less io ? 
 
 8. How many are 18 less 10 ? 38 less io ? 28 less 
 io ? 48 less io ? 68 less io ? 
 
 9. How many are 19 less io ? 39 less io ? 59 less 
 io ? 29 less io ? 49 less io ? 
 
 10. How many are 20 less 2? 30 less 2 ? 40 less 
 2 ? 50 less 2 ? 60 less 2 ? 70 less 2 ? etc, 
 
 11. How many are io l-ss 3 ? 30 less 3 ? 20 less 3 ? 
 40 less 3 ? 60 less 3 ? 50 less 3 ? etc. 
 
 12. How many are io less 4 ? 30 le-s 4? 20 less 4? 
 50 less 4 ? 40 less 4 ? 60 l.^s 4 ': etc, 
 
 (For explanation of terms in Subtraction, sec p. 60 
 
SUBTRACTION. 39 
 
 LESSON XI. 
 
 1. How many are 10 less 7 ? 30 less 7 ? 20 less 7 ? 
 40 less 7 ? 60 less 7 ? 50 less 7 ? etc. 
 
 2. How many are 10 less 8 ? 30 less 8 ? 20 less 8 ? 
 60 less 8 ? 50 less 8 ? 70 less 8 ? etc. 
 
 3. How many are 10 less 9 ? 30 less 9 ? 20 less 9 ? 
 40 less 9 ? 70 less 9 V 50 less 9 V HI-. 
 
 4. 12 less 3 are how many ? 22 less 3 ? 32 less 3 ? 
 
 42 less 3 ? 52 less 3 ? 62 less 3 ? etc. 
 
 5. 13 less 5 are how many ? 23 less 5 ? 33 less 5 ? 
 
 43 less 5 ? 53 less 5 ? 63 less 5 ? etc. 
 
 6. 12 less 6 are how many? 22 less 6 ? 32 less 6 ? 
 52 less 6 ? 42 less 6 ? 62 less .6 ? etc. 
 
 7. 14 less 7 are how many ? 24 less 7 ? 44 less 7 ? 
 34'less 7 ? 54 less 7 ? 64 less 7 ? etc. 
 
 8. 14 less 5 are how many ? 24 less 5 ? 44 less 5 ? 
 64 less 5 ? 34 less 5 ? 54 less 5 ? etc. 
 
 9. 1 6 less 8 are how many ? 26 less 8 ? 46 less 8? 
 36 less 8 ? 66 less 8 ? 56 less 8 ? etc. 
 
 10. 15 less 9 are how many ? 25 less 9 ? 45 less 9 ? 
 
 35 less 9 ? 55 less 9 ? 75 less 9 ? etc. 
 
 1 1. 1 6 less 7 are how many ? 26 less 7 ? 46 less 7 ? 
 
 36 less7 ? 5 6 l ess 7 ? 7 6 l ess 7 ? etc. 
 
 12. 15 less 8 are how many ? 25 less 8 ? 45 less 8? 
 35 less 8 ? 55 less 8 ? 65 less 8 ? etc. 
 
 13. 23 less 6 are how many ? 33 less 6 ? 53 less 6 ? 
 73 less 6? 63 less 6? 83 less 6 ? etc. 
 
 14. 17 less 8 are how many ? 27 less 8 ? 47 less 8 ? 
 
 37 less 8 ? 57 less 8 ? 87 Ic.-fi 8 ? etc. 
 
NOTATION. 
 
 LESSON I . 
 
 1 . What in a single thing called ? 
 A tt nit or out-. 
 
 1. What arc one and one more rail* <! '? " Two/* 
 
 2. Two and one more? " T! 
 
 3. Thivi' ard one more? "Four." 
 
 8. ^ iie terms one, two, three, four, Ac.? 
 
 > HIttK'S Of' number*. 
 
 3. What ia number? 
 
 y umber is a unit, or a collection of units. 
 
 4. How are numbers generally expressed? 
 Uy Figures. or L< ttrrs. 
 
 5. \Vhut is expressing numben by figures called, and 
 Tin- Artthic dotation. It ia so called, be- 
 
 cause it was introduced into Kuroj*- from Arabia. 
 
 6. How many figures does it employ? 
 The ten following: 
 
 I, 2, 3, 4, 5, 6, 7, 8, 9, o. 
 
 tot, two, three, tar, five, six, KTCO, eight, ittt, 
 
 7. What are the first nine called, and why ? 
 
 They ;in- ctilhd sit/n ijicant Jiyurcs, because 
 each always expresses a number. 
 
 They are also called (lit/ its. from digitus, .-Hii: 
 
 .'ise the ancients used to reckon on their lingers, 
 . What is the last called, and * 1 
 
 \ttu(//it. Uvunse when standing alone it has no 
 value. It is also culled zero, or n/"' 
 
 9. How is each of the tir<t nine numbers expressed? 
 By a single fly u re. 
 
NOTATION. 4* 
 
 LESSON II. 
 
 10. What are the first nine numbers called? 
 
 Units of the/i/vtf order;, or simply units. 
 
 11. What is the greatest number expressed by one figure ? 
 
 Nine* 
 
 12. How are numbers larger than nine expressed? 
 
 By forming other orders of units, cullnl 
 
 tens, hundreds, thousands, &c. 
 
 13. How is ten expressed? 
 
 By writing i in the second place, with a cipher 
 on the right; as, 10. 
 
 14. What are figures standing in the second place, called? 
 Tens, or units of the second order. 
 
 15. What is the greatest number expressed by two figures ? 
 
 Ninety-nine. 
 
 16. How is a hundred expressed ? 
 
 By writing i in the third place, with two ciphers 
 on the right; as, 100. 
 
 17. What are figures standing in the third place, called ? 
 
 Hundreds, or units of the third order. 
 
 1. What are the orders higher than hundreds, called? 
 
 Thousands, tens of thousands, hun- 
 dreds of thousands, millions, &c. 
 
 1 . How many simple units make one ten ? " Ten/' 
 
 2. How many tens make one hundred? "Ten." 
 
 3. How many fojw^rafo make one thousand? "Ten." 
 19. What is true as to the increase of the orders of units ? 
 
 They increase from right to left hy the scale 
 of ten. That is, ten of any lower order make one of 
 the next higher order. 
 
N O T A T 1 
 
 120. What places do the different orders ocn. 
 
 ^ii/ijiie units occupy tin- rijht hand pi.; 
 Tens, the second place ; 
 Hundreds, the third pla 
 Thousands, the fourth pi.. 
 Tens of thousand fch place ; 
 
 Hundreds of thousand*. ' 
 Mill inn*, the seventh place, etc. 
 21. What is the effect of moving a figure one plac* 
 right to left, or from left to right. 
 
 >,v/ ten tunes for 
 it is moved from right to left; and i 
 less for every place it is mo\ ^ht. 
 
 U'2. What is the rule for expressing numbers by figures T 
 
 Begin at the /<//, m, \-s of ///' 
 
 yiren orders in their place* tfnrurd the r, 
 
 If an i/ inter rs are omitted, suj 
 
 place* with ciphers. 
 
 Write in fiirnrc- the following nuinliers: 
 
 1. Thirty-seven. 7. One hundred five. 
 
 2. Sixty-nine. 8. One hund. 
 
 3. Seventy-tl;: 9. Two hiuui- 
 
 4. Eighty-live. 10. Four hundred 
 
 5. One hundred two. u. Six hundred fnrty->even. 
 
 6. One hundred ten. 12. Eiirht hundred seventy-four. 
 
 13. Fifteen thousand and forty-five. 
 
 14. Forty-one thousand and ninety-five. 
 
 15. One hundred thousand and ti\v hundr 
 
 16. Six hundred fifty-one tli.msand seven hundred. 
 
 17. Eight hundred forty thousand two hundred ten. 
 
 1 8. One million two hundred ten thousand. 
 
NOTATION". 
 
 
 LESSON III. 
 
 1. When we designate objects as the first, second, 
 third, fourth, &c., what are these terms called? 
 
 Ordinal Numbers. 
 
 2. What is the linger next to the thumb called? 
 The first linger." The next? " The second linger." 
 
 3. The next? The next? 
 
 4. Beginning at the foot 
 of a ladder, what is the low- 
 est round called ? The 
 next? The next? The 
 next? The next? Wha; 
 is the top one in this lad- 
 der? 
 
 5. Beginning at thisend 
 of the class, name the first 
 pupil. The second. The 
 third. The fourth. Th- 
 fifth, and so on to the la>t. 
 
 6. With what regular number does third corns 
 spond ? Fifth V Seventh ? 
 
 7. How many tens in twenty ? In forty ? In fifty ? 
 In seventy ? In sixty ? In eighty ? In ninety ? In 
 ?. hundred? 
 
 Copy and read the following numbers . 
 
 (8.) ( 9 .) (10.) (II.) (12.) 
 
 534 852 1264 7806 9720 
 
 638 548 3076 8520 9608 
 
 437 659 4275 9067 9999 
 
 739 947 8569 &73 . 10000 
 
NUMERATION. 
 
 LESSON IV. 
 
 23. What 'IB the method of reading numbers expressed by 
 ogures. called ? 
 
 Numeration* 
 
 21. Beginning with units, recite the table. 
 
 :III. Period II. Period 
 
 *.'. How read numbers expressed by figures? 
 
 Divide thi-m hUo periods of three figures 
 counting from the right. 
 
 Beginning at the left hand, read the p> 
 cession, and add the name to each, except the last. 
 Copy and read the following : 
 
 1. 107. 8. 20354. 15. 230684. 
 
 2. no. 9. 23200. 1 6. ^007. 
 
 3. 234. 10. 43076. 17. 1000000. 
 
 4. 506. ii. 50643. 18. 5235640. 
 
 5. 730. 12. 62640. 19. 18642065. 
 
 6. 809. 13. 84063. 20. 81000000. 
 
 7. 943. 14. 97810. 21. 463250648. 
 
 iy If this and the next three lessons are deemed too diffi- 
 cult for Deginners, they may be omitted till review. 
 
ROMAN NOTATION. 
 
 LESSON V. 
 
 26. By what other method are numbers expressed? 
 
 By the follow in (/ letters, viz.: J, V, X, L, 
 0, D, M. 
 
 JJ7. What does each of thea? letters denote? 
 
 The letter I, denotes one ; V, five ; X, ten ; L, fifty ; 
 C, one hundred; D, five hundred; M, one thousand. 
 JJ8. How are other numbers expressed by these letters? 
 
 By repealing and combining them, as in the 
 following 
 
 TABLE. 
 
 I denotes 
 
 one. 
 
 XXIV denotes 
 
 twenty-four, &c. 
 
 II 
 
 two. 
 
 XXX 
 
 thirty. 
 
 III 
 
 three. 
 
 XXXI 
 
 thirty one. 
 
 IV 
 
 four. 
 
 XXXII 
 
 thirty-two, &c. 
 
 V 
 
 five. 
 
 XL 
 
 forty. 
 
 VI 
 
 six. 
 
 XLI 
 
 forty -one, &c. 
 
 VII 
 
 srven. 
 
 L 
 
 fifty. 
 
 VIII 
 
 eight 
 
 LX 
 
 sixty. 
 
 IX 
 
 nine. 
 
 LXX 
 
 seventy. 
 
 X 
 
 ten. 
 
 LXXX " 
 
 eighty. 
 
 XI 
 
 eleven. 
 
 XC 
 
 ninety. 
 
 XII 
 
 twelve. 
 
 C 
 
 one hundred. 
 
 XIII 
 
 thirteen. 
 
 CX 
 
 one hundred ten. 
 
 XIV 
 
 fourteen. 
 
 CC 
 
 two hundred. 
 
 XV 
 
 fifteen. 
 
 CCC 
 
 three hundred. 
 
 XVI 
 
 sixteen. 
 
 CCCC 
 
 four hundred. 
 
 XVII 
 
 seventeen. 
 
 D 
 
 five hundred. 
 
 XVIII " 
 
 eighteen. 
 
 DC 
 
 six hundred. 
 
 XIX 
 
 nineteen. 
 
 DCC 
 
 seven hundred. 
 
 XX 
 
 twenty. 
 
 IMVC 
 
 eight hundred. 
 
 XXI 
 
 twenty-one. 
 
 IXXVC " 
 
 nine hundred. 
 
 XXII 
 
 twenty -two. 
 
 M 
 
 one thousand. 
 
 XXIII " 
 
 twenty three 
 
 MD 
 
 one thou. five liund. 
 
 MDCCCLXXV, ouo thousand eight hundred and seventy-five. 
 
46 NUMERATION. 
 
 LESSON VI. 
 
 29. When a letter is repented, what is tin' eff.-rt ? 
 
 Jfs eatae \< r Thus. I one; 
 
 II, tw<>: X, ti-n : XX. twenty, 
 
 :5O. If a Irtti-r is placed before one of greater value, what is 
 the ell' 
 
 The value of the less is taken l'nm the 
 
 ttl. Iff. laced after one of greater value, what? 
 
 The value of the less is ad fled t> tho 
 
 1. What docs X denote? 1 :- Whd XI? 
 
 2. What does V denote? WhatlVf Whd 
 32. II"\v rxprejw tlie numbere from 10 to 20 by letters? 
 
 JU addinf/ the fetters d the lir.-t dcc-ade to 
 
 XL XI!. 
 
 Express the following numbers by letters : 7. ti, 
 i9 2 9> 39 4^ 40, 60, 70, 89, 91, 101, 550, 670, loio, 
 
 Copy and read the following numbers. 
 
 i. IV. 
 
 \XXIX. 
 
 13- ( 
 
 2. VI. 
 
 8. > 
 
 14. CCC. 
 
 j, VII. 
 
 9- ! 
 
 15. !>( 
 
 4- XIV. 
 
 10. LIX. 
 
 1 6. MDL. 
 
 5. XVI. 
 
 II. I. XXIV. 
 
 17. Ml' 
 
 c. XXIV. 
 
 12. LXXXV1II. 
 
 18. .Ml 
 
 ll'.l. In what is t)i' Human N- 
 
 In e 
 
 into \vhirh ! di\idi-d, and in 
 
 hours mi , and wat 
 
THE CLOCK. 
 
 LESSON VII. 
 
 To Tell the Tim* of Day by the Clock. 
 
 3 J. How is the face of a clock divided ? 
 
 A us. Into tirdrc equal parts called 
 marked by the letters, I, II, III, etc. 
 
 35. What is the object of the 
 two pointers, or hands. 
 
 Ans. The short hand 
 tells the hours, and is culled 
 the hour hand ; the Io7ic) one 
 tells the minutes, and is 
 called the minute hand. 
 
 1. When both hands are at 
 XII, what time is it? 
 
 A/is. It is twelve o'clock. 
 
 NOTE. The teacher will explain that when the minute hand 
 
 reaches II, it is ten minutes past one o'clock ; when it reaches 
 
 III, it is fifteen minutes past one, and while the hour hand 
 
 - from XII to I, the minute hand moves entirely around 
 
 the face, and points at XII, &c. 
 
 2. When the minute hand is at VI and the hour hand half 
 way between II and III, what is the time? 
 
 A HP. It is half past two oV 
 
 3. When the minute hand points at IX, what is the time? 
 At) a. It lacks fifteen minutes of three o'clock. 
 
 4. Where must the hands be, to denote ten minutes past five ? 
 
 5. \Vlu>re must they he, to denote half past live'." 
 
 6. Where must they be, to denote 20 minulrs piist ei^ht ? 
 
 7. When the hour hand is past 111, and the minute hand is 
 nt V , wluit tin.e is it? 
 
 R. When the hour hand is near VI and the minute hand at 
 hat? 
 
ADDITION. 
 
 LESSON I 
 
 1. What is Addition? 
 
 Addition is uniting two or more numbers in 
 
 . What is the number obtained by addition railed '! 
 
 The Stint < r Amount. 
 
 3. How is Addition denoted ? 
 
 By a pcrjM'Hflicultfr cross called plus (4-), 
 placed between the numbers to be added. Thu^. 
 expression 4 + 3 shows that 4 and 3 are to be added 
 her, and is read, "4 plus 3," "4 and 3," or 4 
 added to 3." 
 
 NOTE. The term plus signifies more or added to. 
 
 4. How is the equality between numbers denoted ? 
 lljtiro short /tfiraltel lutes, called the sign 
 
 of equality ( = ). The expression 44-3 = 7, *> 
 that 4 increased by 3 equals 7, and is read, "4 plus 3 
 equal 7," or the sum of " 4 + 3 equals 
 Copy and read the following expressions : 
 * 5+3 + 2+o-H8= 10 + 3 + 5. 
 
 2. 6 + 84-04-9 = 2 + 10 + 3 + 8. 
 
 3. One pupil gave h< Cs, another 8, 
 and another 6: how many peaches did a 
 
 SOLUTION. 7 peaches and 8 peaches are 15 peaches, and 6 
 are 21 peaches : therefore all gave her 21 peaches. 
 
 4. If John picks 5 roses from one bush, 9 from an- 
 other, and 7 from another, how many will In- pick ? 
 
 5. How many are 6 quarts, S quarts, and 7 qua. 
 
 6. How many are 18 yards and 9 yards and 4 yi 
 
ADDITION. 49 
 
 LESSON I I. 
 
 To add single columns when two or more numbers, 
 ruining together, make 10* 
 
 i. Find the amount of 5, 6, 3, 7, 8, 4, 6, 9. 
 
 ANALYSIS. Write the numbers one under an- Operation, 
 other, in a perpendicular column, and draw a line 5 
 under it. 6 
 
 Beginning at the bottom and omitting the names 3 
 of the numbers, proceed thus : Nine, nineteen 7 
 (adding 10 for 6 and 4), twenty-seven, thirty-seven 8 
 (adding 10 for 7 and 3), forty-three, forty-eight. 4 
 The amount is 48. 6 
 
 NOTES. i. When two or more number?! to- 9 
 gether make ten, instead of adding these numbers 
 separately, it is better to add 10 at once. 48 Ans. 
 
 2. In all operations both mental and slate, the pupil should 
 add each number as a whole, and not by single units, or by 
 counting his fingers. Counters should be used no longer than 
 necessary to illustrate the different combinations. 
 
 3. Great care should be taken to see that the figures are 
 written with neatness and symmetry, and in perpendicular 
 columns. 
 
 Copy and add the following in like manner : 
 
 (2.) 
 
 (3-) 
 
 (4-) 
 
 (5-) 
 
 (6.) 
 
 (7-) 
 
 (8.) 
 
 (9-) 
 
 8 
 
 4 
 
 3 
 
 9 
 
 4 
 
 7 
 
 6 
 
 8 
 
 2 
 
 6 
 
 2 
 
 4 
 
 7 
 
 3 
 
 9 
 
 7 
 
 7 
 
 5 
 
 6 
 
 3 
 
 2 
 
 6 
 
 8 
 
 9 
 
 2 
 
 2 
 
 4 
 
 2 
 
 3 
 
 4 
 
 7 
 
 6 
 
 3 
 
 6 
 
 3 
 
 8 
 
 5 
 
 5 
 
 2 
 
 8 
 
 7 
 
 5 
 
 7 
 
 6 
 
 8 
 
 2 
 
 5 
 
 7 
 
 6 
 
 5 
 
 5 
 
 3 
 
 2 
 
 3 
 
 3 
 
 8 
 
 6 
 
 3 
 
 6 
 
 2 
 
 3 
 
 8 
 
 6 2 
 
 7 
 
 4 
 
 7 
 
 4 
 
 5 
 
 6 
 
 7 
 
 7 
 
 8 
 
 7 
 
 8 
 
 3 
 
 4 
 
 5 
 
 6 
 
 8 
 
 9 
 
00 AD I) IT lo 
 
 LESSON III. 
 
 Mental Exercises. 
 
 1. A teacher received 6 apples from one of her pu- 
 pil*, 7 from another, and 8 from another: how i 
 apples did she receive from all ? 
 
 2. If you pay 10 cents for a slate, 6 cen i n k- 
 1, and 3 cents for a pencil, how much will 
 
 pay for all ? 
 
 3. If an orange costs 6 cents, a pear 5 cents, and a 
 umon 4 cents, what will they all co 
 
 4. How many are 7 brooms, 3 brooms, and 8 brooms? 
 
 5. How many are 8 days, 7 days, and 6 days ? 
 
 6. How many are 7, and 6, and 3 ? 
 
 7. If Harry receives 6 credits a day for 3 days, how 
 many r'mrks will he IK, 
 
 8. How many are 9 dollars, 6 dollars and 7 dollars ? 
 
 9. How many arc 12, and ;<, ami 9? 
 Copy and add the following : 
 
 w 
 
 W 
 
 (30 
 
 (40 
 
 (5-) 
 
 (6.) 
 
 
 (8.) 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 8 
 
 6 
 
 7 
 
 6 
 
 7 
 
 8 
 
 9 
 
 IO 
 
 9 
 
 7 
 
 9 
 
 6 
 
 7 
 
 8 
 
 9 
 
 IO 
 
 6 
 
 8 
 
 8 
 
 r 6 
 
 7 
 
 8 
 
 9 
 
 IO 
 
 5 
 
 6 
 
 6 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 8 
 
 7 
 
 7 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 9 
 
 8 
 
 8 
 
 6 
 
 7 
 
 8 
 
 9 
 
 IO 
 
 
 6 
 
 6 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 3 
 
 7 
 
 7 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 8 
 
 8 
 
 8 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 9 
 
 9 
 
 6 
 
ADDITION. 51 
 
 LESSON IV. 
 
 To add numbers consisting of two or more Columns, 
 when the sum of each column is less than 1O. 
 
 1. What is the sum of 223, 342, and 132 ? 
 ANALYSIS. Write the numbers one under an- Operation. 
 
 other, units under unite, tens under tens, etc., 223 
 
 and, beginning at the right, add thus : 2 units and 342 
 
 2 units are 4 units, and 3 are 7 units. Set the 7 132 
 under the units' place, because it is units. Next, 
 
 3 tens and 4 tens are 7 tens, and 2 are 9 tens. Set 697 A ns. 
 the 9 in tens' place, because it is tens. 
 
 Finally, i hundred and 3 hundreds are 4 hundreds, and 2 are 
 6 hundreds. Set the 6 in hundreds' place, because it is hun- 
 dreds. An*. 697. 
 
 (2.) (3-) (4-) (5-) (6.) (70 
 
 31 23 24 231 312 413 
 
 24 32 30 324 431 if>o 
 
 II 22 23 132 205 326 
 
 (2.) (3-) (4-) (50 (6.) (7-) 
 
 25 23 30 231 324 403 
 30 42 43 I2 3 230 232 
 24 34 25 404 305 354 
 
 2. A farmer has two flocks of sheep, one containing 
 342, the other 227 : how many sheep has he ? 
 
 3. Write in columns and find the sum of 313 dol- 
 lars, 142 dollars, and 432 dollars. 
 
 4. James has three books, one containing 212 pages, 
 another 320 pages, and another 456 pages : how many 
 pages do all contain ? 
 
52 A D D I T I O 
 
 LESSON V. 
 
 To add numbers consisting of two or more < olnmnft, 
 when the sum of a column U 1 O. or more. 
 
 1. What is the sum of 234 dollars, 525 dollars, and 
 443 dollars ? 
 
 ANALYSIS. Write the numbers one under an- Operation. 
 other, the units under units, etc., and, beginning 234 d. 
 
 at the right, add as before. Thus, 3 unite ar 525 d. 
 
 units are 8 units, and 4 are 12 units, equal to I tea 443 d. 
 
 and 2 units. Set the 2 in units' place, because it 
 is units, and add the i ten to the next column, be- Ant. 1202 d. 
 cause it is the ame order as that column. 
 
 Next, i ten and 4 tens are 5 tens, and 2 are 7 tens, and 3 are 10 
 tens, equal to i hundred and o tens. Set the a or unit's figure, 
 under the column added, bfcaute there are no tent, and add the 
 i hundred to the next column, because it is the ame order as 
 that column. Adding the i hundred to the next column, the 
 sum is 12 hundreds, and this being the last column, we set 
 down the v hole turn. 
 
 NOTE. As soon as the learner becomes familiar with adding 
 numbers which have two or more columns, he should on. 
 name of the order, etc., and pronounce the results only, as in 
 adding single columns. (P. 38, Ex. i.) 
 
 2. What two principles are necessary to be obs- 
 in addition ? 
 
 The numbers must he LiJcr \ntti hers. 
 2d. Units of the stimr nrdrr mvri bo added, 
 each to each. 
 
 3. What are like numbers ? 
 
 Like lumbers are those which express units 
 of the same kind; as, 4 pears and 3 pears ; 5 and 8, etc. 
 
 4. What are unlike numbers ? 
 
 Unlike Numbers are those which express unit* 
 of different kinds; as, 4 dollars and 3 yarda. 
 
ADDITION. f,:j 
 
 LESSON VI. 
 
 Review of Principle*. 
 
 5. How do you write numbers to be added ? 
 
 Write one under another, units under units, etc. 
 
 6. When begin to add, and how proceed ? 
 
 Begin at the right, and add each column separately. 
 
 7. When the sum of a column is less than 10, what is doiie 
 with it ; and why ? 
 
 Set it under the column added, because it is the 
 same order as that column. 
 
 8. When the sum of a column exceeds 9, what do you do 
 with it ? 
 
 Write the units' figure under the column added, and 
 add the tens to the next higher order. 
 
 f). What do you do with the last column ? 
 
 ^'t down the irhole sum. 
 
 1O. How is Addition proved ? 
 
 Begin at the top, and add each column downward. 
 If the two results agree, the work is right. 
 
 Examples for Practice. 
 
 (i.) (') (3-) (4.) (5.) 
 
 233 234 395 382 504 
 
 165 364 265 237 160 
 
 486 246 486 68 439 
 
 283 547 257 385 758 
 
 6. Find the sum of 305 yds., 28 yds., and 420 yds. 
 
 7. Find the sum of 325 dols., 83 dols., and 7 dols. 
 
 8. What is the sum of 436 4-48 + 1 36 + 20 ? 
 
 c> What is the sum of 3450 + 2434- 1789 + 46 ? 
 
54 ADDITION. 
 
 (10.) (II.) (12.) (14.) 
 
 Dollars. Fct. Days. Pounds. Gallons. 
 
 3465 4273 612 7260 8725 
 
 802 6250 7309 39 430 
 
 So^o 367 527 547 57 
 
 2432 5046 6305 9084 53 6 7 
 
 "" "" "" " " r 
 
 15. A raan picked 875 oranges from one tree, 739 
 from another, and 1237 from another: how nuu: 
 
 i<-k from all? 
 
 1 6. One school has 475 pupils, another 630, 
 
 another 568: ln\v many ]>upil> i. 
 
 (I 7 .) (18.) (I 9 .) (20.) (21.) 
 
 4358 3460 4504 6720 8354 
 
 754 58 75 2075 
 5243 8539 7322 5 81 
 
 22. Find the sum of 275 pounds -f 468 pound 
 723 pounds. 
 
 23. Find the sum of 463 yds. + 568 yds. 4-837 
 
 24. Find the sum of 563 gal. +645 gal. -f 750 ; 
 
 (25.) (26.) (27.) (28.) (29.) (30.) 
 
 3 73 3 2 5 4 84 35 56 67 45 
 
 48 30 4 76 5 40 93 27 90 76 
 
 53 33 8 25 3 33 82 82 38 60 
 
 37 45 7 30 2 22 80 75 54 93 
 7- 6 34 3 58 64 40 73 40 
 45 6 4 4 25 7 34 95 67 85 63 
 
 38 7 46 2 76 38 53 64 88 
 53 78 5 6 3 8 43 47 48 90 70 
 
SUBTRACTION. 
 
 LESSON I . 
 
 1. What is Subtraction ? 
 
 Subtract lot i is taking one number from an- 
 
 2. What is the number to be subtracted called ? 
 
 The Subtrahend. 
 
 3. The number from which the subtraction is made ? 
 
 The Minuend. 
 
 4. What is the number obtained by Subtraction called 1 
 
 The Difference, or remainder. 
 
 1. "When we say, 3 from 8 leaves 5, which is the 
 minuend ? The subtrahend ? The remainder ? 
 
 2. When it is said that 6 taken from 14 leaves 8, 
 what is the 6 called ? The 14? The 8 ? 
 
 5. How is Subtraction denoted ? 
 
 By a short horizontal line, ( ) called 
 minus. When placed between two numbers, this sign 
 shows that the number after it is to be taken from the 
 one before it. Thus, 5 3 shows that 3 is to bo taken 
 from 5, and is read " 5 minus 3." 
 
 IE. The term minus signifies less. 
 Copy and read the following expressions : 
 
 1. 8-3 = 10-5. 4- "9 5 = "8 4- 
 
 2. 23-5 = 164-2. 5. 135 + 8=150-7. 
 
 3. 87+4 = 9 8 -7 6. 250 + 7 = 277-20. 
 
 7. 19 dollars 7 dollars = how many dollars? 
 
 8. 15 bushels 8 bushels = how many bushels ? 
 
 9. 23 8 = how many ? 27 10 = how many ? 
 
56 
 
 LESSO Nil. 
 
 ll'hrn rarh rifntre in the Lim-rr \nmber is 
 tlntn th? otit- tihfHT if. 
 
 i. Find the difference between 746 and 214. 
 
 ANALYSIS V. :. number under the Oper 
 
 greater, unit* under unit*, tens under tern, 
 Beginning at the ri^bt, proceed thus: 4 u 
 from 6 units leavo 2 units. Set the 2 in units' 
 place, under the figure subtracted, because it ia Ant. 532 
 units. Next, i ten from 4 tens leaves 3 tens. Set 
 the 3 in tens' place. und re subtracted, becau 
 
 tfns. Finally, 2 hundreds from 7 hundreds!* dreda. 
 
 Set the 5 under the. hundreds' column, because it is 
 
 Solve the following in a similar mann< 
 
 (2.) (3-) (40 (6.) 
 
 435 546 615 768 879 
 
 312 221 314 544 
 
 (7-) 
 575 dole. 
 243 dols. 
 
 (8.) 
 465 yards. 
 234 yards. 
 
 (9.) 
 675 days. 
 372 days. 
 
 do.) 
 4^3 
 
 11. A farmer having 456 sheep, sold 230 of t: 
 how many did he have left ? 
 
 12. If 11 ncome is 685 dollars a 1 his 
 
 - are 360 dollars, how much can he lay a] 
 
 13. What is the difference between 570 and 340 ? 
 
 14. What is the dinVn .oen 700 and 300 ? 
 
 15. What is the dill'm-mr lu-twivn fix hundred 
 forty-five and two hundred twenty-tlm- 
 
SUBTRACTION. 5? 
 
 (16.) (17. (18.) (19.) 
 456 dols. 564 sheep. 678 feet. 784 pounds. 
 324 dols. 234 sheep. 538 feet. 541 pounds. 
 
 (20.) (21.) (22.) (23.) 
 5674 7360 8679 9230 
 351 4230 5360 4020 
 
 Mental Exercise*. 
 
 1. A tailor sold a coat for- 25 dollars, and received 10 
 dollars down : how much is due him ? 
 
 ANALYSIS. Ten dollars from 25 dollars leave 15 dollars. 
 
 2. If you have 17 doves, and sell 8 of them, how- 
 many will you have left ? 
 
 3. Bought a cow for 35 dollars, and sold her for 9 
 dollars less than cost : for how much was she sold ? 
 
 4. A market boy had 44 eggs in a basket, and letting 
 it fall broke 12 : how many remained unbroken ? 
 
 5. William had a 25-cent piece to buy a lunch, the 
 price of which was 15 cents : how much change should 
 he receive ? 
 
 6. A young man is 21 years old to-day: how old 
 he 8 years ago ? 
 
 7. Nine and what number are 23 ? 8 and what 
 number are 32 ? 
 
 8. 7 and what are 35 ? 6 and what are 42 ? 
 
 9. Henry has 10 dollars in the savings-bank : how 
 many dollars more must he get to make 50 dollars ? 
 
 10. There are 25 cows in a pasture : if 9 are taken 
 out, how many will be left? 
 
'>> S U I) T B A C T I O X . 
 
 LESSON III. 
 
 JJ7i/'/i a Firjiire in the Loircr \uwber is Large* 
 t/unt tht- our dltot'f it. 
 
 i. What is the difference 1 745 and 438 ? 
 
 ANALYSIS. Here 8 is larger than 5, and can- Oper 
 not be taken from it. How is this difficulty re- 
 moved ? There are two method* 438 
 
 ist METHOD. We add 10 to the 5, making 15 ; 
 now 8 unite from 15 units leave 7 units. Wo Ant. 307 
 write the 7 in units' place under the figure sub- 
 tracted. To balance the 10 added to the upper number, we 
 add i to the next higher order of the lower, which is equal to 
 added to the upper number. Now i ten and 3 tens are 
 4 tens, and 4 tens from 4 tens leave o tens. Place n 
 
 ; lace, because there are o tena. Finally, 4 hundreds from 
 .Jreds leave 3 hundreds, which we write in hundreds' 
 place. The remainder is 307. 
 
 ad METHOD. Instead of 10 taken at random, we may take 
 i t< n from the 4 trns in the upper number, and add 
 units, making 15. Now 8 from 15 leaves 7, which we set 
 the figure subtracted. Since we took i ten from the . 
 
 are but 3 tens left ; and 3 t<-ns from 3 tens leave o tens. 
 Finally, 4 from 7 leaves 3. The remainder is 307, the save as 
 before. 
 
 NOTE. The process of adding 10 to the upper figure is 
 commonly called " borrowing ten." 
 
 6. What two principles are necessary to be observed in 
 
 subtraction ? 
 
 isi The numbers must be L//.V Xnnihcrx. 
 ad. I'nits of the same order must be eub- 
 tractrd one from the other. 
 
SUBTRACTION. 59 
 
 LESSON IV. 
 
 Review of Principles. 
 
 7. How do you write numbers for subtraction ? 
 
 Write the less number under the greater, units under 
 units, tens under tens, etc. 
 
 8. Where do you begin to subtract, and how proceed ? 
 Begin at the right, and subtract each figure in the 
 
 lower number from the one above it, setting the re- 
 mainder under the figure subtracted. 
 
 9. If a figure in the lower number is larger than the ono 
 above it, how proceed ? 
 
 Add 10 to the upper figure ; then subtract, and add 
 i to the next figure in the lower number. 
 
 10. How is subtraction proved? 
 
 Add the remainder to the subtrahend ; if the SUM is 
 equal to the minuend, the work is right. 
 
 Examples for Practice. 
 
 i. Find the difference between 745 and 280; and 
 prove the operation. 
 
 <*) 
 
 (3-) 
 
 (4.) 
 
 (5-) 
 
 234 dols. 
 
 435 barrels. 
 
 647 gallons. 
 
 730 days. 
 
 1 08 dols. 
 
 260 barrels. 
 
 365 gallons. 
 
 365 days. 
 
 (6-) (7-) (8.) (9.) 
 
 545 6305 5785 7346 
 
 2237 3252 3060 5037 
 
S U B T R A C T I O \ . 
 
 (,0.) 
 
 345 yards. 
 1 60 yards. 
 
 ,,.) 
 520 dols. 
 235 dols. 
 
 671 j >o unds. 
 486 pounds. 
 
 <3-> 
 
 784 quarts, 
 92 quarts. 
 
 .MO ('SO (16.) (I7-) 
 
 3427 6504 8050 9650 
 
 1285 4273 437Q 
 
 1 8. A farmer raised 6256 bushels of wheat, and 
 3460: how much ; unsold? 
 
 19. The price of a house is 6475 dollars, and tl. 
 a farm 7500 dollars : what is the different 
 prio 
 
 20. What is the difference between five thou 
 and twenty-five, and twenty-live hundred and ti- 
 
 a i. What is the difference between tea thousand and 
 -:ul ten hundred and ten? 
 
 22. How many are 4560 dollars less 2345 dollars ? 
 
 23. Bought a lot of goods for 13250 dollars, 
 sold them for 12500 dollars: what was the loss? 
 
 24. 63256 500200? 27. 710237 500420? 
 
 25. 70240 43210? 28. 806430650340? 
 
 26. 85207 60340? 29. 900645 704306? 
 
 30. The population of New York in 1860 was 
 3.880,735; in 1870 it was, 4.370,846: what was th 
 
 31. The population of the United States in 1860 
 was 31,443,321 ; in 1870 it was 38,312,633: wh:: 
 
 the increase? 
 
 32. A man paid $2500 dollars for a farm, and s 
 for 4000 dollars: how much did he mak- 
 
SUBTRACTION. 61 
 
 LESSON V, 
 
 Oral Drill. 
 
 To 4 add 6 ; subtract 3 ; add 9 ; subtract 5 ; 
 2 ; subtract 3 ; add 4 ; subtract 12 ; add 8 ; sub- 
 5 : what is the result ? 
 
 add 1 2 ; subtract 3 ; add 4 ; 
 tract 5 : what is the result ? 
 
 EXPLANATION. The toachor RRTB, " to 4 add 6," the class 
 think 10 ; " subtract 3," the class think 7 ; " add 9," the class 
 think 16; "subtract 5," the class think n; "add 12," the 
 class think 23 ; " subtract 3," the class think 20, etc. 
 
 2. From 8 subtract 2 ; add 4 ; subtract 5 ; add 7 ; 
 subtract 4 ; add 2 ; subtract 5 ; add 4 ; subtract 6 : 
 result ? 
 
 3. To 1 2 add 5 ; subtract 4 ; add 6 ; subtract 8 ; 
 add 7 ; subtract 4 ; add 7 ; subtract 6 ; add 4 : result ? 
 
 4. From 1 3 take 4 ; add 8 ; take 5 ; add 7 ; take 6 ; 
 add 8 ; take 8 ; add 7 ; take 5 ; add 6 : result ? 
 
 5. From 14 take 7 ; add 4; take 3; add 5 ; take 9; 
 add 6 ; take 8 ; add 3 ; take 4 ; add 8 : result ? 
 
 6. To 15 add 5; subtract 6; add 4; subtract 7; 
 add 6 ; add 5 ; subtract 6 ; add 7 ; subtract 8 ; add 9 : 
 result ? 
 
 7. From 20 take 3 ; add 8 ; take 6 ; add 9 ; take 8 ; 
 add 7 ; take 9 ; add 6 ; take 5 ; add 6 : result ? 
 
 8. From 34 take 3 ; add 6 ; take 10 ; add 2 ; take 7 ; 
 add 5 ; take 4 ; add 9 : result ? 
 
 9. To 17 add 8; take 6; add 10; take 8 ; take 3; 
 add 7 ; take 4 ; add 6 : result ? 
 
 10. From 43 take 7 ; add 4 ; add 9 ; take 6 ; take 5 ; 
 odd 10 ; add 20 ; take 6 : result ? 
 
MULTIPLICATION. 
 
 LESSON I. 
 
 To TK \rnrw.-The object of (his Lemon to to dcwfcp the MM of OHM*, 
 as oMMi In Multiplication, and lead the d*M to eee the timikrity of Multi- 
 plication to Addition. 
 
 1. Each pupil may make a star or unit mark i 
 his slate, as I make one upon the blackboard. :: 
 
 2. How many times have you made 01. 
 Otic time. 
 
 3. Make another under the first : 
 
 4. H\v many times have you made i tt 
 Ttro tunes. 
 
 5. Make 2 groups of 2 stars each; as, % :fc, ;}; ^:. 
 
 6. How many times have you made 2 mar.. 
 
 times." 
 
 7. How many arc 2 marks and 2 marks ? 
 
 marks." 
 
 8. I low many are 2 times 2 marks? "4 marks." 
 
 9. The m-xt make 3 groups of 2 stars each; as, 
 
 fc 2> ***> 5JC 2JC. 
 
 10. How many times have you made 2 stars? 
 Three times. 
 
 1 1. How many are 3 times 2 marks ? "6 marks." 
 i :. Make 4 groups of 2 stars each ; as, 
 
 <j ^jy ' *"{ rj wj rjy J 5JC 
 
 13. How many are 4 times 2 stars? "8 sUi 
 
MULTIPLICATION. 63 
 
 LESSON II. 
 
 2 
 
 time* I 
 
 are 2. 
 
 2 
 
 times 
 
 7 
 
 rr 
 
 14. 
 
 2 
 
 " 2 
 
 " 4- 
 
 2 
 
 a 
 
 8 
 
 u 
 
 16. 
 
 2 
 
 14 3 
 
 " 6. 
 
 2 
 
 " 
 
 9 
 
 (4 
 
 18. 
 
 2 
 
 4 
 
 " 8. 
 
 2 
 
 M 
 
 10 
 
 M 
 
 2O. 
 
 2 
 
 " 5 
 
 " 10. 
 
 2 
 
 a 
 
 ii 
 
 (I 
 
 22. 
 
 2 
 
 " 6 
 
 " 12. 
 
 2 
 
 u 
 
 12 
 
 " 
 
 24. 
 
 i. If i lemon costs 6 cents, what will 6 lemons 
 cost? 
 
 ILLUSTRATION. Let the pupil place a group of 6 stars 
 upon the blackboard, representing 6 cents, the price of i 
 lemon ; then will 2 groups of 6 stars each, represent the cost 
 of 2 lemons; as, 
 
 Counting the stars in these 2 groups together, we have 12 
 Btara ; hence, the cost of 2 lemons is 12 cents. Or, by 
 
 ANALYSIS. If i lemon costs 6 cents, 2 lemons will cost 2 
 times 6 cents ; and 2 times 6 cents are 12 cents. 
 
 2. How many are 2 times 4 cents ? 
 
 3. Paid 2 dollars apiece for 2 caps : how much did 
 both caps cost ? Show it. 
 
 4. How many are 2 times 3 fingers ? Show it 
 
 5. At 6 dollars apiece, what will 2 chairs cost ? 
 
 6. What cost 2 desks, at 5 dollars apiece ? 
 
 7. If you ride 9 miles an hour, how far will you ride 
 in 2 hours ? 
 
 8. What cost 2 ban-els of flour, at 10 dollars 9 
 barrel ? 
 
04 MU LT I 1' LI CAT I ON. 
 
 LESSON III. 
 
 3 times I r 
 
 3- 
 
 3 times 7 me 
 
 21. 
 
 3 " 
 
 6. 
 
 3 " 8 " 
 
 -4- 
 
 3 " 3 " 
 
 9- 
 
 - 
 o 9 
 
 27. 
 
 3 " 
 
 I 2. 
 
 3 " 10 " 
 
 30. 
 
 3 " 5 " 
 
 '5- 
 
 3 " ii 
 
 33- 
 
 3 " 6 
 
 1 8. 
 
 3 " M * 
 
 
 i. Louisa bought 3 lead pencils at 5 cents i 
 how much did she pay for all ? 
 
 i pencil coat 5 cento, 3 pencils will coct 3 
 times 5 cento ; and 3 times 5 cento are 15 cento. 
 
 2. What will 3 apples cost, at 2 cents apiec 
 
 3. There are 3 feet in i yard : how man 
 there in 3 yards ? 
 
 4. How many are 3 times 3 rabbits ? 
 
 5. Bought 3 peaches at 4 cents each : , i hey 
 
 
 6. If a car goes 6 miles an hour, how far 
 in 3 hours? 
 
 7. What cost 3 inkstands, at^8 cents ea( 
 
 8. Paid 7 dollars apiece : was the 
 cost of all? 
 
 9. Henry has 3 coops of 9 chickens each : how i. 
 chickens has he in all ? 
 
 10. What is finding the amount of a number t 
 or added to itself a given number of times cal : 
 
 Multiplication. 
 
 11. What is the result obtained by multiplication 
 called ? 
 
MULTIPLICATION. 
 
 LESSON IV. 
 
 4 **** 
 
 i i -^ 
 
 ^ 4-^ 
 
 4*A 
 
 
 
 7 * 
 
 ,28. 
 
 4 " 
 
 2 ' 
 
 * 8. 
 
 4 
 
 a 
 
 8 
 
 32- 
 
 4 
 
 *, ' 
 o 
 
 12. / 
 
 4 
 
 u 
 
 9 " 
 
 36. 
 
 4 
 
 4 ' 
 
 ' 1 6. 
 
 4 
 
 " 
 
 10 " 
 
 40. 
 
 4 " 
 
 5 4 
 
 ' 20. 
 
 4 
 
 ft 
 
 ii 
 
 44. 
 
 4 
 
 6 ' 
 
 ' 24. 
 
 4 
 
 u 
 
 12 " 
 
 48. 
 
 i. \Yhat i 
 
 is the 
 
 difference 
 
 in the 
 
 cost of 4 pens, 
 
 ccni ; apiece 
 
 , and 
 
 3 lemons 
 
 at 4 cents apiece ? 
 
 Iu.i>Ti:.\Tiox. Let the pupil place upon the board 4 
 Croups of 3 stars each, and suppo>c them to rei>resent the cost 
 of 4 pears, at 3 cents apiece- : a.-. 
 
 -::- -:; * :: x -K- # * # * 
 
 Also, l>y 3 irroups of 4 stars each, let him represent in like 
 manner tin- cost of the lemons; as, 
 
 v> :: x x :: :: x x -:: -::- 
 
 Counting the stars in theso ro\vs M-paratt-ly. we find thsit each 
 rmv cfjntains 12 stars. Hence, 4 times 3 cents is the saii,> 
 times 4 cents; consequently there is no dillen-nce in the cost. 
 
 2. "What cost 4 pair of boots, at 5 dollars a pair ? 
 
 3. If you pay 6 dollars a week for board, what will 
 i; cost you to board 4 wee' 
 
 4. AY h ifh is <riv:i(tT, 2 times 6, or 6 times 2 ? 
 Hinw it. 
 
 5. What cost 4 chairs, at 7 dollars each ? 
 
 6. At 12 cents each, what cost 4 slates ? 
 ,'\- and multiply the following: 
 
 (;-) - (9-) (10.) 
 
 312 521 602 821 
 
 4444 
 
MI LTIPLIC AT roir, 
 
 LESSON V. 
 
 5 time. I iirr 5. 5 time* 7 . 
 
 5 10. 5 40. 
 
 5 " 3 " '5- 5 ' 9 " 
 
 5 " 4 - 20. 5 " 10 
 
 5 " 5 5 u ii 
 
 5 " 6 " 30. 5 " 12 - 
 
 i. (iooiMjr ]. blackberries, and sold 
 
 them at (> .Mart : \\hat did they coinc 
 
 a iv 4 quarts: h"\v many <|iiarl- in 5 
 
 gftUoi 
 
 What cost 5 bananas, at 5 < h ? 
 
 4. (Jeorge bought 6 kites, at 5 c \\hat 
 
 did lie nay l'.r tlinn all ? 
 
 5. How many lu>h.-U cf a|>plc> will 5 trees 
 
 v, mi: 7 bvubell t" 
 
 hat CM.-.: 5 f boots, at S dollars a ] 
 
 !l m niai 
 
 10 each d 
 
 8. AVIiat is the COM .f 5 tallies i\: 
 
 9. A furrier sold 51 how 
 much did he i 
 
 10. IT n van!- of i 11 make i dress, how 
 i.iany will he re-jtiiivd t<> make 5 dresses? 
 
 n. Write >i\ ihousind. four hundred and 
 Cojty and multiply the follow 
 
 (12.) (i;>.) (14-) (15 
 
 410 501 610 700 Si i 
 
 5 5 5 5 
 
MULTIPLICATION. 67 
 
 LESSON VI, 
 
 6 time* I are 6. 6 times 7 are 42. 
 
 6 " 2 " 12. 6 " 8 u 48. 
 
 6 " 3 " 1 8. 6 9 < 54. 
 
 6 " 4 " 24. 6 " 10 " 60. 
 
 6 ' 5 30. 6 ii 66. 
 
 6 * 6 " 36. 6 " 12 " 72. 
 
 1. What will 6 chair? cost, nt 4 dollars apiece ? 
 
 2. Sold 5 quarts of cherries, at 6 cents a quart : 
 what did they come to ? 
 
 3. If 6 yards of silk will make i cloak, how many 
 yards will it take to make 6 cloaks ? 
 
 4. In i week are 7 days : how many days in 6 weeks ? 
 
 5. How many Imshels are 6 times 8 bushels ': 
 
 6. At 9 dollars apiece, what will 6 desks cost? 
 
 7. A party of 6 children gathered 10 quarts of nuts 
 apiece: how many did they all rather;' 
 
 8. A pleasure party hired 6 sail boats; each boat 
 carried n persons : how many in the party ? 
 
 9. How many pounds of honey are there in 6 boxes, 
 it' each box contains 12 pounds? 
 
 10. What will 6 penknives cost, at 12 cents each ? 
 
 1 1. Write twelve thousand, and three hundred. 
 
 12. Write ten thousand, two hundred and six. 
 ( >py and multiply the following: 
 
 (13.) (14.) (I5-) ('6.) (n.) 
 
 5111 6llO 7100 8OOO 9010 
 
 66666 
 
08 II V I. T I f LI Ci T 10 
 
 LESSON VII. 
 
 ; time* I are 7. 7 tluim ^ are 49. 
 
 7 ' 7 " 8 " 56. 
 
 7 ; " ; 9 6 3 . 
 
 7 * 4 - 7 ;o - 70. 
 
 7 " 5 " 35- 7 " n 
 
 7 ' 7 i-' . 
 
 1. 1 ..Is 6 pupils how n, 
 
 2. Ai 7 dollar- ;i h.ir 
 
 ; v What cost 7 slates, at 8 
 H..;;I. r jui.l 5 9 ill I 
 ii did In- 11 ? 
 
 5. An- 7 tinirs 5 greater or less thau 6 times 7 ? 
 
 6. If a stage goes 7 miles an hour, how far will it 
 . in 7 ln> 
 
 ,v at ir dollars a ton: 
 
 8. How many quarts will | hear, if 
 
 n 10 quarts? 
 
 9. If a v as 9 dollars a week, how mud 
 
 ,irn in 7 uci-ks? 
 
 10. A iv 7 times 7 DUN | 8 ? 
 
 1 1. 1 7 ni'-loiis conic to ? 
 i-'. il i nd. live hundred seventy. 
 
 C -p. and multiply the following: 
 
 (I*) (I4-) (IS-) (16.) 
 
 3101 5011 4111 8001 9100 
 
 17777 
 
M I' L TI PLICA T ION. 09 
 
 LESSON VI 
 
 8 times I are 8. 8 times "J are 56- 
 
 8 
 
 M 
 
 2 " 
 
 1 6. 
 
 8 " 
 
 8 
 
 a 
 
 64. 
 
 8 
 
 " 
 
 3 "' 
 
 24. 
 
 8 
 
 9 
 
 " 
 
 72. 
 
 8 
 
 (( 
 
 4 " 
 
 3 2 - 
 
 8 " 
 
 10 
 
 ii 
 
 80. 
 
 8 
 
 " 
 
 5 " 
 
 40. 
 
 8 < * 
 
 ii 
 
 
 
 88. 
 
 8 
 
 it 
 
 6 " 
 
 48. 
 
 8 
 
 12 
 
 
 
 96. 
 
 1. What cost 8 quarts of cider, at 4 cents a quart? 
 
 2. If 5 school days constitute a week, how many 
 school days are in 8 weeks? 
 
 3. George spent 6 cents a day for his lunch : how 
 much did he spend in 8 days ? 
 
 4. Sold 7 barrels of flour, at 8 dollars a barrel : what 
 did it come to ? 
 
 5. What cost 8 yards of cloth, at 8 dollars a yard ? 
 
 6. Are 8 times 5 more or less than 6 times 7 ? 
 
 7. In i mile there are 8 furlongs : how many fur- 
 longs are there in 9 miles ? 
 
 8. If 8 young peach trees bear 10 peaches each, how 
 many will all bear? 
 
 9. A teacher has 8 classes in her school, with n 
 scholars in each class : how many pupils has she ? 
 
 10. Which is greater, 8 times 9, or 6 times 12 ? 
 
 IT. Write two hundred and ten thousand and seven. 
 Copy and multiply the following : 
 
 (12.) ' (13. (.4.) (IS-) (i<5.) 
 
 5100 7010 6110 8011 9111 
 
 88888 
 
70 ; r L T i i> 1. 1 < ATI" 
 
 LESSON IX. 
 
 9 tlmm I are 9. 9 times J arc 63. 
 
 9 2 * 1 8. 9 " 8 u 72. 
 
 9 * 3 " 27- 9 " 9 " 8'- 
 
 .> " 4 " 36. 9 " 10 " 90. 
 
 9 " 5 45. 9 ! i 99 . 
 
 9 6 54. 9 " 12 " S- 
 
 T. h i yard an- ;, l'.-i-t : h<>\v many i\ct in 9 yards ? 
 
 2. What cost 4 tables, at 9 dollars each 'i 
 
 3. lln\v far will u boat sail in 9 hours, if she sails 5 
 miles an hour? 
 
 if a liuntiT kill- 6 pigeons at a shot, how many 
 will he kill by 9 shots? 
 
 5. What cost 9 barrels of nnts, at 7 dole, a barrel ? 
 
 6. Paid 9 cents apiece for 8 inkstand- : what ilM 
 they all come to ? 
 
 7. What i.s tlu- diflV: n 9 times 6 ai 
 - 8? 
 
 8. At 10 cts. a quart, what cost 9 quarts of berries ? 
 
 9. In i dollar there are 10 dinu-.s: luw many d 
 are there in 9 dollars ? 
 
 10. Charles obtained 9 merits, ainl 
 
 for each nierr b did he ' 
 
 ir. Which i.- 1 crivater, 9 times 8, or 
 12. \\ ; . one hundred and six thousa; 
 Copy and multiply the following: 
 
 13-) ' '4') (15) (i 6-) 
 
 6101 5001 Son 9111 
 
 9999 
 
A T 
 
 ION. 
 
 
 u 
 
 
 
 
 
 N 
 
 X . 
 
 
 
 IO 
 
 fillies 
 
 7 
 
 are 70. 
 
 10 
 
 
 
 8 
 
 " 80. 
 
 10 
 
 (( 
 
 9 
 
 " 90. 
 
 10 
 
 (( 
 
 10 
 
 " 100. 
 
 10 
 
 u 
 
 II 
 
 " I 10. 
 
 IO 
 
 It 
 
 12 
 
 " 120. 
 
 IO times I are IO. 
 
 10 k> 2 " 20. 
 
 10 3 " 30. 
 
 10 '' 4 " 40. 
 
 10 " 5 <' 50. 
 
 10 " 6 " 60. 
 
 1. What cost 10 tons of coal, at 6 dollars a ton ? 
 
 2. At 10 cents a yard, what cost 7 yards of muslin ? 
 
 3. If a man earns 10 dollars a week, how much will 
 he earn in 8 weeks ? 
 
 4. At 10 dimes each, how many dimes in 9 dollars ? 
 
 5. What is the cost of 10 tables, at 10 dollars api- 
 
 6. At 12 dollars apiece, what cost 10 overcoats y 
 
 7. How many bushels shall I have from 10 
 trees, if each tree bears 1 1 bushels ? 
 
 8. Write eight hundred, and multiply it by 10. 
 
 LESSON XI. 
 
 1 1 1 
 
 times I 
 
 are II. 
 
 I I time* 7 
 
 are 77. 
 
 
 1 1 
 
 - 
 
 " 22. 
 
 ii - 8 
 
 " 88. 
 
 
 II 
 
 - 3 
 
 " 3> 
 
 ii " 9 
 
 " 99- 
 
 
 1 1 
 
 - 4 
 
 " 44- 
 
 II " 10 
 
 " I 10. 
 
 
 II 
 
 - 5 
 
 " 55- 
 
 ii ' ii 
 
 '* 121. 
 
 
 II 
 
 " 6 
 
 " 66. 
 
 II " 12 
 
 " 132. 
 
 
 1. A farmer sent 1 1 chickens to market, each weigh- 
 ing 3 pounds: how many pounds did they all weigh ? 
 
 2. What cost 1 1 thimbles, at 4 cents each ? 
 
 3. At 6 cents each, what will 1 1 tops come to ? 
 
n 
 
 4. What et <t i i }><)iind> of | 
 pound? 
 
 5. JIow mai there in an oivhaid. 
 which has 7 rows and n treo in a : 
 
 6. If i melon is worth 8 peaches, how many pea 
 i melons worth ? 
 
 ;. It' \<>u \v ]'.!. < } lines each d;:y. how many wiK 
 
 in ji da 
 8. At 12 cents a}> d \\ill u knives cost? 
 
 LESSON XII. 
 
 12 time* I are I J. iimr* 7 are 84. 
 
 u " -> - 24. 12 8 * 96. 
 
 I 2 - ^ - 36. I .' " Q ' ! 
 
 I 2 " .} ' 12 ** ID * 120. 
 
 12 - 5 * 60. ' I I 
 
 12 ** 6 i 2 i ' ' ' ; 
 
 1. William lia-> 5 inarhlrs and .I:nn<< In- . 
 
 iy : hn\v niaiiv ni:irl<les has Jan 
 
 2. How many roses will 4 liii-lu- j>r.'<hic(\ if 
 has 12 roses? 
 
 is a mile, what will it cost to rid 
 
 4. At 7 dollars a week, how mm-h will a man FJ- 
 in 12 weeks? 
 
 5. In i dozen there arc T: units: how many units 
 an. there in 9 dozc'n ? 
 
 6. What cost TO dozen eggs, at 12 cents a do/en '? \ 
 
 7. A car ha< s wheels: how man\ to train 
 
M T J. T I P I. I C A T ION. ?.'] 
 
 LESSON XIII. 
 
 Explanation of Terms* 
 
 1. What is Multiplication ? 
 
 Multiplication is finding the amount of a 
 number taken or added to itself, a given number nt 
 times. 
 
 2. What is the number to be multiplied, called ? 
 
 Th< Mnlfipficftnd. 
 
 3. What the number by which you multiply? 
 
 The Multiplier ; and shows bow many times the 
 multiplicand is to be taken? 
 
 4. What in the number obtained by multiplication called? 
 The rroditcf. 
 
 When it is said that 2 times 3 are 6, which is tin* 
 multiplicand? The multiplier ? The product? 
 
 3. What el-^e are the multiplier and multiplicand called? 
 
 K F.MARK. The product is the xam< in whatsoever order the 
 factors are multiplied. Thus, if 4 be represented 
 by a hori/ontal row of 4 counters, and 3 by a + 4- + -f 
 perpendicular row of 3 counters, it is plain by 4- + + + 
 inspection that the horizontal row taken 3 times + + 4- 't- 
 is equal to the perpendicular row taken 4 times. 
 
 (>. How is Multiplication denoted? 
 
 By an ohfiffite rross, called the *ign of nnd- 
 'iplicvi'iun ( x ). Thus, 3x4 shows that 3 and 4 are to 
 e -multiplied together. 
 
 Read the following : 
 
 2x4 = 6 + 2. 4 times 6 = 3 times 8. 
 
 3x6 = 2/9. 3 times 12 = 6 times 6. 
 
M t 
 
 M. iitnl Rxerciae*. 
 
 1. What cost 5 oranges, at 4 cents each ? 
 
 M.YSIS If i orange costs 4 cents, 5 oranges will cost 5 
 4, or 20 cents. Therefore, 5 oranges will cost 20 n 
 
 2. What will 4 pears < tfl cadi !' 
 
 3. If John \ a day, bow m. 
 
 he write in 5 i 
 
 4. What cost 7 writing books, 
 
 5. At 6 dollars aji r, what cost 8 h;r 
 
 6. What c'o-t 9 cloaks, at 10 dollars apiece? 
 
 7. What i- the diJleiviif- 
 times 6? 
 
 8. If i orange is worth f> ai'pl' -. hw many ;: 
 
 an- 12 onmgei vo 
 
 LESSON XIV. 
 
 99'/u-ii t/if Mn/fij:'i> r fi<t* luit ttti. . ami the 
 
 1'riHluct <f tin It /it/ii rr i* /.<>* than J(t. 
 
 i. If i car costs 1304 dollars, what will 2 cars cost ? 
 
 i. YSI*.. \Yriti- the niultiplirr under tin- ' 
 multiplicand, anl Ix-iriiinin^ at tin- oed 
 
 thus: 2 times 4 unit* are 8 unit- > in 
 
 -'ire inultiplii-d. beca 
 
 it i* unil*. 2 t 9et1 ^6c8 
 
 in t'-ns' jilace. !> 
 3 hundreds an- 6 In. n hundreds' pla' 
 
 2 t'niH-s T Ksand. Set 
 
 tlu- 2 in thousjr etc 
 
 (O (3-) (4.) (5.) 
 
 3.? -4 : 2 22210 33 02 
 3 4 
 
M r LT [PLIC ATI o N . ;:> 
 
 Mental K\< r< is ... 
 
 1. What 18 the cost of 7 books, at 6 dollars each ? 
 
 ANALYSIS. Since i book costs 6 dollars, 7 books wil cost 7 
 times 6, or 42 dollars. Therefore, 7 books cost 42 dollars. 
 
 2. What cost 6 barrels of peas, at 9 dollars a barrel ? 
 
 3. How many are 8 times 9 horses ? 
 
 4. At 7 dollars a yard, what cost 8 yards of cloth ? 
 
 5. If a pigeon flies 7 miles an hour, how far will it 
 fly in ii hours ? 
 
 6. What cost 9 pounds of ham, at 12 cents a pound ? 
 
 LESSON XV. 
 
 When the Multiplier lis but otie figure, find the 
 Product of <t Jif/ure is 1O or more. 
 
 i. What will 3 pianos cost, at 536 dollars apiece ? 
 
 ANALYSIS. Since i piano coats 536 dollars, 3 Operation. 
 pianos will cost 3 times 536 dollars. Set the 536 dols. 
 
 multiplier under the multiplicand, as before, 3 
 
 and beginning at the right proceed thus : 3 times 
 6 units are 18 units, equal to i ten and 8 units. Ans. 1608 dols. 
 Set the 8, or units' figure, under the figure by 
 which you multiply, and add the i ten to the product of the 
 next figure, as in Addition. Again, 3 times 3 are 9 tenn, and i 
 ten make 10 tens, equal to i hundred and o tens. Set the o 
 in tens' place, and add the i to the product of the next figure. 
 Finally, 3 times 5 hundreds are 15 hundreds, and i will mako 
 16 hundreds. Therefore, 3 pianos will cost 1608 dollars. 
 
 Multiply the following in like manner : 
 (2-) (3-) (4.) (5-) 
 
 4568 375 6 374o 64346 
 
 2 345 
 
, T i r i i < A T i 
 
 573 8 
 
 4 6 
 
 (II.) (12.) 
 
 65327 548064 7603 
 7 8 9 
 
 14. In i year il. : how many 
 an- thTe in 14 VIM 
 
 15. If i rth 450 d 
 
 ; Hinilar h 'i -"5 dole. 
 
 1 6. In i farm tl. ^20 acres : 
 are I 
 
 17. What are 6 carriages worth, at 750 dollars 
 ;qi- 
 
 18. Multijily 720;^ ]M)und.s by 7. 
 
 19. Multijily S2oo <l)llars 
 
 20. Multiply Q.V15 l.arn-N ],y 9. 
 
 MeutMl F.xvrrUr*. 
 
 T. What is tljc price 
 
 ANAI v-i :ul ? iiiii: 
 
 s, or 90; and 3 
 
 -|iml to i ten and 5 units, whirh mldrd to i/> dollars make 105 
 ilillarj. the answer n-tjuired. 
 
 I. What M 2 nu'ltulroiH. at ;'> dollar- 
 
 3. How many jNuinds aiv 4 times 5'> IN muds? 
 
 4. How many ^allfii- aiv 5 tiim- 6;, -allni 
 
 5. At 8l \vliat will l.o the cu-t f 6 
 
M T L T I I' L I C A T I O X . 77 
 
 LESSON XVI, 
 
 When tin- Multiplier ling two or more Figure*. 
 
 i. Wluit will 104 horses cost, at 245 dollars apiece ? 
 
 ANALYSIS. Since i horse costs 245 dollars, Operation. 
 I-J4 horses will cost 104 times 245 dollars. 245 
 
 Write the multiplier under the multiplicand, 104 
 
 units under units, etc., and beginning at the 
 right as before, proceed thus: 4 times 5 units 980 
 
 are 20 units, or 2 tens and o units. Set the o, 245 
 
 or units' figure, under the figure by which' we 
 are multiplying, and add the 2 or tens to Ant. 25480 dels. 
 the next product. Tin- other figures of the 
 multiplicand are multiplied by 4, and the results set down in 
 like manner. Next, the product by o tens is o ; we therefore 
 omit it. 
 
 .in, i hundred times 5 units are 5 hundreds. We set the 
 5. or units' figure, in hundreds' place, under the figure by which 
 \ve are multiplying, because it is fmmlml*. The other figuren 
 of the multiplicand are multiplied, in like manner. Finally, 
 adding these partial product* together, the result, 25480 dollars, 
 is the whole product required. 
 
 I I. What is m-ant by partial products, and why so called 'i 
 I'fd'tlffl ProtltH'ts are tin* srrrru/ ir^nl/* which 
 arise from multiplying the multiplicand by the respect- 
 ive figures of the multiplier, and arc so called be- 
 cause they are pnrt* of the entire product. 
 Multiply the following in like manner: 
 
 (2.) (3-) (4.) (5-) 
 
 534 3215 43! 53* 
 
 35 42 54 
 
M U L T I I' L 1 L A T ION. 
 
 LESSON XVII. 
 
 1<> \ i. \\ of Pi iii. iples. 
 I .V 1 : \\ \\ ; T<- numbers for mult ii 
 Writ <' flic t/nilti/if 
 
 Him'- 
 
 16. \Vln-n tin- multiplier has but one t:. red? 
 
 . 
 
 iiiiil/iji<' i it, and set dnu'n the result 
 
 Addition. 
 
 17. WIuMi tin- inultiplirr \\s& two or more figarefl, how? 
 
 '//'/// ///' tan 1 by each i 
 
 tij I *cf (If nre of tack j> 
 
 inl fir ' ^um 
 
 1%. IIo\v i> !:;iilti|];-!itMn proved? 
 Multiply thf ninltijilipr by i 
 
 f/i the fir >rk is r( 
 
 Exam 
 
 i. Multiply 65 hy 38, and prove the operation. 
 
 Multiplicand 65 tm- Multiplier 38 
 
 Multiplirr 38 and 65 
 
 520 190 
 
 195 228 
 
 Product Same result as before 2470 
 
 (3-) 
 35670 481. 67086 
 
 75 
 
MULTIPLICATION. 79 
 
 6. Allowing 320 acres to a farm, how many acres 
 are there in 25 farms ? 
 
 7. If i carriage is worth 850 dollars, how much are 
 47 carriages worth ? 
 
 8. What cost 375 acres at 54 dollars an acre ? 
 
 (9-) 10.) (u.) (12.) 
 
 543^5 45467 76734 68659 
 64 68 95 84 
 
 (i3.) (14- (15-) 
 
 5427 6854 7496 
 
 73 127 234 
 
 (17.) (18.) 
 
 37610 74063 
 
 307 278 
 
 21. TIow many oranges will 75 trees produce, if each 
 tree bears 2563 oranges? 
 
 22. What is the product of 563 multiplied by 153 ? 
 
 23. What is the- product of 1275 into 2 6 ? 
 
 24. What cost 367 horses, at 305 dollars apiece ? 
 
 25. What is the product of 430 multiplied by 321 ? 
 
 26. If a railroad car goes at the rate of 288 miles 
 per day, how far will it go in 335 days ? 
 
 :> 7 .) (28.) (29.) (30.) 
 
 3205 5 2 3 6704 7006 
 
 2.\<> 265 405 2613 
 
Ml M T I, 1 1 I' 1. I < A T I O N . 
 
 LESSON XVIII. 
 
 \Vhrn lh Multiplier U 10, 100. 1(100, rfc. 
 
 19. \Vlmt is tho et!'. bet t u fi 
 
 It ri'iiiorrs tin- 1L . 
 
 h-n tint I-M. I'. IM. Q Thu. 
 
 but 30 d< 
 
 20. What, if : . 
 
 ritfiir is N //r/v/ //, 
 
 lv ico. 'I . lut 400 
 
 . .ur hum; 
 i. V 
 
 U .: will 100 ^luwls CMSt, at 58 dollars eu 
 
 >N. 58 iloK x 100= 5800 (1- 
 Jl. How multiply by 10, 100. looa etc.? 
 
 are c //>///////// 
 
 To anna signifies to place after, or 01 
 
 3. How ma: :rs nll>v, 
 3'>j days to a year? 
 
 4. What is the pr.ulurt <>f 4:1 multiplied by 100 ? 
 
 . many an- icoo tl 
 
 V IOOO. 
 
 ;. Kind tbe pn>dnrt of 256 multiplied by 1000. 
 Multiply 43 SS by 1000. 
 Multipl\ i oooo. 
 
 10. Multiply 07063 by 10000. 
 
 11. Multiply 6504 by 100000. 
 
MULTIPLICATION. 81 
 
 LESSON XIX. 
 
 When one or both factors have ciphers on the right. 
 
 i. What cost 30 city lots, at 2500 dols. apiece ? 
 
 ANALYSIS. Since i lot is worth 2500 dols., 2500 d. 
 
 30 lots must be worth 30 times 2500 dols , and 30 
 
 2500 dols. x 30=7500 dols. 
 
 We multiply the significant figures 25 by 3, Ans. 75000 d. 
 and to their product annex as many ciphers as 
 we find on the right of the multiplier and multiplicand, which 
 i three. The result is 75000 dols. 
 
 22 . How proceed when one or both factors have ciphers on 
 the right? 
 
 Multiply the significant figures together ; and to the 
 result annex as many ciphers as arc found on the right 
 of both factors. 
 
 () (3-) (4-) (5-) 
 
 42000 3503 32000 8000 
 
 6 200 300 900 
 
 Ans. 252000 Ans. 9600000 
 
 6. What is the product of 9000 into 300 ? 
 
 7. Multiply 365 by 200. 
 
 8. Multiply 258 by 5000. 
 
 9. Multiply 3000 by 327. 
 
 10. Multiply 80000 by 94. 
 
 11. Multiply 4000 by 3000. 
 
 12. Multiply 3200 by 5400. 
 
 13. If T acre of land produces 40 bushels of wheat, 
 wh.il will 3000 acres produce? 
 
DIVISION. 
 
 LESSON I. 
 
 To TBACHXM. The deeiffn of this Leon IK to tfmtfop the MM of Km*, 
 M nied In /NrMon, and tort the popU to MM the rtniferUy < 
 
 i. I li.tv. i j>oncils: if I hand i of them t- 
 many sliall 1 
 
 j. If I hand you another, how man 
 
 How many times ha\- I handed yon oft 
 
 many tinu-s can i jM-ncil In- taken f'r 
 
 pone 
 
 5. Ii .; prar- in a tVuit di>h : if I take I of 
 
 them. ho\\ many will 
 
 It' I take i more, how mai 
 
 many tii. ir !" 
 
 Tli /'</ titm ^. 
 
 8. How many tinu-s can i j in $ 
 
 pemf 
 
 9. How many tim-s i in 3 '.' " .? times." 
 
 10. Ih-iv are 4 apples : it' I pass I t> the first pupil, 
 to the second, i to the third, and i to the fourth, 
 
 how many times shall I have passed an apple ? 
 n. How mnny will he left? Show it with 
 
DIVISION. 83 
 
 LESSON II. 
 
 To TEACHERS. The object of this Lesson is, to illustrate the forma- 
 tion of the Division Table of 2. 
 
 1. Let each make two stars upon his slate as I make 
 them upon the blackboard. ^f & 
 
 2. If you take 2 stars from 2 stars, how many will 
 be left? "None." 
 
 3. How many times are 2 stars contained in 2 stars ? 
 One time. 
 
 4. Make two groups of 2 stars cadi ; as, 
 
 ~- ::- # x 
 
 5. If yon erase 2 of these stars, how many will be 
 left ? "^Two." 
 
 6. If you erase 2 more, how many ? " None." 
 
 7. How many times are 2 stars contained in 4 stars? 
 Ttro times. 
 
 8. Make 3 groups of 2 stars each ; as, 
 
 9. I low many times are 2 stars contained in 6 stars? 
 
 times. 
 
 I.-t the clafs continue the illustration, and write out tho 
 . as below. 
 
 2 in 2, i tinn. 2 in 12, 6 times. 
 
 2 in 4, 2 tin i 2 in 14, 7 times. 
 
 2 in 6, ' 3 times. 2 in 16, 8 times. 
 
 2 in 8, 4 time-. 2 in 18, 9 times. 
 
 2 in 10, 5 times. 2 in 20, 10 times. 
 
 10. If Joseph can buy i pencil for 2 cents, how 
 m.iny pencils can he buy for 8 cents ? 
 
LESSON 111. 
 
 3 in 3, i i 3 in 18, 6 times. 
 
 3 in 6, 2 times. 3 in 21, 7 times, 
 
 3 in 9, 3 times. 3 in 24, 8 times. 
 
 3 in J2, 4 times, 3 in 27, 9 tin 
 
 3 in 15, 5 times. 3 in 30, 10 tin. 
 
 i. II- .w in ;:ny oranges at 3 cents each can George 
 
 liny for 12 ce: 
 
 u/rsis.Since 3 cento will buy i orange, 12 
 >M many as 3 cents are contained times in 12 cents, \ 
 
 i i.-.-. 'I ; 
 
 2. If 3 apples ;r i jviifil, 
 are 6 apples worth!' 
 
 3. At 3 cents a yard, how many yards of tape can 
 
 you liny for 9 cents? 
 
 4. How many threes in 15 ? In ? r V In 
 
 5. How many times can you taki- 3 apples fr>m a 
 fruit dish containing 15 a[ -MO\V it. 
 
 6. llo\v many n 
 
 7. What is finding how many times one numlx-r id 
 containr.l in another called ? 
 
 Division. 
 
 8. What is the result obtained hy division calle> 
 The <>ttotii>nt. 
 
 Copy and divide the following: 
 
 (9^ (10.) (II.) (12.) (I 3 .) 14.) 
 
 3)24 - ' 1 
 
1) I V I S I -V . Mo 
 
 LESSON IV. 
 
 4 in 4, i time. 4 in 24, 6 times. 
 
 4 in 8, 2 times. 4 in 28, 7 times. 
 
 4 in 12, 3 times. 4 in 32, 8 times. 
 
 4 in 1 6, 4 times. 4 in 36, 9 times. 
 
 4 in 20, 5 times. 4 in 40, 10 times. 
 
 1. A teacher having 12 apples, divided them equally 
 among 4 pupils: how many did each receive ? 
 
 ANALYSIS. Since 12 apples were divided equally among 4 
 pupils, each pupil received as many apples as 4 is contaim-d 
 tinii-H in 12 ; and 4 is in 12, 3 times. Therefore, each pupil 
 iv eivrd 3 appi< 
 
 2. If you give 8 marbles to 4 boys, how many will 
 each receive !' 
 
 3. Henry paid 16 cents for 4 pears: how much was 
 that apiece ? 
 
 4. If you divide 20 pounds of flour equally among 4 
 persons, how many pounds will each receive? 
 
 5. How many fours in 16 ? In 20? In 24 ? 
 
 6. Sold 4 vests for 28 dollars : what was that apiece ? 
 
 7. A teacher bought 4 slates for 40 cents : what was 
 the cost of each ? 
 
 8. If you pay 36 cents for 4 quarts of chestnuts, 
 what will that be a quart ? 
 
 9. How many fours in 36 ? In 24 ? In 32 ? 
 
 Copy and divide the following : 
 
 (10.) * (ii.) (12.) (13.) (14.) (15.) 
 4 20 4 32 4 28 4 36 4 24 4 4c 
 
D 1 V 1 S 1 U N . 
 
 LESSON V, 
 
 5 in 5. i ; 5 in 30, 6 times. 
 
 5 in 10, 2 ti,;. 5 ,. 
 
 5 in 15, 3 times. 5 in 40, 8 tin. 
 
 5 in 20, 4 times. 5 in 45, 9 tin; 
 
 5 in 25, 5 times. 5 in 50. 10 times. 
 
 1. If you cKfidi 10 marbles i ial parts, how 
 many will tin-re he in each j>art? 
 
 2. If you pay 15 eeiits for 5 yards' 
 will thai 
 
 3. Bought 5 quarts of milk for 20 
 that a qof 
 
 4. If 30 children are seated equally on 5 ben 
 how many will there be on a ben 
 
 5. If 5 guns cost 40 dllui>. what will i gun c<'- 
 
 6. A man having 35 acres of land, fenced it into 5 
 equal pasture-: ho\\ many acres to a pa 
 
 7. If you walk 45 miles in 5 
 will you walk j 
 
 8. A tea 1 50 dollars in eqn 
 
 :ig 5 of his hi - : what did each r- 
 
 9. Ayonni: man paid 40 dollars for boar 
 wa< that per week / 
 
 10. George received 45 cents for picking 5 quai 
 strawberries : what was that a quai 
 
 Copy and divide the following: 
 
 (II.) (12.) (I 3 .) (14.) 
 
 5) 2 5 5)30 5)35 
 
DIVISION. 8? 
 
 LESSON VI. 
 
 6 in 6, i time. 
 6 in 12, 2 times. 
 6 in 1 8, 3 times. 
 6 in 24, 4 times. 
 
 6 in 36, 6 times. 
 6 in 42, 7 times. 
 6 in 48, 8 times. 
 6 in 54, 9 times. 
 
 6 in 30, 5 times. 6 in 60, 10 times. 
 
 1. II mv many yard< of ribbon at 6 cents a yard can 
 you buy for 18 cents V 
 
 2. If you put 6 oranges in a basket, how many bas- 
 kets will be required to hold 36 oranges ? 
 
 3. If I pay 12 dollars for 6 books, what will the 
 books cost me apiece ? 
 
 4. In 6 pages the printer made 24 mistakes: how 
 many mistakes was that to a page? 
 
 5. How many quarts of milk, at 6 cents a quart, 
 can be had for 36 cent 
 
 6. At 6 dollars apiece, how many muffs can be pur- 
 chased with 42 dollars? 
 
 7. How many times can you take 6 marbles from 4-S 
 marbles ? 
 
 8. If Samuel gains 6 credits each day, how many 
 .vill it take him to gain 54 credits ? 
 
 9. If a man lays up 6 dollars a week, how long will 
 it take him to lay up 60 dollars ? 
 
 Copy and divide the following : 
 
 (10.) (n,) (12.) (13.) (14. (15.) 
 
 6)30 6)24 6i.j2 6)4.^ 660 654 
 
i) i v i s i u x . 
 
 LESSON VII, 
 
 7 in 7, it; 
 7 in 14, 2 times. 
 7 in 21, 3 times. 
 7 in 28, 4 times. 
 7 in 35, 5 time* 
 
 ; m 42, 6 timci 
 7 in 49> 7 ' 
 7 in 56, 8 : 
 7 in 63, 9 ; 
 
 7 in 70, 10 ' 
 
 1. If 7 yards of twist are worth 21 cents, f 
 yard worth ? 
 
 2. i -'3 pages in 7 
 pages will she ivad in i day? 
 
 'ns, how many times 7 lemons? 
 ; In 7 days there is i week : how many weeks in 42 
 
 5. If San ford shoots 35 squirrels in 7 days* how in 
 will he shoot in i day ? 
 
 6. II- uv many sevens in 63 ? How many in 56? In 
 28? In 35? In 
 
 7. 1 >st 56 cents, h \\ill 
 i pound cost ? 
 
 8. If 7 loaves of bread will last a family i 
 how many \ ill 49 lo; = 
 
 9. In a peach orchard there are 63 trees with 7 
 in a row : how n, 
 
 10. How ma: ; pencils make 56 
 
 11. If 7 dozen e<rs cost 70 cents, what cost i dozen ? 
 Copy and divide the following : 
 
 (12.) (13.) (M.) (15-) ('* (70 
 
 7)21 7)56 7)70 
 
DIVISION 
 
 : J 
 
 LESSON V I I I. 
 
 6 times. 
 
 7 thins. 
 
 8 in 48, 
 8 in 56, 
 8 in 64, 
 8 in 72, 
 8 in 80, 10 time.-. 
 
 8 times. 
 
 9 times. 
 
 8 in 8, i i. 
 
 8 in 1 6, 2 times. 
 
 8 in 24, 3 tin; 
 
 8 in 32, 4 tiii. 
 
 8 in 40, 5 tii; 
 
 1. At 8 cents apiece, how many writing-books can be 
 had for 24 cents? 
 
 2. Ho\v many times can you take 8 chairs from a 
 row of 32 chairs? 
 
 3. In 8 quarts there is i peek : how many pecks are 
 there in 40 quart > ? 
 
 4. How many eights are in 56 ? In 48? In 64 !- 
 
 5. How many classes of 8 can he formed of 72 
 pupils ? 
 
 6. Paid 48 cents for 6 slates: what is that, apiece ? 
 
 7. A laundress paid 64 cents for S pounds of starch ; 
 what was that a pound ? 
 
 8. How many times can you draw 8 quarts of vin- 
 egar from a <-ask containing 80 quarts? 
 
 9. How many 8-pound rolls can he made from a ke ; 
 of butter containing 56 pound-? 
 
 to. William picked 8 quarts of blackberries, and 
 sold them for 48 cents: what was that a quart ? 
 n. How many times 8 in 32 ? In 24 ? In 72 ? 
 
 Copy and divide the following : 
 (12.) (13.) (14.) (15.) (16.) (17.) 
 
 8 
 
 8 48 
 
 8'.6 4 
 
 8)56 
 
 8'' 7 2 
 
 880 
 
.Ml DIV.1SIOX. 
 
 LESSON IX. 
 
 9 hi 9, i time. 9 in 54, 6 times. 
 
 9 in 1 8, 2 times. 9 in 63, 7 times. 
 
 y in 27, 3 9 in 72, 8 times. 
 
 9 in 36, 4 9 in 81, 9 times. 
 
 nines. ;n ,o, 10 times. 
 
 I. A teaciier having 27 pllpiU Ui: 
 
 -ua: lnw many \\eic in each cli 
 At 9 doi is can be had 
 
 dollars ? 
 
 3. A larmer planted 54 pcat-h trees in 9 equal rows: 
 how many did In- put in a row ? 
 
 4. Joseph rau-ht 45 fish in 9 hours: how many was 
 
 IT hour? 
 
 mor gathered 63 lnislu-ls <>f a] in 9 
 
 trees: how many bushels did tin? a\cra-- 
 
 6. How many times can 9 be taken from 36 ? 1 
 45 ? From 54 ? l ; n>m 63 ? 
 
 7. If yon pay 9 conts a quart for blackberries. ho\v 
 many quarts can you i 
 
 8. If a hunter catches 9 pigeons at 
 
 h 8 1 pigeons ? 
 
 9. At 9 cents a pack, how many packs of 
 era* lit for 90 cents? 
 
 IQ. How many nines in 45? In 36? 11154? In 
 
 [i*) ('2- i.v) (M-^ ('5-) 
 
 9Uq 9 81 9 72 
 
DIVISION HI 
 
 LESSON X 
 
 10 in 10. i time. 
 10 in 20, 2 times. 
 10 in 30, 3 times. 
 10 in 40, 4 times, 
 10 in 50, 5 times. 
 
 10 in 60, 6 times. 
 
 10 in 70, 7 time.*?. 
 10 in 80, 8 times. 
 10 in 90, 9 times. 
 10 in 100, 10 times. 
 
 1. Sarah paid 40 cents for ribbon, which was 10 cents 
 a yard : how many yards did she buy 'i 
 
 2. In 10 cents there is i dime: how many dimes are 
 there in 60 cents ? 
 
 3. It' you pay 10 cents a mile fora horseback ride, 
 how many mih-s can you ride lor 50 cents? 
 
 4. If 10 chestnuts arc worth i orange, how many 
 oranges are 30 clu-stnuts worth V 
 
 5. At 10 dollars each, how many aecordcons can 1 o 
 purchased for 60 dolla; 
 
 6. How much hay. at 10 dollars a ton, can be bought 
 with So dollars? 
 
 7. How long will it take a horse to go 60 miles, if In? 
 goes 6 miles an hour ? 
 
 8. Ten lads paid 90 cents for the use of a sail-boat : 
 how much was that apiece ? 
 
 9. Ten dollars make i eagle : how many eagles in 
 100 dol>. 
 
 10. How many tens in 40 ? In 50 ? In 90 ? 
 
 Copy and divide the following : 
 
 (n.) (12.) (13.) (I4-) (i5-) ( l6 -) 
 
 1060 1050 1070 10)90 10)80 10)100 
 
1 1 V I < I 1) N . 
 
 LESSON XI. 
 
 Explanation of Term*. 
 
 1. What is 1>. 
 
 Dit'ision is finding how many times one nir. 
 U contained in another. 
 
 2. What is the number to be divided, called? 
 
 Diriih'ntl. 
 
 :{. '!').. ftumb r to 4h Uto by ? 
 Thfl IHrisrtr. 
 
 4. v !ie number obtained 1 
 
 Qtiofteftf. 
 
 5. What in tin- i,umUr /</T, called? 
 
 I ft nniitul* / . 
 
 \\ IK n it is said that 2 is < :nul 
 
 i OfW, which i-s tin- ' Thf d The 
 
 |U. : ivnuiiiidiT I" 
 
 REMARK. A proper remainder is always lea than 
 
 6. I' <lt'noted? 
 
 I short /loriztmtft? line Utwecntwo 
 (-J-), called th v 
 
 7. When placed between two numbers, what does it H 
 I; number &v 
 
 hy the one after if. Thus, 15 : -3. >lnws that 15 
 IK- divided hy 3, and is ivad. u 15 divided h\ 
 . How else i n-d? 
 
 By irrithifj Ihe diri- ;<l<nd \\\ 
 
 short lino hetween them; as - 1 /. 
 
 ,'V and read the following: 8-7-2 = 4 : . 4 + 
 
 S-f-4-4 .- = 20-4; V^7 - 6 + 2. 
 
DIVISION. 03 
 
 LESSON XII. 
 
 To TEACHERS. The design of this Lesson is to illustrate the (iro objfrfs, 
 or daises of examples, to which Division it? applied. 
 
 1. Charles has 6 cents to buy apples which are 2 
 cents each : how many can he buy? 
 
 ANALYSIS. Since 2 cents will buy i apple, 6 cents will buy 
 as many apples as 2 cents are contained times in 6 cents. The 
 object here is to find how many times one number is contained 
 in another. 
 
 Let the 6 cents be represented by 6 counters ; as, 
 
 + + + + + + 
 
 Separating them into groups of 2 counters each, we have 3 
 groups. Therefore, he can buy 3 apples. 
 
 2. James has 6 oranges to be divided equally be- 
 tween his 2 brothers: how many will each receive? 
 
 ANALYSIS Since 2 brothers are to receive 6 oranges, each 
 will receive i orange aa often as 2 is contained in 6. The object 
 here is to divide 6 oranges into 2 equal parts, and find how 
 many there are in each part. 
 
 LI t the 6 oranges be represented by 6 counters ; as, 
 
 + + + + + + 
 
 Separating them into two groups, putting i counter in each, 
 then another, and so on, till the counters are exhausted, we 
 have 3 counters in each group. Therefore, each brother will 
 three oranires. 
 
 9. To what two classes of examples is Division applied '.' 
 
 l-'irst. Those in which it is required to find how 
 many times one number t'.s contained in another. (See 
 examples, pp. 83, 84.) 
 
 Second. Those in which it is required to divide a 
 number into equal parts. (Sec examples, pp. 85, 86." 
 
LESSON XIII. 
 
 K. In th< arner 
 
 will observe that tin- di\ i^-r and -ii\ idend ure the same d> 
 
 i the quotient i> tiiinf. or nn ,'l'*1r<irt nun 
 In the N ftmil, tin- divi.-or and dividend are different denom- 
 '<*, and the y>iti< >it IB the saiue denomination as the 
 The proceasof reasoning in tl 
 
 !>ut the jirnrtiral operation is the Kam 
 v //;/</ one number is contained in anotlier, 
 \\hich accords with the definition of Division. 
 
 i. A i;inn< I 30 l*>: 
 
 jually among 6 lads: what part, ami ! 'i dil 
 
 i latl 
 
 rr, i lad I 
 <>f 30 pounds ; and is 5 pounds. 
 
 > bought 
 for 20 cents ? 
 
 >s Since 5 cents will buy i \\ 
 huy n^ many as 5 cents ar i tiuies in 
 
 i.i 4 time.-. Thert-fure. 20 vnt.< will buy 4 whistles, 
 
 3. To \\liich class does K n.i:'/ \\ ; 
 2? Wl.;- 
 
 4. It' 6 iii.-ii can earn iS dollars per day. how much 
 can i man earn in the .<am 
 
 5. At 8 cents a <iuart. ho\v much milk can be hail 
 
 nts? 
 
 6. If a teaclirr having- 60 pupils puts 12 in a class, 
 !i!>w many classes will he have ? 
 
 1lo\v many drum*, at 9 dollars each, can )->e hou-ht 
 for 108 dollar 
 
DIVISION. 0.-) 
 
 LESSON XIV. 
 
 Slate Exercises in Short Division. 
 
 i. How many apples, at 2 dollars a barivl, ran you 
 obtain for 4602 dollar- '.- 
 
 ANALYSIS. Write the divisor on the left of OJH ration 
 the dividend, with a curve line between them, and 2)4602 
 proceed thus: 2 is contained in 4, 2 times ; write 
 the 2 under the figure divided, for it is the ,n)tc Ana, 2301 b. 
 or<l' r as that figure. Next, 2 is contained in 6, 3 
 times ; write the 3 under the figure divided, for the same 
 reason. 2 is contained in o, no times ; write a cipher in the 
 |iiotient. 2 is in 2. i time; .-ft the i under the figure divided. 
 
 (2.) ( 3 .) (4- (5-) 
 
 2)"420 ^09 48048 
 
 (6.) (7.) (8.) (9. 
 
 6)56o6 7)7070 8)8008 9)9000 
 
 Mental Exercise*. 
 
 1. How many balls, at 8 cents, can Henry buy 
 for 50 cent?, and how many cents will he have left? 
 
 2. If you devicle 54 chestnuts equally among 6 of your 
 companions, what part and how many will each re- 
 ceive ? 
 
 3. How many times is 7 contained in 38, and how 
 manv over? 
 
I V 
 
 LESSON XV. 
 
 \\luii lh I)i\U in itnl . \ac M> m . ich 1'ljfur* 
 
 of Hi. l)i,i,I. 
 
 i. Mow many yards of cloth, at 4 dollars a 
 a tailor buy for 126027 dull.. 
 
 is. Since he can buy i yard f>r 4 ^. 
 dollars, for 126027 dollars he can buy as many 4)126027 
 yards as 4 is contained times in 126027. 
 
 ite the numbers and divide as before. An*. 31506} y 
 But the divisor is not contained in the first 
 figure of the dividend, therefore we find how manv 
 contained in the first is, 4 is in 12, 3 times. Set 
 
 iind'T tin ri-lit hand figure divided. Again, 4 is i: 
 and 2 remainder. Set the i under the figure divided, and pre- 
 
 the remainder mentally to the next figure, mak 
 4 is in 20, 5 times. Set the 5 under the figure 
 
 t. 4 is n< d in 2, we therefore put a nphrr in 
 
 lotient, an<: 2 to the next figure, as if a r 
 
 d-r. making 27. Now 4 is in 27,6 time's and 3 reran 
 NVritinir this last remaind* the 
 
 in. 
 
 Copy and divide tin- following in a similar mai; 
 
 (3-) (4.) (5-) 
 
 45 4)56368 6)15006 6)8 
 
 681 1 3001 J 
 
 (70 (8.) 
 
 4)78400 5)60903 6)84500 
 
DIVISION. 97 
 
 LESSON XVI. 
 
 Review of Principle's. 
 
 10. "When the results are carried in the mind, and the qno- 
 ily is set down, what is the operation called ? 
 
 Short J)h'i#ioH. 
 
 11. How divide by Short Division f 
 
 Place the divisor on the left of the dividend, ami 
 beginning at the left, divide each figure lij it, setting 
 the result under tin- figure divided. 
 
 lii. If the divisor is not contained in a figure of the divi- 
 dend, how proceed? 
 
 Put a cipher in the quotient, and find how many 
 timr* /hi' (liriwr is contained in the next two figures. 
 
 13. If a remainder arises from any figure before the last, 
 how proceed ? 
 
 rrefix it mentally to the next figure, and dicide as 
 fofore. 
 
 14. If from the last, how? 
 
 Place it over the divisor, and annex it to the 
 quotient. 
 
 15. How is Division proved ? 
 
 Multiply the (liri.^jr and quotient together, and to 
 the product add the remainder. If the result is equal 
 to the dividend, the work is right. 
 
 Examples for Practice. 
 
 i. How many books, at 5 dollars each, can be ob- 
 tained for 18038 dollars ? Ans. 3607 and 3 over. 
 
98 n i v i > i <> N. 
 
 (3-) (40 (50 
 
 3)27506 4)60745 5)4i378 
 
 10. How long will it take Julia to braid 560 .- 
 hate, if she braids 4 each day ? 
 
 11. If a 111:111 \\a. .11 hour, how long w ill 
 it take him to go i ooo miles ? 
 
 Into h<>u many fields can a form of 360 acres be 
 led, each field containing 6 acres? 
 
 13. At 8 dollars a barrel, how many barrels of ; 
 
 can IM ha 1 f.r 640 dollars? 
 
 14. In i \\n-k there are 7 days: how many weeks 
 are in 365 days, and how many days ov 
 
 15. Divide 54672 by 3. 16. Divide 45060 
 17. !>i\ ; .de 60456 by 4. 18. Divide 72036 
 10. Divide 46075 by 7. 20. Divide 66408 ' 
 I, s '373 by 9. 22. Divide 90457 
 
 23. A < built 5 houses at a < !f) 55 
 
 dollars : what was the cost of each ? 
 
 A miiKT sent 40260 pounds of coal to n 
 : how many pounds was that to a o 
 
 bought a 5200 dollars, and paid 
 
 in 4 annual pa\ : 
 . \<ar? 
 
 26. How many mik's HUM a l.!nl llv |>,-r day, to 
 niako 2600 miles in 8 days? 
 
 27. If a ma. 10 doll;;' g will 
 it take him 1 > .>i*-nd ^650 d>ll.i 
 
DIVISION. 99 
 
 ', /'', :..]:' '' : 
 LESSON XVII. 
 
 Slate Exercises in Loug Division. 
 
 i. Divide 14120 by 3, using Long Division. 
 
 Div. Div'd. Quotient 
 
 First. Find how many times the divisor 3)14120(4706] 
 is contained in tin- first, or first two figures 12 
 
 on the left of the dividend, and set the quo- 
 tient 4 on the right, with a curve line be- 21 
 tween them. 21 
 /. Multiply the divisor by this 
 quotient figure, and set the product 12 020 
 under the figures divided. 18 
 
 Third. Subtract this product from the 
 figures divided. Fourth. Annex to the 2 Rcm. 
 
 remainder 2, the next figure of the divi- 
 dend, making 21 for a new partial dividend. 
 
 Dividing. in-fore, the third partial dividend is 2. 
 
 But the divisor 3 is not contained in 2. We therefore place a 
 cipher in the quotient, and bringinir down the next figure, 
 divide as before. Finally, placing the remainder arising from 
 the last figure over the divisor and annexing it to the quotient 
 the result is 47063. 
 
 NOTE. To prevent mistakes, it is customary to place a 
 mark under the several figures of the dividend, when brought 
 down. 
 
 py and divide the following by Long Division. . 
 (*) (3-) (4-) (5) 
 
 43328 3'3564 54570 6 5 2 56 
 
 '6.) (^ (8.) (9.) 
 
 645735 8^56450 7^65384 9' 
 
I > I V I S i 
 
 LESSON XVIII. 
 
 Review of Principles. 
 
 10. \Vhen the n*uU*ot the several rteps and the qu 
 are all set down, what is the operation called ? 
 
 17. \Vhut i.s tin- fust step in Long Division? 
 
 rhnl /tfJtr nuinii tinu'x the di 
 
 I in tlie fewest figures on the left of the dividend 
 that will runt din it. 
 
 I . The second ? 
 
 Muftijtfu f/ic f/i'-fs(u' 
 and set /// 'ic figures divided. 
 
 19. The third? 
 
 Subtract t/tc j trot I act from the figures di~ 
 
 4O. The fourth? 
 
 AIUH-.I- remainder the next 
 
 for a new partial dicidcnd ; tlicn divide as 
 
 V. 
 
 4 1 . What is to be don< with the final r- 
 
 'he divisor, and annex it to the </ 
 
 NOTES. i. If tin- p*n-i,,f* of tv :igure 
 
 placed in t 
 quotient figure is too large, and therefore mupt i 
 
 2. If the remaindrr is ?qn<il to or yreater t ior, 
 
 the (juoticnt li.: it.- i.s too snia t be incretued. 
 
 10. llow many tiiiu- is 15 (ntaiiu'd in 105.- 
 
 AN limn - S i;.-. the divisor is not 
 
 tained in tin- fn>t two tijrun-s of the divi- 15)10523(701,'^ 
 dend. we find lnw many times it is o 
 
 ! in the lii>t -liat 
 
 \\ 1! mntuin it ; then inulti]i1\ 
 
DIVISION. 301 
 
 Examples for Prac'lice.' ' 
 
 1. Divide 1506 by 23. Ans. 655*. 
 
 2. Divide 2536 by 8. 7. Divide 34568 by 24. 
 
 3. Divide 3745 by 12. 8. Divide 44605 by 21. 
 
 4. Divide 4678 by 15. 9. Divide 66431 by 32. 
 
 5. Divide 5168 by 9. 10. Divide 75054 by 37. 
 
 6. Divide 6238 by 25. n. Divide 96387 by 45. 
 
 12. A drover laid out 5600 dollars in cattle, at 
 25 dollars a head : how many did he buy ? 
 
 13. If a man can earn 36 dollars a month, how long 
 will it take him to earn 432 dollars ? 
 
 14. A man invested 9765 dollars in land, at 20 dol- 
 lars an acre : how many acres did he buy ? 
 
 15. Allowing 63 gallons to a hogshead, how many 
 hogsheads can be filled from a cistern holding 7000 
 gallons ? 
 
 1 6. How long will 15000 dollars support a person 
 whose expenses are 75 dollars a week? 
 
 17. A captain distributed 3150 pounds of flour 
 among a company of soldiers, giving each 45 pounds: 
 how many were in his company ? 
 
 1 8. Allowing 52 weeks to a year, how many years in 
 5252 weeks? 
 
 19. At 95 dollars apiece, how many horses can be 
 purchased for 9800 dollars ? 
 
 20. If a person travels 58 miles a day, how long will 
 it take him to travel 3480 miles ? 
 
 21. Divide 80045 by 61. 23. Divide 85784 by 63. 
 
 22. Divide 75007 by 56. 24. Divide 90705 by 75. 
 
10-j I) I V 1 
 
 LESSON XIX. 
 
 To find the Quotient Figure when th< Divisor U 
 
 1. I>i\i<lr 12328 by 382. 
 
 : we take 3 for a trial divisor, <">; rnt ',>,. . 
 
 H in contained in 12, 4 times. But multiply. 382)12328(32 
 
 ing 8 bjr 4, we have 3 to add to tin- ],n*lmt ..f 1146 
 tin- next figure, and 3 added to 4 times 3, 
 
 make 15, which is larger than 12, the figures 868 
 
 (1. Hence 4 is too Imrp- for tin 764 
 
 1.. .: 
 
 aiul proceed as before. Jfem. 104 
 
 2*2. How find the quoti.-nt figure, when the divisor is 
 
 lurp- '. 
 
 Tul f figu re of the divisor for a trial divisor, 
 
 nd how 11. rs it is contained in the first or 
 
 f wo figures of the divid <lue aUoir 
 
 for carnjitxj the tens of / the second figure 
 
 of the divisor into the quotient f 
 
 2. Divide 53643 by 213. 5. Divide 678543 by 503. 
 
 3. Divide 64078 by 345. 6. 1 
 
 4. Divide 43 8 4<> by 456. 7. Divide 830245 by 2345. 
 
 LESSON XX. 
 
 When the DivUor i 10, 1OO, 1OOO, 
 
 i. Ho\v iiiaiiy horses, at 100 dollars a] i be- 
 
 bouglit l\r 1545 dollars? 
 
 g n rijilior fmm tho ^y -iiti--n. 
 
 \ a MiimlN-r, <Ii>ide* it by 10 ; for, earh i <x>)i5 45 
 liiTun- in the nuiir .ved one place 
 loth ri-l:t. a\ M. g 12.) . 45 ^*. 
 
DIVISION. 103 
 
 In like manner, cutting off* two figures from the right of a 
 number, divides it by 100; cutting off three, by 1000, etc. 
 
 As the divisor is 100, it is only necessary to cut oft' two figures 
 on the right of the dividend ; those left, are the quotient, and 
 cut off, the remainder. 
 
 23. How proceed when the divisor is 10, 100, 1000, etc.? 
 
 />//> the riijht of the dividend cut off as many figure* 
 as there are cipher* in Ho 1 divisor. The figure* left ici!i 
 he the <j >inti<' tit ; ///o.sr cut off, the remainder. 
 
 2. Divide 564 by 100. 5. 39467 by 10000. 
 
 3. Divide 6531 by 1000. 6. 72364 by 100000. 
 
 4. Divide 8000 by 1000. 7. 200000 by 100000. 
 
 8. Divide 2354 by 20. 
 
 ANALYSIS. We cut off the cipher on Operation. 
 
 the right of the divisor, and the figure 4 2(0)23514 
 on the right of the dividend ; then divide 
 
 by 2, the other figure of the divisor. Quo't, 117,14 Item. 
 The result, 117, is the rjuotient, and 4, 
 
 the figure cut off, being annexed to the remainder i, is the true 
 remainder. 
 
 21. How proceed, when the divisor is composed of sig- 
 nificant figures, with ciphers on the right? 
 
 I. Cut off the ciphers on the right <>f the divisor, and 
 a* iiiiniy figures on the right of the dividend. 
 
 II. Jh'vidc the r<'ni<ihihi<i part of the dividend by the 
 remaining part of the divisor for the quotient. 
 
 III. Annex the figures cut off to the remainder, and 
 t]n> res u If a- ill be the true remainder. 
 
 9. Divide 6533 by 20. n. Divide 43681 by 210. 
 10. Divide 42345 by 30. 12. Divide 48642 by 2300. 
 
In4 li I v I - I c, 
 
 LESSON XXI. 
 
 Oral Drill. 
 
 To TEACHBM.-Bcttcr remits will be obtained by Oral Drill*, aftortf, 
 and frtquent, Uun from Korea of example* recited In 
 
 i To 3 add 4; subtract 2 ; multiply by 4 : .!' 
 by 2 ; subtract 4 ; multiply by 5 : divide by i 
 
 Ex i or. The teacher names the number and the 
 
 operation to be performed slowly at first ; the class ]- 
 operation mentally. Thus, tin- teacher says, " to 3 add 4, " tin- 
 class think , class think 5; "mult 
 
 the class think 20, and so on. 
 
 2. From 8 take 5 ; add 3 : multiply by 4 : divi.i 
 iiiltiply by 5 ; i.ik- 4 : divide by 2 : result '/ 
 Multiply 4 by 9 : divide by 6 ; add 7 ; subtract 3 ; 
 divide by 5 ; multiply by 8 ; add 4: result ? 
 
 4. Divide 15 by 3; multiply by ' 
 by 9; multiply by 8; add 10 ; take 5 : n-sult ? 
 
 From 15 take 7; multiply by 6; di\ 
 add 12 ; take 3; add 9 : by 6 : result ? 
 
 6. To 14 add 6; divide by 5: multiply by 8; take 
 5; divide by 3; add 3 ; multiply by 5 : result? 
 
 7. Multiply 7 by 6; add 8; divide by 10; multiply 
 by 7; t;il by 3; multiply by 8: r 
 
 8. Divide 45 by 9 ; multiply by S ; take 10: divide- 
 by 6 ; multiply by 7 ; add 10 ; add 8: re>ult ? 
 
 u 25 take 7; divide by 6 : multiply 1 
 add f> ; divi.i : multiply by 10 ; di\ 
 
 multiply by 20; divide by 10; add 30: divide by 8 : 
 
FRACTIONS. 
 
 LESSON I. 
 
 1. If a unit is divided m^^^^^m 
 into two equal parts, what 
 
 is eacli part cul, 
 
 One half. 
 
 2. If divided into three 
 equal parts, what are the 
 parts called ? 
 
 Third* 
 
 3. If divided into four 
 equal parts, what are the 
 parts called ? 
 
 Jfowrth*. 
 
 1. Draw a line the length of your book, and divide 
 it into halves. Into thirds. Into fourths. 
 
 2. If divided into seven equal parts, what are the 
 parts called ? If divided into ten, what ? Into twelve ? 
 
 3. What is meant by a half ? (See Q. i.) 
 
 4. What is meant by a third ? Two thirds ? A 
 fourth? Three fourths? By fifths? Eighths? 
 
 5. How many halves make a unit or one ? How 
 naiiy thirds? Fourths? Sixths? Tenths? 
 
 6. What is a half of 2 cents ? 
 
 ANALYSIS If you divide 2 cents into 2 equal parts, one of 
 pjirts is i cent. 
 
 7. What is a half of 4? Of 6 ? Of 8 ? 10? 12? 
 
FRACTIONS. 
 
 LESSON II. 
 
 i. What part of 2 is i ? "<>,. half/' 
 B, What part of $ is 1 ? "One third." 
 
 3. What part of 3 is 2? 
 
 ANALYSIS. Two b two times i ; therefore, two is 2 times 
 i third, or two thirds of 3. 
 
 4. What part of 4 is i ? Is 2 ? Is 3 ? 
 
 5. Wli;. 5 is I I Of 8J83? Of i 
 
 I divide 6 pencils equally among 3 pupils, what 
 part, and how many, will each ; 
 
 ANALYSIS. <">! rdof3. Therefore, each v 
 
 i third part. And i third part of 6 pencil* ia 2 pen 
 
 7 If I di\idc 10 apples equally among 5 girls, \\hat 
 part, and how many, will each i 
 8. How many hal\-s in tuo apples? 
 
 ANALYSIS. In i apple there are two halves, and In 2 a; 
 there most he 2 times 2 halves, which are 4 halves. 
 
 9. How many halves in 4 ? In 5 ? In 6? In 10? 
 i o. How many halves in 3 and i 1 
 ANALYSIS . Sim in nne there are 2 halves, in 3 there are j 
 times 2 or 6 halves, and i half will make 7 halves. 
 
 1 1. How many thirds in 4 and 2 tli 
 i:. How many fifths in 4 and 3 fit' 1 
 
 13. How many units in 4 hah 
 
 ANALYSIS. Since in 2 halv. - i unit, in 4 halves 
 
 are as many units as j halves are contained times in 4 
 halves, whirh i? 2 times. Ant. 2 units. 
 
 14. ll..w many units in 6 halves? In 9 thirds? In 
 8 fourth 
 
; E ACT IONS, 107 
 
 LESSON III. 
 
 Explanation of Term*. 
 
 J. When a number or thing is divided into equal parts, 
 what are the parts callo! ''. 
 
 fractions. 
 
 5. From what do these parts take their name ? 
 
 From the number of ef/tttt/ parts into which 
 the unit is divided. 
 
 6. How are fractions commonly expressed? 
 
 Hy jif/ tires written above and below a line, called 
 the numerator and denominator; as J, J, r 7 T . 
 
 7. Where is the Denominator placed, and what show? 
 The Denominator is written below the line, 
 
 and shows into hoiu many c^iial jHtrfx the unit is di- 
 vided. 
 
 . Where the Numerator, and what does it show ? 
 
 The Numerator is written above the line, and 
 shows liow many jmrf* arc expressed by the fraction. 
 
 i. Express the following fractions by figures : One- 
 half, Two-t hirds, One-fourth, Three-fourths, Four-fifths, 
 I -'iv --eighths, Nine-tenths, Five-thirds, Seven-fourths, 
 ]' )iir-tburt hs, Twelve-fifteenths, Nineteen-twentieths. 
 
 ( O))v and read the following fractions: 
 
 () (3- (4-) ($.) (6.) (7.) 
 
 5 s 1 A 4 
 
 i I * ' A 
 
 J f A A ii ft 
 
FRACTIONS. 
 
 LESSON IV. 
 
 1. If George has 3 half dollars, and his father L 
 him 2 halves more, how many dollar* will IK- ha*. 
 
 ANALYSIS. 3 halves and 2 halves are 5 halves ; and 5 half 
 dollars ure equal lo 2 and I half dollars. 
 
 2. How inai Mirths and 5 i J and J? 
 
 3. How many are 4 fifths and ? Jand}? 
 
 4. The price of a top is 2 and i half cents, and that 
 of a \\histl.- 3 and i half cents: what i.- the price of 
 both? 
 
 *. 2 cents and 3 cents are 5 cents, and i half and 
 i half are 2 halves, or I c< . added to 5 makes 6 cento. 
 
 uy dollars are 3 dollars and ;, f Mirths 
 added to 5 dollars and 2 f< Mirths? 
 
 6. If you h. i give away 3 fourths .f it, 
 
 how much will you have left? 
 
 ANALYSIS. In i ] 4 fourth*-, n ml 3 fourths from 
 
 ;th leave i fourth. 
 
 ;. : ' I !'-..m 7 fifths leave how many? J fro: 
 
 8. 5 riirliths from 9 eighths leave h<w ma;: 
 
 9. Henry's 1 ! ; fourths yards long, 
 and he lost 2 and i fourth yards: how lor. 
 
 part left ? 
 
 A\\I.Y<IS. c ynnls from 5 yards leave 3 yards, and i 
 from 3 fourths leaves 2 fourths. Therefore, the part 
 l.-ft was 3 and 2 fourths yards long. 
 
 10. If you have 7 eighths of a dollar. :id 3 
 eighths, how niueh will you have 1< 
 
!' II A <_' T 1 ^ S . 109 
 
 LESSON V. 
 
 1. What will 4 apples cost, at i half cent each ? 
 
 ANALYSIS. Since i apple costs i half cent, 4 apples will 
 cost 4 times i, or 4 half cents : and 4 half cents equal 2 cents. 
 
 2. What cost 3 plums, at i third cent apiece ? 
 
 3. What cost 8 marbles, at i fourth cent apiece? 
 
 4. What cost 5 pencils, at 2 and i half cents apiece? 
 ANALYSIS. Since i pencil costs 2 and i half cents, 5 pencils 
 
 will cost 5 times as much. Now 5 times 2 cents are 10 cents, 
 
 and 5 times i h:.lf cent are 5 halves, equal to 2 and i half 
 
 which added to 10 cents make 12 and i half cents. 
 
 5. James bought 6 oranges, at 4 and i half cents 
 eaeh : what did they come to ? 
 
 6. How many cents are 4 times 6 and r fourth cents? 
 
 7. II"W many are 8 times 5 and 3 fourths? 
 
 8. How many are 7 times 4 and 3 fifths ? 6 times 
 
 *j? 
 
 9. If a prar costs 4 cents, what will i half a pear 
 cost ? 
 
 i.Y-qs. If i pe:ir f>sN 4 cents, i half a pear will cost 
 i half of 4 cents, which is 2 cents. 
 
 10. If you pay 12 cents for a pie, what must you pay 
 third of a' pi' 1 ? What is of 12? 
 
 IT. At 10 dollars a hanvl. what cost i fifth of a bar- 
 rel of flour ? What is } of 15 ? 
 
 12. Charles gave 3 marbles to his brother, which 
 were i half of all he had : how many had he? 
 
 LYSIS. Since 3 marbles are i half the number, 2 halves 
 mr the whole number) must be 2 timca 3 marbles, which arc <> 
 marbles. 
 
11(1 III ACTION 
 
 LESSON VI. 
 
 i. If 2 pounds of butter cost f of a dollar, v. 
 i | .mind cost? 
 
 M.YSIS. i is i half of 2. therefore, i pound will cost I 
 half as much aa 2 pounds, and i half of J is j of a dollar. 
 
 . If 3 yards of muslin cost j of a dollar, what will 
 i yard cost? What is J of j ? 
 
 ;. I; M luiy a pear for 3 cents, \vi of a 
 
 can you buy for i cent ? 
 
 4. At 6 dollars a yard, what part 
 
 can you buy f<>r i dollar? ;< -liars? 
 
 5. At 4 cents a yard, how much elastic cord can I 
 luiy for 5 cents? 
 
 ANALYSIS. Since 4 cents will buy i yard, i cent 
 fnurth of a yard ; and 5 cents will buy 5 times i fourth, i 
 arc 5 fourths, or i yard and i fourth. 
 
 6. At 8 cents a pound, how much maple s 
 
 .id fr i ; c.-nts? 
 
 hire a barrel, how much flour can be 
 bought for 27 dollars? 
 8. If i yard of braid cost.- 
 
 v Since 3 thirds (i yard) cost 6 cents, i thir.1 
 'Iiirdnf6< 2 cents. Again, if i third of a 
 
 s, 2 thirds will cost 2 times 2, or 4 cento. 
 
 I :' i IH. iiiul of almonds costs 25 cents, how nr 
 \\ill ,'id cost ? 
 
 10. What will ] of a l-arrcl of crauhcrrics 
 at U dollars a hanvl ? 
 
.Virfcel. Jtronz,. 
 
 UNITED STATES MONEY. 
 
 1 . What an- 1h<- denominations of U. S. money? 
 Ku.irlc-. dll; i r-. dimes, cents und mills. 
 
 2. Recite the TADLK. 
 
 10 mills (ni.) arc 
 TO cents 
 
 10 dimes " 
 
 10 dollars " 
 
 i ecu I, rf. 
 
 i dime, (/. 
 
 i dollar, dol. or $. 
 
 i ca^le, E. 
 
 100 cents = i dollar; 50 cents = dollar. 
 25 cents .'. dollai-: \2\ cents I dc"ar. 
 
lit LTBD > T \ T i: B M (i s L v . 
 
 :i. II'i-.v arc tl:- < > "in-i >f tli- I". S. divided? 
 
 Into y ins, and i ins. 
 
 4. Name the coins of each. 
 
 i. Tin- f/otff t-tthis are the double-ea 
 ha[f- - !e </o/for and threat 
 
 pieces. 
 
 i i: N///VT COilM 
 
 "v.and <t 
 
 3. The minor <<>; t , ^ kA five-cent and 
 
 three-cent j)iece^. and the bronze 
 
 i. How i s? 
 
 ANALTSI> are 10 cent* ii. in 3 dimes 
 
 there are 3 times 10 ceuts, which are 30 < 
 
 ny cents in 4 dimes ? In 6 
 
 3. How ni;i. iu 8 dels.? In iodol&? 
 
 4. llou nianv liinies in 40 i-nite? 
 
 is i dime in 10 cents, in 40 
 there are as many dimes as 10 cents are contained times in 40 
 
 !i is 4 times. An*. 4 dimes. 
 
 5. If y dimes in 20 . 
 
 6. II.. w many dollars in 20 (!' : 
 
 7. Ho\v many dollars in 250 cents? In 45: 
 .'. Il.iw is 1 . S. money expressed? 
 
 J>' '' of the if- 
 
 in'/ h ///' -. // the first 
 
 in-', places on ///' /////// ; mills in the next, ami pa 
 (i mill in f/ic XIIIT* ,///. 
 
 - nn- r\],rr.-sr,! ' '// dvllarn, and 
 
 linn-* by ten* of fent*. Tlius. 5 eagles ar* U $50, and 
 
 <> (iiines as 60 c< 
 
 if tlo inn expressed 
 
 ijihtr must !> )>rrlix<-d t> it. 
 
I N 1 T K I) S T A T E S MONEY. 113 
 
 8. Write twenty dols., twenty cts., and 3 mills. 
 
 A us. $20.203. 
 
 9. Write fifty-six dols., thirty-seven cts., six mills. 
 
 0. How is U. S. money read? 
 
 Read the figures on the left of the decimal point as 
 dollar* ; thw in the first two places on the right a* 
 cents ; the next as mills ; the others as parts of a in ill. 
 
 10. Copy and read $78.35 ; $106.37 ; $308.735 ; 
 $430.064; $57240; $60200. 
 
 ADDITION OF U. S. MONEY. 
 
 11. What is the sum of $20.465; $6.28; and $12 ' J . 
 
 ANALYSIS. We write dollars under dollars, $20.465 
 
 cents under cents, etc., and add in the usual WMV, 6.28 
 
 placing the decim<il jioi/it in the amount under 12.00 
 
 those in the numbers added. (P. 112, Q. 5.) 
 
 $38.745 
 7. How add U. S. money? 
 
 Write dollars under dollars, cents under cents, etc., 
 and add as in simple numbers, placing the decimal 
 point in the amount under those in the numbers added. 
 
 NOTE. If any of the given numbers have no cents, their 
 place should be supplied by ciphers. 
 
 (12.) (I3-) (14.) (IS-) 
 
 342.375 460.508 653.36 846.258 
 
 45.26 5340 40.457 6 -7 
 
 840.385 675.235 892,295 75-345 
 
 1 6. What is the sum of $375.408 ; $8.254; $235 ; and 
 $100.40? 
 
lit INI T i; i. 
 
 17. A man paid $5 625 for a hat, $18.50 1 
 and $7.375 for a vest : \\hat did he pay for all !' 
 
 1 8. taught a pair of gloves for $1.75. a tan 
 for $0.87 cents, and a parasol for $6..- 5 : \\ hat did she 
 pay for all ? 
 
 19. A man owes $85.08 for board, $12.50 fur 1 
 and $58.70 for clothes : how much does he owe for all ? 
 
 SUBTRACTION OF U. 8. M< 
 
 i. A man having $128.60, paid $47.735 1(>r a cow: 
 how much had he left ? 
 
 ANALYSIS. We write the less number under Optr 
 the greater, dollar* '.Ian, cents under $128.60 
 
 cento, etc. Subtract in the usual way, and place 47-735 
 
 the decimal point in the remainder under that in 
 
 III.- Mil.trnh. :<!. (P. 112, Q. 5.) Ant. $80.865 
 
 V How subtract United States money? 
 HV/7' the less number under the greater, dollar* un- 
 <l> r dollars, cents under cents, etc., and . 
 
 inbers, placing the decimal point in the re- 
 ider under that in th* subtrahend. 
 
 NOTE. If either of the pi von numbers has no cent*, 
 place should be supplied by ciphers, 
 
 (*) (3-) (4.) 
 
 >H $43.605 $107.38 $95.305 $100.00 
 
 35-45 73-625 17-003 10.75 
 
 6. From $15.38 take $12.30. 
 
 7. IV. >m $no take $68.40. 
 
 8. A man bought a horse for $250, and paid $118.50 
 down: liuw much do<j> he -till owe fr i 
 
UNITED STATES MONEY. 115 
 
 MULTIPLICATION OF U. S. MONEY. 
 
 i. What will 8 chairs cost, at $12.375 apiece? 
 
 ANALYSIS. Since i chair costs $12 375, 8 chains Operation. 
 will cost 8 times $12.375. We multiply in the $12 375 
 
 usual way, and from the right of the product 8 
 
 IK tint off three figures for cents and mills, because 
 tin re are three places of cents and mills in the Ans. $99.000 
 multiplicand. 
 
 9. How multiply United States money ? 
 
 Multiply as in simple number*, and on the r if/hi of 
 the product, point off as many figures for cents (mil- 
 mills as there are places of cents and mills in the mul- 
 tiplicand. 
 
 NOTE. In United States Money, as in simple numbers, the 
 multiplier must be considered an abstract number. 
 
 (2.) (30 (4-) (5-) 
 
 Mult. $25.40 $50.625 $9545 $435 
 
 //// 8 9 15 24 
 
 
 (6.) 
 
 (7-) 
 
 (8.) 
 
 (9-) 
 
 Mull. 
 
 6207 
 
 $75.835 
 
 $463.05 
 
 $7584-25 
 
 By 
 
 45 
 
 5 2 
 
 62 
 
 75 
 
 10. What will 12 pounds of starch cost, at $0.125 a 
 pound V 
 
 11. At $0.375 a pound, what will 25 pounds of but- 
 ter come to ? 
 
 12. What will 20 yards of cloth cost, at $6.75 a yard ? 
 
 13. A miller sold 35 barrels of flour at $10.50 a 
 barrel : what did it come to ? 
 
 14. What cost 100 hats, at $5.50 apiece? 
 
116 t N i i :: i It Off] 
 
 Of P. 8, M<N \:\ . 
 
 1. A man bought 6 sleds for 21.4;: \\luit wa.- that 
 apiece ? 
 
 ANALYSIS. i Bled is i eixth of 6 sleds; therefore, 6)$2i.42. 
 i sled will ooet i sixth of $2142, which is $3.57. -i. $3.57 
 
 10. How divide U.S. money? 
 Divide as in simple numbers, < '.-e right ( 
 
 //W/V/// point off as in res for cents and 
 
 '-re are places of cents and / 
 
 NOTE. For dividing money by money, or by a decimal <li\i- 
 eor, the learner is referred to the Author's New i 
 \v Practical Arithm* 
 
 2. Divide $25.65 by 5. 5. Divide $ 100.60 by 10. 
 
 3. Divide $36.48 by 8. 6. Divide $276 b\ 
 
 4. Divide $63.72 by 9. 7. Divide $360 by 20. 
 
 8. A man sold 7 barrels of flour for $63.70: 
 much did be I 
 
 9. If you pay $25.74 for 6 yards of clotb, what will 
 that be a yard i" 
 
 10. If I pay $14.875 for 7 crates of peacht -. how 
 niiu-h will they cost me a crate ? 
 
 1 1. A bookseller sold 5 slates for $0.685 : what waa 
 that apiece ? 
 
 12. If you divide $1648 equally among 4 poor 
 sons, how much will each receive? 
 
 13. If 8 yards of broadcloth cost $56.40, what will i 
 yard cost? 
 
 14. If 7 pair of gloves cost $15.75, what is that 
 a pair? 
 
(.' OM I'O U X 
 
 T A n L KS. 
 
 L17 
 
 ENGLISH MONEY. 
 1 1 . What are the denominations ? 
 
 Pounds, shillings, pence, and farthings. 
 1 2. Recite the TABLE. 
 
 4 farthings (qr. or far.) are i penny, 
 12 pence " i shilling, 
 
 20 shillings " i pound, 
 
 s. 
 . 
 
 . The p^ind sterling is repre- 
 1 i-nted by a ^old coin callfd a xvtcrciyn, 
 s.ml its value is 414.866?,. 
 
 Tin- value of mi Knirlish Milling is 24.', 
 ; and that of a pinny, about 2 
 cento. 
 
 Sovereign. 
 
 TROY WEIGHT 
 13. For what is Troy weight used? 
 
 For \vei}jliing//o/(/, .v//m\ 
 I I. What are the drinumnations ? 
 
 Pounds, ounces, pennyweights, and grains. 
 
 15. Recite the TAIJI.K. 
 
 24 grains (yr-) are i pennyweiglit, pwt. 
 20 pennyweights " i ounce, oz. 
 
 12 ounces " i pound, Ib. 
 
 lb. oz. pwt. pr. 
 
 1. I low many ounces in 3 pounds? In 4 pounds ? 
 
 2. In 40 pwt., how many ounces? In 42 pwt. ? 
 3 In 2.\ ounces, how many pounds? In 39 
 
t!8 
 
 M ro i- N i. I A i: ! 
 
 \v !-;K; HT. 
 Hi. F..r \vlmt H Avoirdupois <l? 
 
 ' \Nri-llilii: ;i . 
 
 17. What are t us? 
 
 Tons, hundreds, pounds, and ounces. 
 
 18. Recite the TABLE. 
 
 16 ounces (oz.) are i pound, ll>. 
 
 100 IM.U. i hundred weigl 
 
 20 cwt, or 2000 Ibs., " i t<>n. '/'. 
 
 8 ounces are i pound. 4 ounces are pound. 
 
 ih. 
 
 IE The onnfe is often divided into halt**, quarters 
 In l)iisiin-<H. tlu- f/n/m. tin- 7'/</r//rof 25 Ibe., and the /rWn of 
 56 Ibe., are not used as units of Avoirdupois Weight. 
 
 1. How many ounces in 2 pounds? In 3 poun 
 
 2. How many ounces in 2 pounds and 5 uin 
 
 3. In 20 ounces, how many pound 
 
 4. In 32 ounces, how many pound*? In 42 ounces? 
 
 5. In 40 hundred weight. luw many t" 
 
 6. Il"\v many hundreds in 3 t- 
 
 7. How many hundreds ii 
 
COMPOUND TABLES. 
 
 119 
 
 APOTHECARIES' WEIGHT. 
 
 19. For what is Apothecaries' Weight used ? 
 For nii.riiHj t/iK/ici/tcx. 
 
 20. What are the denominations? 
 
 rounds, ounces, drams, scruples, and grains. 
 
 21. Recite the TABLE. 
 
 20 grains (gr.) are i scruple, sc., or 3. 
 
 3 scruples 
 8 drams 
 12 ounces 
 
 i dram, dr., or 3 
 i ounce, oz., or 
 i pound, ft> 
 
 LINEAR MEASURE. 
 
 22. For what is Linear Measure used? 
 For measuring lines, distances, etc. 
 
 23. What are the denominations ? 
 
 I A-iiLTues, miles, furlongs, rods, yards, feet, inches. 
 21. Recite the TABU-:. 
 
 12 inches (in.) 
 3 feet 
 
 1 6J feet, or 5 yards" 
 
 40 rods * 
 
 8 fur., or 3 20 rods " 
 
 are 
 tt 
 
 3 miles 
 
 foot, ft. 
 
 yard, yd. 
 
 rod, perch, or pole, r. or p. 
 furlong, fur. 
 
 mile m. 
 
 league, 
 
 in. 
 
 1 in. 
 
 2 in. 
 
 3 In. 
 
 NOTE. The inch is commonly divided into halves, fourth*, 
 , or truths ; pometimrs into f/rrff/h*, culled linen. 
 
I'.'O : N ] I 
 
 1. (reorge may draw a strait it lin*- i m :pon 
 Markhoanl: tin- otli.-rs on 
 
 2. V 2 in. li!<_r. 3 in. loin:. 6 in. 1 
 
 3. Bow tang is your Arithmetic? II..\\ How 
 long i H.I\\- u 
 
 [OW ln:r i- this tal>K- ? II\v \, 
 
 5. II.>\v many inches in 3 IVri ? In 5 i 
 
 6. 1 1<>\\ man;. 3 yards? In 
 
 7. How many IV < -t in 5 yards and t 
 
 1 .w many feet in 24 in.? In 30 in.? In 36 
 !Iow manyyards in 9 IVet ? In 15 ft.? In 2; 
 
 >TH >: 
 
 2.%. For what Is Cloth Measure used? 
 
 r niraMiriiiLT dotiis. laces. rill>o- 
 20. i Imxv.lividedt 
 
 . uhich II 
 
 f'-ir ih-', etc, 
 
 J7. ;;. 
 
 3 ft, or 36 in. 
 
 - 
 
 9 in. " 
 
 4i in- 
 
 n. 
 
 yard. //>/. 
 
 half ; j | 
 
 qua; . J yd. 
 
 \ ! 
 nth " -fg 
 
 ; '7, Flemi- Mger 
 
 <-n<nl is practically obsolete. 
 
 1. How many yards in S half;. 
 
 2. IIow many yards in 16 fourth-!' In jS ! 
 
 3. I low many yards in i ; . 
 
< O M P U X 1) T A li I . 
 
 
 S Q r A II E MEASURE. 
 2. For what is S<iuare Measure used? 
 
 For measuring surfaces ; as, land, flooring, etc. 
 
 29. What are the denominations? 
 
 Acres, square rods, square yards, square feet, 
 and square inches. 
 
 30. Recite the TABLE. 
 
 144 square in. (x//. ///. are i square foot, sq.ft. 
 () square feet " i square yard, .sy/. //</. 
 
 30 square yards, or ) " ( i square rod, 
 272^ square t ) ( perch, or pole, 
 
 1 60 sijiuuv r " i acre. A. 
 
 640 a " i s([tuire mile, *. ?.'?. 
 
 r. 
 
 1. A Sf/Hffi'f- is a rectilinear figure 
 which has four equal sides, and four 
 ri'jlit a 
 
 2. \stfiiff re inch is a square, each 
 Bide of which is mn' inch in Iciiirth. 
 
 3. A sfjn<tr<' t/<ii'ft is a square, each 
 Bide of which is one yard in length. 
 
 g fq. ft. rr , Pq . yd. 
 
 . i. Tin f any s(|iuirc 
 
 fiirurc. also of a bo<jk, a table, a room, 
 '!<.. are ri'jlit <irtf/les. 
 
 2. Tlie acre was formerly divided into 4 roods ; but, in 
 , the rood is no longer used as a unit of measure. 
 
 1. Make a riirht jingle upon the blackboard. 
 
 2. Make a square inch. 
 
 3. Make a square whose side is 3 inches. 6 Indies. 
 

 COM m I N 1 TA I, I 
 
 4. Make a square foot A <<[\\ 
 
 5. Di\ik' ;i S'|iia:v \anl into ><j 
 
 I >ivide a square foot into stjuuiv in< ! 
 
 7. HM\V many -<|i; 
 
 8. How many 8411 a r 
 
 CUBIC MEA> 
 
 31. For what is Cubic Measure used? 
 
 i- measuring solids; as, timber, boxes of goods, 
 the capacity of rooms, ships, etc. 
 
 39. What are the denominations? 
 
 Cords, cubic yards, cubic feet, and culi< 
 
 inches. 
 33. Recite the TABLE. 
 
 1728 cubic inches (cu. in.) arc 
 
 27 cul.i'- " 
 
 128 cubic feet 
 
 I (Ml).i(' font, 
 I CO 
 
 x. A cube is a regular solid bounded by fix equal 
 
 called ita faces. 
 
 2. A riibir in 1-Ji is a cube, each aide 
 
 of \vhirh is a square inch. 
 
 3. A cubic foot is a cube, each aide 
 of which is a square foot. 
 
 4. A cubic utirtl is a rube. each side 
 of which is a square yard. 
 
 5. A Cortf of woo.] i* n pile 8 ft. 
 lontj. 4 ft, wide, and 4 ft. hi^rh ; for, 8 x 
 4x4 = 128. 
 
 6. A Card Foot = 16 on ft. .an-: 
 
 loiiir 4 ft. wi.ir. ami } ft, high. 8 cord 
 
 
( M P U X D T A B L E S . l&J 
 
 NOTES. i. Timber is now measured by cubic feet ami 
 Inches 
 
 2. The old cubic ton of 40 feet of round timber, or 50 feet of 
 hewn timber, has fallen into disuse. 
 
 1. Draw a cubic inch. 
 
 2. Draw a cube- whose sides arc 2 inches square. 
 
 3. Draw a cubic foot. 
 
 4. How many inches long and wide must a block be 
 to form a cubic foot ? 
 
 5. How many ilrt high is a cubic yard ? 
 
 6. How many cubic feet in 2 cubic yards? 
 
 DRY MEASURE. 
 Ji I. For what is Dry Measure used? 
 
 For measuring 4rrt*> /rtttf, salt, etc. 
 
 JJ5. What are the denominations ? 
 
 Chaldrons, bushels, pocks, quarts, and pints. 
 :*. Krrit.- tin- TABLE. 
 
 2 pints (pt.) arc i quart, qt. 
 
 8 quarts " i peck, p/c. 
 
 4 pecks, or 32 qts., " i bushel, bu. 
 
 36 bushels " i chaldron, ch. 
 
 y s bu. pk. y t pk. qt. pt. 
 
 N< IK. The dry quart is equal to i^ liquid quart nearly. 
 
 i. Fn 6 pints, how many quarts? In 12 pints? 
 2 Iii 12 quarts, how many pi (!:. s ? In 16 quarts? 
 
124 
 
 ii"\\ many quarts in 3 peck.-; In ; pr ;-. 
 .;. 11. i\v many quaris in 5 , 
 5. In 5 pecks, how many 1 
 '. How many bushel* I IQB? In 15 p 
 
 7. How many quarts in 2 1 
 & H"W many quarts in i bushel and i p- 
 9. How many j.ini - ks ? 
 
 D MEASURE. 
 :tT. For what is Liquid Measure used? 
 
 38. What are tin- <i<-Mouniuuinna? 
 
 -heads, barrels, gallons, quarts, pints, 
 :::>. Ut-cite the TABLE. 
 
 4 gills (gi.) 
 
 2 pints i iuart, 
 
 4 quarts i L':ill>n, gaL 
 
 31 J gallons i borreL />cr.. 
 
 63 gallons, or 2 bbls., " i \\<^j;A\ci\(\. hhd. 
 
 hhd. bar. gaL ; 
 
 i. Licjuid Measure is often called Wine M 
 2. Beer Measure is practically obeolet.* in this .in>try 
 
 i. How many L r ilN in ^ pint- V In 6 pii 
 
 j. Hew many pints in 3 quarts ? In S quar - 
 
M I'O L' >, 1) T A 15 L KS. 
 
 123 
 
 3. How many quarts in 3 gallons? Ill 4 gallons? 
 
 4. How many quarts in 5 gallons and 2 quarts ? 
 
 5. In 1 6 quarts, how many gallons ? 
 
 6. In 8 pints, how many quarts? In 12 pints? 
 
 7. How many quarts in 13 pints? In 20 pints? 
 
 8. In 15 gills, how many pints ? In 20 gills ? 
 
 9. How many quarts in 6 gallons and 3 quarts '.' 
 
 CIRCULAR MEASURE. 
 
 40. For what is Circular Measure used ? 
 
 For measuring c//</lrs, latitude and Invtjitu.dc* 
 the -mot inn of the heavenly bodies, ete. 
 
 41. What are the denominations? 
 
 Signs, degrees, minutes, and seconds. 
 
 42. Recite the TABLE. 
 
 60 seconds ") are i minute, 
 
 60 minutes i derive, 
 
 30 degr " i sign, * 
 
 360 deg:- " i cireumterence, c or dr. 
 
 NOTE. Signs are used only in Astronomy. 
 
 A Cirrfe is a plane figure bound- 
 ed by a curve line, every part of 
 which is equally distant from a 
 point within called the center. 
 
 The adjoining figure is a cir- 
 ri-. A D E B F is called the 
 circumference ; A B, the diameter ; 
 C A. C D, C E, etc., radii ; and A D, D E, arcs. 
 

 i-o i N D TA i; : 
 
 M I SC K L 1. A \ 
 12 things ;uv i d 
 12 doz. " I gross. 
 
 20 I 
 
 
 24 sheets are i quire ] 
 
 20 ([uires " i ream. 
 
 2 1 
 
 5 humllca " i 
 
 3 are i 1 
 
 4 leaves '* i <iuarto, or 4t<x 
 
 8 leaves " i >, tavo, or 8vo. 
 
 .cs u i duodecimo, or 12 mo. 
 
 18 leaves " i cightern n 
 
 2^ Icavea " i mo. 
 
 The tonn- 
 
 her ol leaves into which a sheet of paper is folded in i. 
 
 4 in. - i hand, for measuring the height of horses. 
 
 n in. = i span. 
 
 18 in. = i rui 
 
 (, ft t= i fathom, for measuring depths at eea. 
 
 32 Ibs. = 
 4 81bs. = 
 
 i bu. of oats. 
 ur ^ 
 56 Ibs. = i " rye, or salt. 
 
 58 Ibe. = 
 60 Ibs. = 
 62 Ibs. = i ' beans. 
 
 100 pounds = i quintal of dry fish. 
 
 196 pounds = i barri'l of tlour. 
 
 200 pounds = i barrel of fish, beef, or pork. 
 
 280 pounds = I barrel of salt. 
 
YA 
 

 
 s NEW GRADED SERI 
 
 
 COMPLETE IN THREE BOOKS. 
 
 
 L NEW MENTAL ARITHMETIC. 
 
 uta. 
 
 IL NEW RUDIMENTS OF ARITHMETIC. 
 IE. NEW PRACTICAL ARITHMETIC. 
 
 rl.OO. 
 
 complefc 
 
 
 TK\ are usiug . 
 
 Th^ to 
 
 /./)// ^ 
 im n vi i i 
 
 / 
 
 4 If /Ml Mill,. UK, II 
 
 h I Y TO UK M 1 1 l< . 
 
 N B I- 1 particular! 
 
 Lil>< i ntrodi^t : ^fl| 
 
 '