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This item Is filmed at the reduction ratio checked below/ Ce document est filmA au taux da rMuction indiquA ei-deaaout. 10X 14X itx 22X 2tX SBX 7 12X IfX aox 2«X atx 32X ils iu Jifier me age The copy filmed here has been reproduced thanka to the generosity of: Ssminary of Quabtc Library The imeges appearing here are the beat quality possible considering the condition and legibility of the original copy and in lieeplng with the filming contract specificationa. L'exempiaire film* fut reproduit grice A la gin4ro8it4 de: Siminair* ds Qu4b«c BibliothAque Lea images suivantes ont 4t6 reproduites avec lo plus grand soin. compto tenu de la condition et de la nattet* de rexomplairo film*, at an conformit* avec lea conditions du contrat da filmage. Original copies in printed peper covers ere filmed beginning with the front cover and ending on the lest pege with a printed or iilustrsted impres- sion. or the back cover when appropriate. 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Meps, platea. charta. etc.. may be filmed et different reduction ratioa. Thoae too large to be entirely included in one expoeure ere filmed beginning in the upper left hand corner, left to right end top to bottom, aa many framee aa required. The following diagrama illuctrate the method: Lea cartes, planches, tableaux, etc.. peuvent Atre filmto A dea taux de riduction difftrents. Lorsque le document est trop grand pour Atra reproduit en un soul clichA, il est filmA A pertir de I'angie supArieur geuche, de geuche A droite. et de haut en baa. en prenent le nombre d'images nAceesaire. Lea diagremmes suivants illustrent le mAthode. rrete Belure. □ 32X 1 2 3 1 2 3 4 6 6 *m ' ) •■(^ -:« l^: * -■?-■ -^' IJ' B# ^* THE BRITISH NORTH AMERICAN ARITHMETIC, CONTAIiriNO ELEMENTARY LESSONS K rOR THE YOUNGER CLASSES IN COMMON SCHOOLS. /^•..^^•ttRftr>fljQBle expressly for the BRITISH provinces. "-v K. ''•^ ■.,::- 1 «^ A TEACHER. STEREOTYJ'Kl) BY LYMAN THUUSTUN AND CO. BOSTOH. STANSTEAD, L.. C. PrBLlSIlED BY WALTON & GAYLORD. 1833. PREFACE, IN a syslematic course of general education, Arithmetic cluinis a place among the primary objects. Its elementary exercises, wiien rationally conducted, are adapted to the capacities of chil- dren ai a very eaily age. Its influence on tlie character of cliil- dren, iii developing tiie reasoning faculties, and liabituating the mind to inve.stigaiioii, is highly conducive to progress iit every other branch of knowledge. Notwithstanding the obvious truth of the above remark, the practice of postponing Arithmetic t'll pupils arrive at the age of nine or ten years, still prevails to u very great extent, and calls /or the attention of those, to whom the concerns of popular education are intrusted. The puipose of this Manual is, to facilitate the instruction of the younger classes in common schools. The plan of the lessors accords wilh the method of instruction practiced in the school at Stantz, by the celebrated P«;stalo/zi. The method of illustration, by the use of cuts, and the location of unit marks under questions, it is hoped will be found to be an improvement. The work has been confined to the simple elements of arith- meiic. with a view of rendering it a suitable introduction to the "Subsequent study of the science from books, which are already in use, and which are thought to bo deficient in elementary exer- cises. The slate and pencil are not required, in the performance of the lessons. On the title page, will be seen, a drawing of an im- ])roved structure of iha Abacus. It is a convenient apparatus lor iHusirating ttie combinations of numbers, and may bcusedincon- •lexioti with these lessons, although it is not indispensablt. ^ r. E. PUBLISHER'S PREFACE. 'J'Jie ))ublic generally, and school teachers in part!( ular, iiave hjiig felt the need of using books jMi })ared particularly for our own schools, instead oi these written lor the United States, or for foreign counlries. in the present work, this difficulty is ^•hviated hy the language being adapted to the cur- rt iicy ol' Cnnada. U has been prepared and stereotyped at consid- tr.ible expense, and the publishers are confident iljMt its merits will ensure it a cordial reception by jtruvnts and tojichers. tiictic cluiriKs y exercises, ilies of cliil- ctcr of cliil- )ituutii)g tliu !ss in every bvious truth tliinelic t'll •cvails to a R, to whom struclion of 'instruction P«istaiozzi. lie JocntioM r»d to be an Is of arith- tion to the alreudy iti Inrf excr- inceof the of an im- paratus for sedincou- j!t. 1'. E; liers i/i ; books instead foreign ;ulty is he cur- consid- nfident ion bv ARITHMETIC. NUMERATION. Xote to Teachers. All the lessons in Numeration, are designed to be performed while the learnere have their books open. LESSOiV I. Here is the picture of some apples: count them. One, two, three, four, five, six, seven, eighth nine, ten. LESSON II. Count the stars in each line across this page. * ^', ^A"" ^i' -)<" i^ i^ i^ =>);* # ■^ 1 1 ^w^ ^i ■^'^ v"^ -w^^ -»ji!^ 5.k^ ^li^ ^<^ ^', 0>> ^J: i;^ i^ i^ 4C ^/, ^f, ^f, 4(g ^i^ -i^ 2^t ^f -1^ -7^ ^<^ •^^ ■7r '/r '^'C' ^(c ^Sc 5-c 4'f =5i^ 4J^ 4^ # ^ •^f, ^>\'^ ^r- V ^f How many stars are seven stars and one star.' # # # ^ ^ # # # How many stars are eight stars and one star? "^^ V 4f ^^ ^f 4f ^ff ^<^ i^ How maiiy siars are niiie stdfs and one star.' :ii: :^ ^j= 45c =^ :}}: :^5: :«c :Jjc # ^ NUMERATION. 6 ' Note to Teachers. The design of the preceding lessons has been, to teach the names, and the comparative magnitude of numbers, from one to ten The teacher sljould now inform the pupils, that numbers are repre- tmteA bv figures. He may direct them, to obtam the names of the figures by counting the iu.it marks, (from left to right,) which stand against the figures severally, in the following table. As this exercise will end t<. fix a mental association of each figure with die number of units, which t •esenti^, the lesson should not be omitted, even by children, who are al- rep re ladv able to read figures. I I I I I LESSON IV. I I I I Mill M I I I i I III MM I M I II II M h' 2 6 I I I M 1. ^ 8 9 io NUMERATIOiX. Note to Teachers. The purpose of tlie following lesson », to teuclf Counting, and Redding Figures, as high aa one hundred. It will easily be effected, by e^eircising tlie learners in reading the nuinliers, written in columns; and, at the sainc time, leading tliem to observe the analogic*, two — twenty.: three — thirty; four— forty: &c. 1 One, 2 two, 3 three, 4 four, 5 five, 6 six, 7 seven, 8 eight, 9 nine, 10 ten, 11 eleven, 12 twelve, 13 thirteen, 14 fourteen, 15 fifteen, 16 sixteen, 17 seventeen, 18 eighteen, 19 nineteen, 20 twenty, 21 twenty-one, 22 twenty-two, LESSON V. 34 thirty -four, 67 sixty-seven, 35 thirty-five, . 68 sixty-eight, 36 thirty-six, 69 sixty-nine, 37 thirty-seven, 70 seventy, 38 thirty-eight, 71 seventy-one. 39 thirty-nine, 40 forty, 41 forty-one, 42 forty-two, 43 forty -three, 44 forty-four, 45 forty-five, 46 forty-six, 47 forty-seven, 48 forty-eight, 49 forty-nine, 50 fifty, 51 fifty-one, 52 fifty-two, 53 fifty-three, 54 fifty-four, 55 fifty-five. 23 twenty-three, 56 fifty-six, 24 twenty-four, 57 fifty-seven, 25 twenty-five, 58 fifty-eight, 26 twenty-six, 59 fifty-nine, 27 twenty-seven, 60 sixty, 28 twenty-eight, 61 sixty-one, 29 twenty-nine, 30 thirty, 31 thirty-one, 32 thirty-two, 33 thirty-three. 62 sixty-two, 63 sixty-three, 64 sixty-four, 65 sixty-five, 66 sixty-six, 72 seventy-two, 73 seventy-three, 74 seventy-four, 75 seventy-five, 76 seventy-six, 77 seventy-seven, 78 seventy-eight, 79 seventy-nine, 80 eighty, 81 eighty -one, 82 eighty-two, 83 eighty-three, 84 eighty-four,' 85 eighty-five, 86 eighty-six, 87 eighty-seven, 88 eighty-eight, 89 eighty-nine, 90 ninety, 91 ninety-one, 92 ninety-two, 93 ninety-three, 94 ninety-four, 95 ninety-five, 96 ninety-six, 97 ninety-seven, 98 ninety-eight, 99 ninety-nine, 100 one hundred. I i If, to (eucll 1 will easily I, written in e analogici, seven, eight, nine, ty, ty-one, ty-two, ty-three, ty-four, ty-five, ity-six, ity-seven, ity-eight, ity-nine, ^-tvvo, ^ -three, |r-four,' -five, -six, ^-seven, r-eight, ^-nine, ^-two, |r-three, r-four, >r-five, ^'-six, |r-seven, ^-elght, ^-nine, undred. I NUMERATION. 7 Note to Teachers. The pupila having been accustomed to coneider each line of units separately, it will now be necessary for the teacher, to give tlieni an example of continuing the count from line to line. He thould, also, instruct tliem to take into one view, all the lineM of stars, which tliey count, in order td obtain a just idea of the number. LESSON VI. 42, ^ M, ^ ^ M, ^ M, M, M. Mg ^ ^U Mf ^ Mg M^ AU ^ Mf TT TV* T^ T^ "TV* W "TP TS* TP W jyu ' 4£r TrTf'J^^w'«*T!pTS''7rT?' .j^ JL ^ «Sf» "Sfr «¥» ^tf» «tf' «M' «Mf T^ TP TV TP *«* TT "TV* W Tv" vT J^ ^ ^ ^ ^ ^t "^ ^ ^ 4t» TT Tf T^ TP Tv •W TV TV TV* T^ ^^ 4^ 4^ ^ 4^ ^ 4f> .^ J/» 4£, TPT^TrTV*TV*TV*TPTV*TV*Tl? Jl. Jf. ^ .U. ^ M^ ^ 4«. ^ .u. TrTPWT^TV*T'rTV*T^TrT^ ^ J^ ^ ^ JUU J^ J^ 4^ ^ ^ T^ T^ T^ T? TV* TT TV* TV" TP T^ How many stars are there in the upper line, counted across the page, iVoni left to right ? If you count the stars in the first and second line together, how many will they make } In three lines, how many stars are there ? In four lines, how many stars are there } In five lines, how many stars are there ? In six lines, how many stars are there ? In seven lines, how many stars are there ^ In eight lines, how many stars are there ? In nine lines, how many stars are there ? In ten lines, how many stars are there ? What numbers are expressed by these figures ? 30 50 20 60 40 80 70 90 10 100 32 51 24 63 45 89 77 98 16 99 8 ADDITION. ]'i ,1 n ADDITION. Xotc to Teachers. In .ill the following cxerci?P3, (until we arrive at Mi.sccUaneous Extiinplcs, page 43,) tlic pupils miiflt annwer the quc^tion^, and recite the sectione of the tables appended to the several lensons, with their books cloescd. LESSON I. How many trees are 1 tree and 2 trees ? Henry's sister gave him 1 apple, and his mother gave him 3 more. How many apples had Henry ? 1 and 3 are how many .'' James found 1 pear under the tree, and John gave him 4 more. How many had James then ? 1 and 4 are how many .'' Sarah's brother gave her one cherry, and her mother gave her 7 more. How many had Sarah then ? I and 7 are how many ? ot ho J the on Ta be committed to memory, and recited verbatim. and 1 are 2 and 2 are 3 and 3 are 4 and 4 are 5 and 5 are 6 and G are 7 and 7 are 8 and 8 are 9 and 9 are 10 and 10 are 11 I I u. ; arrive at qucstionp, sons, with I mother nry ? nd John jn? !!• mother inr pm 'im. are 7 are 8 are 9 are 10 are 11 ADDITION. LESSON II. 9 2 houses are on one side of a street, and 2 on the other side. How many are there on both sides ? 2 chairs are on one side of a room, and 4 on the other side. How many are there on both sides ^ 2 and 4 are how many ? 1 Suppose 2 hats are in one place and 5 in another ; liow many will there be, if we put them together.^ 2 and 5 are how many .'' There are 2 lamps on one side of a table, and 7 on the 9ther side. How many lamps are there in ^1 ? 11 ^ and 7 are how many If 2 candles were burning on one table, and on another, hew many would there be on both ^ 2 and 10 are how many ? 10 11 11 1 1 i To be recited. 2 and 1 ^re 3 2 and 6 are 8 2 and 2 are 4 2 and 7 are 9 2 and 3 are 5 2 and 8 are 10 2 and 4 are 6 2 and 9 are 11 2 and 5 are 7 2 and 10 are 12 Ft- I < I! ■ \0 ADDITION. - LESSON III. 3 birds are on one branch of a grape vine, and 2 on another branch. How many en both branches.-^ 3 and 2 are how many? 3 boys are up to recite, and 3 others are coming to recite with them. How many will there be? William owns 3 fish-hooks: if he should buy 6 more, how many would he then have? 3 and 6 are how many? uuu JuuuuJ Jane put 3 pins into a cushion, and Lucy put in more. How many were there in the cushion then? 3 and 9 are how many ? III! Andrew had 3 marbles, and, returning from school, he found 10 more. How many had he then? . 3 and 10 are how many? ^QQ90 To be rtcited. 3 and 1 are 4 3 and 2 are 5 3 and 3 are 6 3 and 4 are 7 3 and 5 are S 3 and 3 and 3 and 3 and 6 are 9 7 are 10 8 are U 9 are 12 3 and 10 are 13 1 boi I i I ' ADDITION. II !, and 2, ranches ? e coming .e? d buy 6 put in 1 then ? n school, f Note to Teachers. The numbers embraced in the succeeding ques- tions are represented by unit marks, respectively placed under each ques- tion. The learners may be directed^ to count Ihese marks, as they have been accui^tomed to count tlie pictures LESSON IV. If you had 4 pence in one pocket and 3 in the other, how many pence would you have in both pockets? 4 and 3 are how many.'' III! Ill Joseph had 4 marbles, and his brother gave him 4 more. How many marbles had Joseph then.-* nil MM If you had 4 nuts in your pocket, and I should give you 5 more, how many would you then have.-* 4 and 5 are how many.'' MM Mill Sophia put 4 pence into a charity fund, and Augus- ta put in 7 pence. How many pence did both put in? 4 and 7 are how many? MM IIMIII If you had 4 pins on one sleeve, and 8 on the other, liow many pins would you have on both sleeves? 4 and 8 are how many? MM IMMIM Samuel gave 4 pence for a picture, and 9 pence for a book. How many pence did he give for both of theni^ 4 and 9 are how many? MM lllllllll re 9 re 10 re 11 re 12 re 13 To be recited. 4 and 1 are 5 4 and 6 are 10 4 and 2 are 6 4 and 7 are 11 4 and 3 are 7 4 and 8 are 12 4 and 4 are 8 4 and 9 are 13 4 and 5 are 9 4 and 10 are 14 nil i 12 ADDITION. i :!! n LESSON V. Daniel gave 5 pence for a bow, and 1 penny for an arrow. How many pence did both of them cost.'' 5 and 1 are how many.? mil I 5 boys are on one end of a form, and 3 on the other end. How many boys are on the whole form.^ 5 and 3 are how many.^ Mill III Harriet owned 5 school-books and 5 story-books. How many books did Harriet own in all? HIM II III Susan has 5 plums, and George has 7. If George give his to Susan, how many will she then have.? 6 and 7 are how many.? HIM 1 1 1 1 1 1 I 5 boys are playing at foot-ball on one side, and 8 on the other side. How many boys on both sides.? 5 and 8 are how many.? 1 1 1 1 1 1 1 1 1 1 1 1 1 How many pence would it take to buy two picture- books, if one cost 5 pence and the other 9 pence.? 5 and 9 are how many.? Mill lllllllll If an orange cost 5 pence, and a book 10 pence^ how many pence will it take to buy both of them.? 5 and 10 are how many.? Mill lllllllll! If mon i h II out I To be recited . 5 and 1 are 6 5 and 6 are 11 5 and 2 are 7 5 and 7 are 12 5 and 3 arc 8 5 and 8 are 13 5 and 4 arc 9 1 5 and 9 are 14 5 and 5 arc 10 5 and 10 are 15 I Hi' ' ADDITION. IS 3nny for an 1 cost? )ii the other rm? tory -books. If George have ? e, and 8 on jides ? I two picture- ' pence? II Ic 10 pence y fthem? Ill are 11 are 12 are 13 are 14 are 15 LESSON "I. If I put 6 books down in pile, and you put on 4 more, how many books will there be in the pile? Illill ill! 6 books and 5 books, would be how many books? illill 1 1 1 1 i How many bonnets are 6 bonnets and 6 bonnets? ^ Illill 1 1 1 1 II 6 hats and 9 hats together, are how many hats? Illill llillllll i 6 and 1 are 7 6 and 2 are 8 6 and 3 are 9 6 and 4 are 10 6 and 5 are 11 To be recited. 6 and 6 and 6 and C and 6 are 12 7 are 13 8 are 14 9 are 6 and 10 are 15 16 LESSON VII. If I pull out 7 quills from a bunch, and then pull out 3 more, how many shall I have taken out? I 1 1 1 1 1 1 III 7 quills and 6 quills together, are how many quills? iiiiiii Mini How many hats are 7 hats and 7 hats together? mill I ill MM How many pencils are 7 pencils and 9 pencils? Mlliil liililili To he recited. 7 and 1 are 8 7 and 6 are 13 7 and 2 are 9 7 and 7 are 14 7 and 3 are 10 7 and 8 are 15 7 and 4 are 11 7 and 9 are 16 7 and 5 are 12 ■ 7 and 10 are 17 i ■ i • in 14 ADDITION. LESSON VIll. Richard has 8 chestnuts and David has only 2. How many will there be, if they put theni together? Mill M I II How many apples are 8 apples and 3 apples? MM III I III How many raisins are 8 raisins and 6 raisins? M 11 1 II I 1 1 1 1 1 1 8 pins and 8 pins together, are how many pins? Illillll llllllll To be recited. 8 and 1 are 9 8 and 2 are 10 8 and 3 are 11 8 and 4 are 12 8 and 5 are 13 8 and 6 are 14 8 and 7 are 15 8 and 8 are 16 8 and 9 are 17 8 and 10 are 18 LESSON IX. James has 9 buttons on the front of his jacket, and 2 on the back. How many has he on the jacket? II Mlllll II How many buttons arc 9 buttons and 8 buttons? II III II ! I Mi I I III How many pence are pence and 9 pence? I II li M M II II 11 II I How many dollars are 9 dollars and 10 dollars? II lllllil Mllllilll To be recitf.d. 9 and I are 10 9 and 2 are 11 9 and 3 are 12 9 and 4 are 13 9 and f) are 14 9 and G are 15 9 and 7 are 16 9 and 8 are 17 9 and 9 arc 18 9 and 10 are 19 ijji' ADDITION. 15 3 only 2. together? esi nsr pins: II 14 15 16 17 18 acket, and icket? ittons . I I Ml )llais ? MM re 15 re 16 re 17 re 18 re 19 LESSON X. If I should call 10 boys to the desk, and then should call 4 more, how many boys would be called.'* 1 1 1 I I II I I I III I 10 boys and 6 boys, would be how many boys."* 1 1 1 II 1 1 I 1 1 I I I I I I How many houses, are 10 houses and 8 houses.^ 1 1 1 I I 1 1 I I I I I 1 1 1 1 1 1 How many men, are 10 men and 10 men together.^ 1 1 I 1 1 1 1 I i I I I I I I I I III To be recited. 10 and 1 are 11 10 and 2 are 12 10 and 3 are 13 10 and 4 are 14 10 and 5 are 15 10 and 6 are 16 10 and 7 are 17 10 and 8 are 18 10 and 9 are 19 10 and 10 are 20 Note to Teachers. I have attempted, in the preceding lessons, to present to the eye and mind of leiirncra, a clear view of tlie union or ad- dition of small numbers, in forming b^'ger numbers. It now remains, to fix the sums of the several additions m the memory. F'or this purpose, the teacher may embrace each of the following combinations in two sepa- rate questions. For example, (Lesson XI, combination first,) 9 ana 4 are how many ?-^Then,4 and 9 are how many ? XI. XII. XIII. XIV. 9 and 4 9 and 6 8 and 6 9 and 5 6 and 3 8 and 1 5 and 3 7 and 3 8 and 5 6 and 6 10 and 9 4 and 4 2 and 2 10 and 8 8 and 8 10 and 3 10 and 4 5 and 4 6 and 4 S and 4 7 and 7 8 and 2 9 and 2 5 and 2 4 and 1 3 and 2 10 and 6 7 and 4 9 and 7 9 and 3 3 and 3 10 and 5 5 and 5 7 and 6 7 and 2 Sand 7 JO and 1 6 and 5 4 and 3 6 and 2 9 and 9 IQ and 2 7 and 5 8 and 3 4 and 2 9 and 9 10 and 7 10 and 10 M'V 16 SUBTRACTION. V: 1 W SUBTRACTION. Note to Teachers. Children, wlio have learned juldition, may easily be taught subtraction, by leading them to observe the cori'c.«piiitdence oftlie two operations. Questions in addition, (distinguished by Itulic print,) are therefore connected with tlie questions in subtraction. The teacher must here inform the learners, tliat the cipher, ( ) reprc- fsents nothing of itself, being used only to occupy a place. LESSON I. There was 1 pitcher on the table, but a careless boy knocked it off. What is left on the table.'' I, taken from where there was 1, leaves what.^ of i 2 trees stood near by, but the wind has blown 1 them down. What number is left standing? 1, taken from 2, leaves what number.'' 3 chairs were standing in a row, but a child has thrown 1 of them down. How many are upright.'' 1 from 3 leaves how many? How many are 1 and 2? 7 sugar loaves are on a shelf; one of them has the top broken off. How many of them are whole ? 1 from 7 leaves how many ? How many are 1 and 69 I i i i i i i To be committed to memory, and recited verbatim. I from 1 leaves 1 from 2 leaves 1 1 from 3 leaves 2 1 TTom 4 leaves 3 1 from 5 leaves 4 1 from leaves 5 1 from 7 leaves 6 1 from 8 leaves 7 1 from 9 leaves 8 1 from 10 leaves 9 SUBTRACTION. 17 hn, may easily Imdence of tlie (lie print,) arc [>"> ( ) repre- |a careless le? what? )lown 1 of '■ child has H'ighi? 'c 1 and 29 I ni has the Die? e 1 and 69 n Hm. ■ves 5 ves 6 ves 7 ves 8 ves 9 There handles. LESSON II. are 3 pitchers, 2 of What number of them i which have s whole? broken 2 from 3 leaves what number? How many are 2 and 1 f sent 5 boys came up to recite, but 2 of them were back, for having no lesson. How many recited ? 2 from 5 leaves how many? How many are 2 and 3? 7 bottles were standing on a table, but 2 of them are turned down. How many are still upright? 2 from 7 leaves how many? How many are 2 and 5:^ A A A d i Edward has 9 lead pencils, and he has pointed 2 of them. How many has he, which are not pointed? 2 from 9 leaves how many? How many are 2 and 7? Harriet has 11 pins, but 2 of them have lost their heads. How many have their heads on? 2 from 11 leaves how many? How many are 2 a7ul 9 7 I I I f I 2 from 2 leaves 2 from 3 leaves 1 2 from 4 2 from 5 2 from 6 leaves 2 leaves 3 leaves 4 To be recited. 2 from 7 leaves 5 2 from S leaves 6 2 from 9 leases 7 2 from 10 leaves 8 2 from 11 leaves 9 18 SUBTRACTION. i*i! 'I I • ;f i i : II ; I|: ;i' ■li! 1, I I h I LESSON III In a certain fold there are 5 sheep; 3 of ihem have lain down to rest. How many are standing.'' 3 from 5 leaves how many.'* How many are 3 and 2? 6 hens were in a farm yard, and a boy frightened 3 of them away. How many of them remained? 3 from 6 leaves how many.'' How many are 3 and 3? Robert has 12 quills ; 3 of them have the tops cut off, and the others are whole. How many are whole? 3 from 12 leaves how many? Hoto many are 3 and 0?^ 8 cups are on the table, and 3 of iheni are bottom upward. How many are right side up? 3 from 8 leaves how many? How many arc 3 and 5? 10 wine glasses are on a waiter, 3 of which are bottom upward. How many are right side up ? 3 from 1 leaves how many ? How many are 3 and 7 ? To be recited. 3 from 3 leaves 3 from 4 leaves 1 3 from 5 leaves 2 3 from 6 leaves 3 3 from 7 leaves 4 3 from 8 leaves 5 3 from 9 leaves 6 3 from 10 leaves 7 3 from 11 leaves 8 3 from 12 leaves 9 i SUBTRACTION. 19 of ihera ling? 3 and 2? frightened led? he 3 and 3? e tops cut |are whole? re 3 071(1 i are bottom trc 3 and 5? which are up ? are 3 and 7 ? iVoic to Teachers. 1 !ic pupils luunt Ik; inlorinL-il, that the unit marks, which are inclined, represent tho number to be subtracted j and those which are upright, show tlic number tliat will be left. LESSON IV. JO boys were playing ball ; 4 of them became tired, and went home. How many were left ? mill//// Thomas put 8 chestnuts into the embers to roast, and 4 of them were burnt. How many were saved ? 4 from 8 leav^es how many ? Hoiv many are 4 and 4? Mil//// Charles had 12 marbles, but he gave his brother James 4 of them. How many had he left ? 4 from 12 leaves how many ? How many are 4 and 8? 1 1 II II 1 1//// Mary had 9 apples, and she roasted 4 of them for her sick father. How many had she left? 4 from 9 leaves how many? How many are A and 5? Mill//// 7 bells were ringing last Sabbath ; 4 of them ceased before the rest. How many continued ringing ? 4 from 7 leaves how many ? How many are 4 ami 3 ? 1 1 1 //// 13 sheep were feeding in a pasture, and 4 of them had lambs. How many of them had no lambs ? 4 from 13 leaves how many ? How many are 4 and 9 ? Illllllll//// i To be recited. eaves 5 ■A 4 from 4 leaves 4 from 9 leaves 5 eaves 6 .1 4 from 5 leaves 1 4 from 10 leaves 6 eaves 7 f 4 from 6 leaves 2 4 from 11 leaves 7 eaves 8 W \ 4 from 7 leaves 3 4 from 12 leaves 8 eaves 9 A 4 from 8 leaves 4 4 from 13 leaves 9 -!^ * if :■ J- '■ 1 1 >- * '' - i! J 1^ if if ■ 1 i.' . iif 1 f ■ f H. : ; 1 If : f i:l|i J Hi* I « r :J! ^ SUBTRACTION. LESSON V. 6 scholars may hold up their right hands — ^now 5 may put them down — how many are still up ? 5 from 6 leaves how many ? How many are 5 and 1 ? I ///// James had a recess of 10 minutes, and stayed out only 5. How many more might he have stayed ? 5 from 10 leaves how many ? How imny are 5 and 5? 1 1 1 1 1 ///// A good larmer had 13 cows, and all but 5 of them were red. How many of them were red ? o from 13 leaves how many ? How many are 5 and 8? 1 1 1 1 i 1 1 1 ///// Of 9 men that were in a stage-coach, 5 alighted be- fore the end of the route. How many rode on ? 5 from 9 leaves how many ? How many are 5 and 4? 1 1 I I ///// A ship's crew consisted of 14 men, 5 of whom died while at sea. How many arrived safe in port ? 5 from 14 leaves how many ? How many are 5 and 9? I lllillll ///// Sarah had a party, to which she invited 11 young ladies ; only 5 of them came. How many kept away ? 5 from 1 1 leaves how many ? How many are 5 and ()?■ I I I I I I ///// A front yard had 8 elms standing in it ; 5 of them are cut down. How many are yet standing .'' 5 from 8 leaves how many ^ How many are 5 and 3? I I I ///// To be recited. 5 from 5 leaves 5 from 10 leaves 5 5 from 6 leaves 1 5 from 11 leaves 6 5 from 7 leaves 2 j 5 from 12 leaves 7 5 from 8 leaves 3 ' 5 from 13 leaves 8 6 from 9 leaves 4 ! 5 from 14 leaves 9 I SUBTRACTION. 21 ds — now 5 re 5 and 1 ? stayed out lyed ? tre 5 and 5 ? 5 of them trc 5 and 8 ? lighted be- on ? •e 5 and 4? vhom died rt? re 5 «nrf 0? 11 young ept away ? e 5 awrf () ? 5 of them » e 5 and 3? yes 5 ves 6 ves 7 ves 8 ves 9 LESSON VI. 9 doves were picking oats before the door, and a dog drove off 6 of them. How many remained } 1 1 1 ////// 6 pence taken from 8 pence, leave how many ^ 1 1 ////// Ann had 14 pins, and lost 6. How many were left .' 1 1 1 1 1 1 1 1 ////// Take 6 books from 12 books — how many remain ? 1 1 1 1 1 1 ////// To be recited. 6 from 6 from 6 from 6 from 6 leaves 7 leaves 1 8 leaves 2 9 leaves 3 6 from 10 leaves 4 6 from 11 leaves 6 6 from 12 leaves 6 6 from 13 leaves 7 6 from 14 leaves 8 6 from 15 leaves 9 LESSON vn. Henry's pear tree had 15 blossoms on it; 7 of them dropped off; the rest ripened. How many ripened .'' 1 1 1 1 1 1 1 1 /////// 7 pence taken from 11 pence, leave how many ? 1 1 1 1 /////// 7 pence taken from 16 pence, leave how many ? 1 1 1 1 1 1 1 1 1 /////// Take 7 books from 12 books — how many remain? 1 1 1 1 1 /////// To be recited. 7 from 7 leaves 7 from 8 leaves 1 7 from 9 leaves 2 7 from 10 leaves 3 7 from 11 leaves 4 7 from 12 leaves 5 7 from 13 leaves 6 7 from 14 leaves 7 7 from 15 leaves 8 7 from 16 leaves 9 !■ . I?' Hi p ||: ;if ' li: : 'iliiil II i I ill 22 SUBTRACTION. LESSON VIII. There are 14 lessons in subtraction ; you have now studied 8 of them. How many remain to be studied ? i 1 1 1 1 1 //////// 8 hats taken from 12 hats, leave how many hats ^ II II //////// Take 8 pins from 16 pins how many remain } 1 1 II 1 1 1 1 //////// 8 pins taken from 15 pins, leave how many pins ? 1 1 1 1 1 1 1 //////// Tobei recited. 8 from 8 leaves 8 from 13 leaves 5 8 from 9 leaves 1 8 from 14 leaves 6 8 from 10 leaves 2 8 from 15 leaves 7 8 from 11 leaves 3 8 from 16 leaves 8 8 from 12 leaves 4 8 from 17 leaves 9' LESSON IX. Stephen purchased 16 quills, to use in writing after using 9 of them, how many had he left ? 1 1 1 1 1 1 1 ///////// 9 quills taken from 13 quills leave how many ? 1 1 1 1 ///////// Take 9 nuts from 17 nuts how many remain ? 1 1 1 1 1 1 1 1 ///////// John had 18 quills and lost 9 : how many remain ? 1 1 1 1 1 1 1 1 1 ///////// To be recited. 9 from 9 leaves 9 from 10 leaves 1 9 from 11 leaves 2 9 from 12 leaves 3 9 from 13 leaves 4 9 from 14 leaves 6 9 from 15 leaves 6 9 from 16 leaves 7 9 from 17 leaves 8 9 from 18 leaves 9 SUBTRACTION. 23 LESSON X. Eliza has 14 books in her library, and she has read through 10 of them. How many has she yet to read ? 1 1 I I ////////// Take 10 books from 17 books — how many remain ? I I I I I I I ////////// Take 10 pence from 16 pence — how many remain ^ 1 1 1 1 1 1 ////////// Take 10 pence from 18 pence — how many remain? I I I I 1 1 I I ////////// To be recited. 10 from 10 leaves 10 from 11 leaves 1 10 from 12 leaves 2 10 from 13 leaves 3 10 from 14 leaves 4 10 from 15 leaves 5 10 from 16 leaves 6 10 from 17 leaves 7 10 from 18 leaves 8 10 from 19 leaves 9 Note to Teachers. The following connexions of numbers may be em- braced in questions by the teacher; tlius, — 3 from 4 leaves how many 1 XI. 3 from 4 5 from 14 8 from 8 10 from 19 7 from 8 2 from 11 9 from 18 4 from 13 2 from 3 9 from 11 4 from 8 3 from 12 4 from 9 3 from 10 5 from 12 7 from 9 XII. 8 from 17 9 from 15 5 from 8 7 from 16 6 from 11 2 from 8 10 from 14 8 from 13 6 from 9 1 from 10 9 from 13 2 from 6 5 from 10 8 from 14 7 from 12 1 from 3 XIII. 10 from 12 8 from 10 3 from 7 6 from 14 2 from 9 7 from 13 9 from 17 4 from 6 7 from 14 3 from 11 4 from 12 2 from 5 4 from 11 9 from 16 3 from 9 6 from 12 5 8 6 7 5 9 6 7 10 4 3 5 8 3 6 9 XIV. from 7 from 11 from 10 from 15 from 9 from 12 from 13 from 11 from 16 from 12 from 6 from 13 from 16 from 8 from 15 from 14 ^w %- 34 MULTIPLICATION. MULTIPLICATION. •ill' :1; LESSON I. On Monday morning, Andrew's father told him, that he would give him one new book for every time he recited correctly, during the week. On Satur- day it appeared, that he had recited correctly only once. What number of books did he receive ? Once 1 is what number .'' /.'■/■ Charles caught 1 fish, every time he went out to angle. How many did he catch in going 2 times? 2 limes 1 are how many ? A young cooper worked three days, and made 1 barrel each day. How many barrels did he make ? 3 times 1 are how many ? Stephen lost 1 ball, every time he went upon the common. How many did he lose in going 4 times r 4 times 1 are how many ? ^ To be committed to memort;, and recited verbatim. Once 1 is 1 2 limes 1 are 2 3 times 1 are 3 4 times I are 4 r» times 1 are 5 6 times 1 are 7 times 1 are 8 times 1 are 9 times 1 arc i 8 9 10 times 1 are 10 MULTIPLICATION. 26 LESSON II. A boy has 2 hands : how many hands have 2 boys ? 2 times 2 are how many ? ■:::u2>' A rabbit has 2 ears : how many ears have 3 rabbits ? 3 times 2 are how many ? ..^^ ..Vk awt; rui^ James caught 2 fishes, every time he went fishing. How many did he catch, in going 4 times ? 4 times 2 are how many ? very time he went to the A Clerk lost 2 keys, every time lie went to theatre. How many did he lose, in going 5 times .'i times 2 are how manv ? 5 times 2 are how many Harriet lost 2 pins every time she went to school. How many did she lose, in going 7 times } 7 times 2 are how many ? II II II II II II To be recited. Once 2 is 2 6 times 2 are 12 2 times 2 are 4 7 times 2 aro 14 3 times 2 are 6 8 times 2 are 16 4 times 2 are 8 9 times are 18 5 times 2 are c 10 10 times 2 are 20 36 MULTIPLICATION. -n LESSON III. When the sails of a ship are furled, her masts are distinctly seen. How many masts has 1 ship ^ Once 3 is how many .-* Since 1 ship has 3 masts, how many have 2 ships .'' 2 times 3 are how many .'' Richard was learning to write, and he used 3 quills every week. How many did he use in 3 weeks .'' 3 limes 3 are how many ? If 1 fork have 3 j»oints, how many have 4 forks ? 4 limes 3 are how many ? '/ y .# xf/ We generally fir.'l 3 clover leaver, growing upon one slem. How innny leiivos grow upon 5 stems ' 5 times 3 are liow many ? I X/> ^' r To bf rffitrd. ^ Once 3 is 3 2 limes 3 are 6 3 times 3 are J) 4 tijnes 3 are 12 ^^ linu's 3 are 15 G times 3 are 18 7 times 3 are 21 H limes 3 are *4 9 limes 3 are 27 10 times 3 arc 30 asls are I ships \ d 3 quills ucks ? 4 Ibrks ? owinj^ upor )n 5 stems ' * are 18 are 21 are 24 are 27 MULTIPLICATION. LESSON IV. m 3 horses are trotting off without riders. Each horse has 4 feet : how many feet have they all ? 3 times 4 are how many ? 2 boys went a fishing, and each of them caught 4 trouts. How many trouts did they both catch ? 2 times 4 are how many ? MM MM A lady, who had 4 daughters, gave each of them 4 books. How many did she give them all ? 4 times 4 are how many ? MM MM MM MM G chairs are standing in a row, and each chair has 4 legs. How many legs have all the chairs ? 6 times 4 are how many ? MM MM MM MM MM MM Lucy has 5 picture books, which cost 4 pence apiece. How many pence did they all cost ? 5 times 4 are how many ? MM MM MM MM MM Susan gets 4 merit-marks, every time she recites. How many does she get, in reciting 7 times ? 7 times 4 are how many ? * 4 4 4 4 4 4 4 To be recitfd. Once 4 is 4 2 times 4 are 8 3 times 4 are 12 4 times 4 are 16 5 times 4 are 20 6 times 4 are 24 7 times -t •^'•e 28 8 times 4 are 32 times 4 are 36 10 times 4 are 40 «re yo ♦Tlif loRrnera may be InHtructvd to splcrt any four mnrkK alKtve, «ad fount thciu an many timrH oh there arc/uttr< in th)- line of flgunn. MULTIPLICATION. !■;! 1 LESSON V. 4 houses are situated so that each house presents 5 windows. How many do they all present ? 4 times 5 are how many ? Js A I I I I B H As H I A ship-master gave to 2 little boys, 6 oranges apiece. How many oranges did he give to both ? 2 times 5 are how many ? Mill mil Mary reads 5 pages of history every morning. How many pages does she read in 3 mornings ? 3 times 5 are how many ? mil mil mil If I pay 6 pence for riding over the bridge once, how many must I pay for riding over 5 times ? 5 times 6 are how many ? mil iiiii mil mil iiiii If a pupil get 5 merit-tickets for ever) week of perfect lessons, how many can he get in G weeks r 6 times 5 are how many ? 5 5 5 5 5 5 Stephen performs 6 lessons every day. How many lessons does he perform in 8 days ? 8 times 6 are how many .'' 55555555 To be recited. Once 5 is 5 6 times 5 are 30 2 times 5 are 10 7 times 6 are 36 3 times 5 are 15 8 times 5 are 40 4 times 5 are 20 9 times 6 are 45 5 times 5 are 25 10 times 5 are 50 MULTiPLICATION. 2? lents 5 ft LERSON VI. If there be 6 rounds in one ladder, how many rounds are there in 5 bidders of the same length ? 5 times 6 are how many ? If a hymn consist of 3 stanzas, and each stanza of lines, how many lines are there in the hymn ? 3 times 6 are how many ? mill llliil HUM 4 men went out in a hunting party, and each man had 6 hounds. How many had they all ? 4 times 6 are how many ? mill mm mm mm If a carpenter put 6 panels into one door, how many panels does he put into C doors ? 6 times 6 are how many ? 6 6 6 6 6 6 I have only G sheep, and my neighbour has 8 times as many. How many has my neighbour ? 8 times 6 are how many ? • G 6 6 () 6 6 G G James has 7 books, and every book bas (> pictures in it. How many pictures are liicre in all ? 7 times are how many ? 6 6 6 6 6 6 6 To be i*«rt7« are 12 3 times f) are 18 4 limes 6 are 24 T) times are 30 »i times T) are 36 V times (> are 42 8 times (> are 48 times () are r»4 10 time's are t>0 30 MULTIPLICATION. LESSON VII. If 1 hair-comb have 7 teeth in it, how many teeih have 3 haii -combs of the same size .'* 3 times 7 are how many ? If 4 boys stand up to read, and each boy read 7 lines, how many lines will they all read ? 4 times 7 are how many ? iltlill lllllii illllll fliiill If you had 7 marbles in each of your 2 hands, how many marbles would you have in all ? 2 times 7 are how many ? fliiill llillli If I give you some raisins 7 times, giving you 7 raisins each rime, how many will you have ? 7 time? 7 are how manv ? If you should buy 6 oranges, and pay 7 pence apiece for them, what would the whole cost ? # C times 7 arc how manv ■ If I pay 7 pence for one lead pencil, how many pence must I have, to pay for S lead pencils .'' 8 times 7 are how many ? waj To be recited. Once 7 is 7 2 times 7 are 14 3 times 7 are 21 4 times 7 are 2S 5 times 7 are 35 f) times 7 arc 42 7 limes 7 are 49 8 times 7 are 50 9 times 7 are 63 10 limes 7 are 70 MULTIPLICATION. 31 i LESSON VIII. 4 wheels are on an engine, and each whc:l has 8 spokes. How many spokes in all the wheols ? 4 times 8 are how many ? 2 wagons went to market, carrying 8 barrels of cider apiece. How many did they both carry ? Z times 8 are how many ? lililll! Illllfij If there be 8 leave.^ in one writing-book, how many leaves will there be in o writing-books } o limes 8 are iiow many ? Illlllll llllilil lllliin A fishing party went out in 7 boats, and each boat carried 8 persons. How many went in the party '" 7 times 8 are how many .'' 8 8 8 8 8 8 8 If 8 pence be paid for one writing-book, how many pence must be paid for 6 writing-booki- ? 6 times 8 are how many ? 8 8 8 8 8 8 Henry was 8 weeks in this book, but Harry Sloth was 5 times as long. How long was Harry ? 5 times 8 are how many r 8 8 8 8 8 To be recited. Once 8 is 8 2 times 8 are 16 3 times 8 are 24 4 times 8 are 32 6 times 8 are 40 6 limes 8 arc 4fi 7 times 8 are 56 S times 8 are 64 9 times 8 are 72 10 times S are bO 32 MULTIPLICATION. :^i LESSON IX. Edward has 2 jackets, and on each jacket there are 9 buttons. How many buttons are on both ? Illllllll lllllllll How many quills have 3 boys ; each boy having 9 ? lllllllll lllllllll lllllllll If one book cost 9 pence, what will 6 books cost ? 9 9 9 9 9 9 If one book cost 9 pence, what will 8 books cost ? 99999999 To be recited. Once 9 is 9 2 times 9 are 18 3 times 9 are 27 4 times 9 are 36 5 times 9 are 45 6 times 9 are 64 7 limes 9 are 63 8 times 9 are 72 9 times 9 are 81 10 times 9 are 90 LESSON X. if you take 10 steps in crossing the room once, how many would you lake in crossing 3 times } llllllllll llllllllll llllllllll How many teeth in 6 rakes; each rake having 10? 10 10 10 10 10 10 What cost 8 books, at 10 pence for each book ? 10 10 10 10 10 10 10 10 What cost 7 books, at 10 pence for each book ? 10 10 10 10 10 10 10 Tob ' recited. Once 10 is 10 6 times 10 arc 60 2 times 10 are 20 7 times 10 are 70 3 times 10 are 30 8 times 10 are 80 4 times 10 are 40 9 limes 10 are 90 5 times 10 are 50 ; 10 times 10 are 100 3 5 2 4 7 1 7 5 1 3 2 MULTIPLICATION. 33 t there zing 9 ? Mil cost ? cost ? 9 54 63 72 81 90 m once, illM iving 10? 10 ook ? } 10 book ? 10 c 60 e 70 e 80 e 90 e 100 9 LESSON XI. Joseph made a number of stars upon his slate, arranging them in such order, that they appeared in rows two ways. Viewing them one way, there were 3 rows of ten stars each — thus, there were 3 times 10 stars. Viewing them the other way, there were 10 rows of 3 stars each — thus, there were 10 times 3 stars. How many stars did he make ? M, M. JiU 4^ M. Mt ,iU ^ 4k ^ M, M, M, M, M, M, ^ M, ^ 4^ 41, M0 M, ^ M, Mf M, ^ M, Jig John and Ezra compared their marbles as follows. John placed his, 5 in a row, and had enough to make 4 rows. Ezra placed his, 4 in a row, and had enough to make 5 rows. How many had each boy ? • e««« % 9 m • « • Xote to Teachers. Embrace the following conibinjiuoiig in ']i;^tion!i, thus, — 3 times 6 arc how many 1 — 6 times 3 are how iimi:y ? Kmbraced in !,ni»im XI. 3 times 6 5 times 8 times 2 times 10 2 4 7 1 7 5 1 3 2 times time limes times time times times 7 4 9 5 10 9 4 XII. 1 time 8 6 times 6 8 times 10 4 times 2 times 2 times 3 times 6 times 5 times 2 times 10 9 times 9 XIII. XIV. 5 8 3 9 7 6 3 times 5 3 ti 9 times 10 4 ti 8 times 8 3 ti 4 times 6 4 ti 2 times 9 2 ti 6 times 10 4 til 3 time] 3 5 til 2 tiiiie;^ 7 7 til 3 times 4 2 til 5 tinK^i, 7 3 til 7 tunes JO 10 til imes 7 mes 4 mes 10 mes 8 mes 5 mes 7 mes 10 mes 8 mes 6 mes 8 mes 10 ^ DIVISION. I>IVISION. ffdIU to Teachers. The correspondence of Division and Muitiplica- nton, if not discovered by the pupils, should be pointed out to them. LESSON I. When Alfred was sick one of his school-mates brought him 8 grapes ; but his physician said, h' must eat only one at a time. How many times coulu he have 1 grape, before ihey would all be gone ? How many times 1 are there in 8 .'' If I pay one penny for every time I walk over the bridge, how many times can I go over for 4 pence ? How many times 1 are there in 4 ? Mil A certain farmer has 6 oxen, and it takes 2 of them to make one pair. How many pairs of oxen has he ? How many twos are there in 6 .'' UUU John can carry 2 sticks of wood at once ; and he has 8 sticks to carry off. How many times must he go ^ How many times 2 are there in 8 .'' UUUU My purse contains 16 pence. Large quills are 2 pence apiece ; so I can buy one quill for every 2 pence in the purse. How many can I buy ? How many times 2 are there in 16 .'* uuuuuuuu To be committed to memory, and recited verbatim. 2 in 2, once 2 in 12, 6 times 2 in 4, 2 times 2 in 14, 7 times 2 in 6, 3 times 2 in 16, 8 times 2 in 8, 4 times 2 in 18, 9 times 2 in 10, 5 times 2 in 20, 10 times DIVISION. 85 ItipHca- LESSON II. If 12 pence were upon the desk, and I should be- gin taking them off, three at a time, how many times might I take off 3, before they would all be off ? How many threes are there in 12 > LUUJUJUJ David had IS sticks of wood to carry up stairs, and he could carry only 3 at a time. How many times had he to go, in order to carry up the whole ? How many times 3 are there in 18 l^ LUUJUJIUUJUJ A sportsman shot 3 plovers every time he fired. How many times must he fire, to shoot 15 plovers i How many times 3 in 15 ? How many are 5 times 3 ? inilllllllllll Jane gets 3 merit-marks for every perfect lesson. How many lessons must she recite, to get 21 marks? How many times 3 in 21 .•* How many are 7 times 3 f HJUJLULUlUUJUJ If 3 books be required to supply one scholar, how many scholars may be supplied from 9 books .'' How many times 3 in 9.'* How many are 3 times 3 ? UJUJUJ Francis has 24 pence, with which he is going to buy oranges, at 3 pence apiece. How many can he buy .'' How many times 3 in 24 } How many are 8 times 3? lijiiJLIJUJ LUUJUJUJ To be recited. 3 in 3, once 3 in 18, 6 times 3 in 6, 2 times 3 in 21, 7 times 3 in 9, 3 times 3 in 24, 3 times 3 in 12, 4 times 3 in 27, 9 times 3 in 15, 5 times 3 in 30, 10 times 86 DIVISION. f^ LESSON III. If 4 horses be required to draw one stage-coach, how many stage-coaches might 12 horses draw? UiJ UJJ ILU How many times 4 pages, in a book of 24 pages ? LLU liU U_y ILLJ UJJ LLU How many times 4 pages, in a book of 16 pages ? UU UU LLU U_U How many times 4 pages, in a book of 20 pages ? LUJ LLU UJJ LLU UJJ To be recited. 4 in 4, once 4 in S, 2 times 4 in 12, 3 times 4 in 16, 4 times 4 in 20, 5 times 4 in 24, 6 times 4 in 28, 7 times 4 in 32, 8 times 4 in 36, 9 times 4 in 40, 10 times LESSON IV. If you write 5 lines in a writing-book, every day, how many davs would it take to write 20 lines .'' UlU UlU uuj u jjj In a row of 10 seats, how many times 5 seats .' UIUUJJJ In a row of 15 seats, how many times 5 seats ^ LUJJLLUJUJU In a row of 25 seats, how many times 5 seats .'' UlU LUU ULU LllU "ill 5 5 5 5 To be recited. n 5, once 5 in 30, 6 times n 10, 2 times 5 in 35, 7 times n 15, 3 times 5 in 40, 8 .times n 20, 4 times ll 5 in 45, 9 times n 25, 5 limes li 5 in 50, 10 times DIVISION. 37 LESSON V. 18 boys were in a rank, and were asked, how many times 6 boys there were ? You may tell. LLLiJU LLILU LLLU J In a rank of 12 boys, how many times 6 boys ? LLliUlllIU In a rank of 30 boys, how many times 6 boys .'' LLLLU UJLLU ULLLU ILLL! J J'"M In a rank of 24 boys, how many times 6 boys ? liJLL'J LLLLU LLL" JJ LLLLU 6 in 6, once 6 in 12, 2 times 6 in 18, 3 times 6 in 24, 4 times 6 in 30, 5 times To be recited. 6 6 6 6 6 n 36, 6 times n 42, 7 times n 48, 8 times n 54, 9 times n 60, 10 times LESSON VI. The first class, in a certain school, consists of 28 girls. How many times 7 girls are in the class ? I III III I II in; ILLLL! J LLULL! J How many times 7 girls, in a class of 21 girls ^ LLLLLU UJilU ""i ll How many times 7 girls, in a class of 42 girls ? 7 7 7 7 7 7 How many times 7 |;irls, in a class of 56 girls ? 77777777 To be recited. 7 in 7, once 7 in 42, 6 times 7 in 14, 2 times 7 in 49, 7 times 7 in 21, 3 times 7 in 56, 8 times 7 in 28, 4 times 7 in 63, 9 times 7 in 35, 5 times 7 in 70, 10 times 1 38 DIVISION. LESSON VII. Emeline's picture-book consists of 3.2 leaves. How many times 8 leaves are contained in the book ? 1 1 1 1 1 1 1 1 1 1 8 1 1 M 1 1 M IS 1 1 1 1 1 1 1 1 1 1 3 Vs y V. " V ___? v^ / In a book of 24 leaves, how manv times 8 leaves ? M 1 1 1 1 M H M III I ; i M 1 1 1 1 In a book of 46 leaves, how many times 8 leaves ? 8 8 8 8 8 8 In a book of 64 leaves, how many times 8 leaves? 8 8 8 8 8 8 8 8 To be recited. 8 ] n 8, once 1 8 in 48, 6 times 8 n 16, 2 times 1 8 in 56, 7 times 8 in 24, 3 times 1 8 m 64, 8 tunes 8 in 32, 4 times 8 in 72, 9 times 8 in 40, 5 times 8 in 80, 10 times LESSON VIII. There is a school of 27 boys, and boys are in •ach of the classes. How many classes are there ? 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 M I M it M 1 1 j In a school of 45 bovs, how many times 9 boys .^ 9 9 9 9 9 In a school of 63 boys, how many times 9 boys ? 9 9 9 9 9 9 9 In a school of 8i boys, how many times 9 boys ? 9 99999999 To be recited. 9 in 9, once j^ 9 in 54, 6 times 9 in 18, 2 times I 9 in 63, 7 times 9 in 27, 3 times ; 9 in 72, 8 times 9 in 36, 4 times 9 in 81, 9 limes 9 in 45, 5 times 9 in 90, 10 time? leaves . book ? iin eaves ? eaves ? javes ? 8 les les nes lies lies s are tn here ? LU Ijoys ? boys ? boys ? I 9 mes mets mes me.s me? DIVISION. 39 LESSON IX. A farmer, who keeps a flock of 30 sheep, has a separate fold for every 10. How many folds has he ? (jmmmj ; i ii ii 1 1 1 1 ; 1 1 1 n 1 1 1 1 How many times 10 sheep, in a flock of 50 sheep ? 10 10 10 10 10 How many times 10 sheep, in a flock of 40 sheep f 10 10 10 10 How many times 10 sheep, in a flock of 70 sheep ? 10 10 10 10 10 10 10 10 in 10, 10 in 20, 10 in 30, JO in 40, 10 in 50, Xotc to Teacher itito questions, thus- X. 4 in 36 3 in 18 5 in 40 2 in 4 4 in 40 7 in 49 1 in 4 7 in 63 5 in 25 1 in 10 5 in 72 2 in 8 6 in 54 1 in 8 6 in 36 S in 80 4 in 20 To be recited. once I 10 in 60, 6 times 2 times i 10 in 70, 7 times 3 times 10 in 80, 8 times 4 times 10 in 90, 9 times 5 times 's. The following —How many times XI. 2 in 16 2 in 6 3 in 27 6 in 42 5 in 30 2 in 20 9 in 81 6 in 48 3 in 15 9 in 90 8 in 64 4 in 24 2 ip 13 6 in 60 3 in 9 2 in 14 3 in 12 10 in 100, 10 times numbers may be embraced in 4 are there in 36 1 XII. XIII. 5 in 35 9 n 72 7 in 70 9 n 54 5 in 45 10 in 80 3 in 21 9 n 27 4 in 16 7 n 42 3 in 30 8 in 48 4 in 32 9 m 18 2 in 10 10 in 60 4 in 28 7 in 14 5 in 50 7 in 35 7 in .56 9 in 45 2 in 18 7 in 21 3 in 24 8 in .32 10 in 70 7 in 28 9 in 36 10 in 50 6 in 18 8 in 56 9 ill 63 ; io in 100 40 DIVISION. •t It • Note to Teachers. It. will be perceived, that, in llic pnjcediiig exam- ple*, Division has been viewed in only one of its purposes — that of investi- gating the number of times a small number is contained in a larger. We have now to pursue the same process, fur the purpose of dividing tlie larger number into as many equal parts, as there arc nnit^ in tiie smaller number, and discovering the magnitude of one of the parts. James and tween them, are 6 raisins. LESSON XIV. Henry had six raisins, to divide be- They said, 'We are 2 boys, and there Now if each of us take up one raisin, then two raisins will be taken up ; therefore, we can each of us take up as many raisins, as there are twos in the six.' How many could each boy take up .'" UUU When a number is divided into 2 equal parts, one of the parts is called, one half of the number. , What is one half of 6.' Ill III Three boys, George, John and Thomas, found 6 marbles, and wished to share them equally. George said to the others, ' Here are 3 boys of us : let u.s find how many times 3 marbles there are, and then we can each of us take 1 marble from every 3 mar- bles.' How many marbles did each boy zel? LULU When a number is divided into 3 equal parts, one of the parts is called, one third of the number. What is one third of 6 .' 11 11 11 4 little girls, who own eight books together, wish to divide tlieir books, and take their shares. As ma- ny times as 4 is contained in 8, so many books must each girl have. How many must each girl have ■'' UJJLUJ When a number is divided into 4 equal parts, one of the parts is called, one fourth of the number. What is one fourth of S .' 11 11 11 11 pi le I)lVISIO\. 41 p_g exani- investi- |er, \V<. I'le larger numbor. «e he- 'll ere raisin, jve can Ire twos I?' fts, one What nmd 6 eorge let us d then 3 mar- Notc to Tfarfiti's. The learnoi-s inay ho roterred, il" nrccti.sary, Jo the pifaniMes of the srcoiul, fourth and sixth (jiiestions in the next prrcoding ies-ioi), for answers to the first three qncs-tions in this lesson. LESSON XV. Wlmt do we mean by one half oi' a number ? What do we mean by one third of a number ? What do we mean by one fourth of a number ? What is one half of 2 pence ? One third of 3 pence ? One fourth of 4 ? One fifth of 5 ? One sixth of C ? One seventh of 7 ? One eighth of o ? One ninth of 9 ? One tenth of 10 ? o boys had 20 marbles to share between them, and the oldest boy performed the division. He said, ' One boy must have one fifth of the marbles. One fifth of 5 is 1, and one fifth of 20 is as many times 1, as there are fives in 20.' To prove what he said, ho placed the marbles in a row, and, after rolling out I from every 5 for himself, requested the other boys to roll out theirs. How many did each boy take ? O ~s r • s, one What wish ' ma- miist ave.^ one • 4#. There are 13 windows in a house. How many of them are open, while only 6 of them are shut.' 4. If a house have 6 windows open, and 7 win- flows shut, how many windows has the house.'' .'). How many squares of glass are there in a win- dow, that has 4 squares in length, and 3 in width .'* 6. If 10 barrels of cider can be carried in one wagon, how many can be carried in 4 wagons.'' 7. A wagoner sold 10 barrels of cider, at 3 dollars n barrel. How many dollars did he receive.'^ LESSON III. 1. It takes 4 boys to play a game at ball. How many games can 24 boys play, at the same time.'' Solution, 'ii hov's can jilay as many glumes as there mc fours in '^4. -i is contained in 24, 6 times. 2. How many oranges can you piu'chaso for 27 pence, when they are sold at 3 pence apiece.'^ 3. If oranges can be purchased for 3 pence apiece, how many pence will 9 oranges cost? 4. A boy, who had 1 1 pence, paid 9 pence for a football. How many pence had he left? 5. The sun rises every day, and there are 7 days in a week. How inany times does it rise in 7 weeks? C William was sick, and was confined to the house 49 days. How many weeks was he sick? 7. There are 7 questions in this lesson, and 7 in the next preceding lesson. How many in both? MISCELLANEOUS EXAMPLES. 45 LESSON IV. 1. One of 5 brothers, who owned 30 doves in company, sold his share. How many did he sell? Solution. 1 boy is one fifth of 5 boys, and he sold one fifth of 30 doves. One fifth of 30 is 6. 2. A farmer, who raised 48 lambs, found, that 1 of every 6 was black. How many were black? 3. In fishing, this morning, I caught 13 fishes ; but 7 of them escaped. How many had I remaining? 4. There were 5 pears upon each of 3 young pear trees. How many pears were there in all? 5. There are 8 rose bushes on one side of a garden path, and 8 on the other. How many on both? 6. If it take 8 squares of glass for a window^, how many squares are required for 8 windows ? 7. A boy gave 40 kernels of corn to 5 ducks How many kernels were there for each duck? LESSON V. 1. Martha is 10 years old, and Maria is 7 yeu old. What is the difference in their ages? Solution. We take 7 yenrs from 10 years, and U. number left is the difference. 7 from 10 leaves 8. 2. A certain farmer has 20 sheep and 10 lambs How many more sheep than lambs has he? 3. A boat crossed the ferry with 6 horses, ant- returned with ,5. How many both ways? 4. If a baker use 18 barrels of flour in 9 weeks, how many barrels does he use in one week? 5. How many weeks will 21 barrels of flour last a baker, who uses 3 barrels every week? 6. There are 9 lines ruled upon one page of my writing-book. How many are there on 5 pages? 7. If you have 17 pence, and pay 7 of them for a writing-book, how many will yon have left? 40 MISCELLANEOUS EXAMPLES. Mt LESSON VI. 1. If you wished to divide 54 nuts equally among boys, how many would you give to eacli boy? 2. What is one sixth of 6? of 54? of GO? ;3. One day, there were 7 girls at school, and 5 limes as many boys. How many boys were there? 4. How many are 5 times 7? 5 tunes 5? C? ;*). How many oranges can be purciiased for 25 pence, when they are sold at 5 pence apiece? C). How many times 6 in 25? in 50* in 35? 7. Richar' gave 9 pence for a kite, and 8 pence for a line. How much did he give for both? 5. How many are 9 and 8? 9 and 1? 9 and 4? 9. George answered 11 questions, and Stephen 6. How many more did George answer, than Stephen? 10. U are how many more than 6?' than 9? 7? 11. If 4 boys pay 40 pence for breaking a square of glass, how many pence does each boy pay? 12. What is one fourth of 4? of 40? of 20? W( m tu m cc cc LESSON Vll. 1. Of the 9 pictures which hung in my room, I liave taken down 3. How many remain hanging? 2. 3 from 9 leaves how many? 3 from 8? 3. I have 8 cows, but my farm will feed twice as many. How many will my farm keep? 4. How many are twice 8? twice 6? twice 9? 5- If you had 7 pins in one sleeve, and 5 in the other, how many would you have in both? G. How many are 7 and 5? 7 and 3? 7 and 9: 7. A landlord, who had 10 rooms, received 20 men to lodge. How many might he put in a room? 8. What is 1 tenth of 20? of 40? of 60? 9. If G boys put 6 books apiece upon the table, how many books will there be on the table? 10. How many are G times G? 6 times 8? 9? 11. James found a cluster of 14 grapes. After giving me 7 of them, how many had he left ? 12. 7 from 14 leaves how many? 7 from 8? m P 4I inong re? o ov 25 jence 14? hen 6. hen ? 7? square 00 m, I IS? wice as ;e9? ) in the mdO? 20 men te table, 9? 3. After 3? - ■ MISCELLANEOUS EXAMPLES. LESSON YIII. 47 1. At 9 o'clock, John was asked, what o'clock it would be 3 hours after that time. You may answer. 2. How many are 9 and 3? 9 and 6? 9 and 4? 3. Suppose a goldsmith can make 7 finger ring? in one day, how many can he make in 6 days? 4. How many are G times 7? G times 8? 10? 5. James has 6 story books, and Sarah h?" ^ pic- ture books. Who has the greater number of books? 6. 6 from 6 leaves how many? 6 from 11? 7. 24 persons rode to the city in 3 coaches. How- many were there to ride in each coach? 8. What is one third of 24? of 15? of 12? 9. If 8 persons can ride in one coach, how many coaches are required to carry 24 persons? 10. How many times 8 in 24? in 72? in 80? 11. A coachman has 4 coaches, and for every coach, has 4 horses. How many horses has he? 12. How many are 4 times 4? 4 times G? 9? LESSON IX. 1. If we plant 5 kernels of corn in one hill, in how many hills should we plant 45 kernels? 2. How many limes 5 in 45? in 30? in 20? 3. Caroline has read 10 pag^es, in a book of 111 pages. How many pages has slie yet to read? 4. 10 from 19 leaves how many? 10 from 20? 5. 16 chairs arc placed in equal numbers on the 4 sides of a room. How many are on one side? G. What is one fourth of IG ? of 4 ? of 36 ? 7. There were 6 geese in the pond, and 6 others on the shore. What was the whole number? 8. How many are 6 and 6? 6 and 4? 6 and 9? 9. On a high mountain I found 7 eagles' nests, and in each nest, 2 eaglets. How many eaglets in all? 10. How many are 7 times 2? 7 times 4? 8? 11. If one writing desk accommodate 3 scholars, how many desks are required for 15 scholars? 12. How manv times 3 in 15? in 9? in 27? 48 MISCELLANEOUS EXAMPLES. d. ' LESSON X. 1 . How many are 3 and 3 and 3 and 3 and 3 and 3? Then 6 times 3 are how many? How many are 6 and 6 and 6? Then 3 times 6 are how many? 2. How many times 7 are there in 28? What is one seventh of 7? What is one seventh of 28? 3. How many times 4 are there in 28? What is one fourth of 4? What is one fourth of 28? 4. If we take 4 and 4 and 4 from 12, what will be left? Then how many times 4 are there in 12? 5. If we take 5 and 5 and 5 from 15, what will be left? Then how many times 5 are there in 15? 6. How many are 7 times 4? How many times 4 are there in 28? What is one fourth of 28? 7. How many are 8 times 5? How many times 5 are there in 40? What is one fifth of 40? S, How many are 9 times 7? How many times 7 are there in 63? What is one seventh of 63? 9. What is one eighth of 8? How many times 8 are there in 56 ? What is one eighth of 56 ? 10. What is one ninth of 9? How many times 9 are there in 90? What is one ninth of 90? 11. What is one tenth of 10? How many times 10 are there in 100? What is one tenth of 100? 12. If you should be 3 times as long in going through the next book, as you have been in going through this, when shall you get through it? THE ESD OF FART FIRST. !fy 'SHlf. .>>S£>!^...'^^-'1.'^<.^