IJ R W S E ' S 
 
 Erun. 
 
 :OM«INKD WITH 
 
 EiLSY LESSONS 
 
 MENTAL ARITHMETIC. 
 
 FOR BEGINNPRS. 
 
 BY REV. GEO. Y. BKOWNE, A. M 
 
 TUSCALOOSA ALA. 
 
 ATLANTA, GA : 
 ITXiiVISrivL.IN- PRINTING HOUSE. 
 
 J. 1. TOON, PUBLISHER AND PROPRIETOR. 
 
 1865. 
 
 S 
 
COL. GEORGE WASHINGTON FLOWERS 
 MEMORIAL COLLECTION 
 
 DUKE UNIVERSITY LIBRARY 
 DURHAM, N. C. 
 
 PRESENTED BY 
 
 W. W. FLOWERS 
 
pessa«- 
 
 I BROWNE'S 
 
 o — ' 
 
 COMBINED WITH 
 
 EASY LESSONS , 
 
 MENTAL ARITHMETIC. 
 
 FOR BEGINNERS. 
 
 BY REV. GEO. Y. BROWNE, A. M. 
 
 TUSCALOOSA, ALA. 
 
 ATLANTA, GA. : 
 FRANKLIN PRINTING HOUSE. 
 
 J. J. TOON, PUBLISHKB AXD PROPRIBTOB 
 
 L 
 
 assess ■ 
 
 1865. 
 
Tr /! . 
 H 
 
PREFACE. 
 
 No apology is deemed necessary for presenting; this little work 
 to tbe j.ublic. As fur as it goes, it contains the results of more 
 than twenty years' experience in practical instruction in this 
 department of the duties of the Southern school room. 
 
 One important feature, too frequently overlooked by those 
 who prepare books of instruction for very little children, has 
 been steadily kept in view in its preparation. The book is 
 adapted to tbe supposed progress in reading of its little studentsj. 
 Indeed, it is (bought thai it may be used profitably as a reading 
 book for the class of pupils for whom it is designed. 
 
 Another feature is that the thinking faculty of the learner is, 
 from the beginning, kept in constant, but not too laborious exer- 
 cise. It is hoped that the lessons are sufficiently progressive for 
 the brightest pupils, yet uot too much so for those of average 
 ability. 
 
 Whether the series, of which this may perhaps be the "Prinv 
 er," will ever be completed, will depend partly upoo the reception 
 it may meet with, and partly upon the author's other pressing 
 duties in the school room and in the pulpit, 
 
 G. Y. B. 
 
 Eufacla, Alabama. 
 
 
 P80750 
 
INTRODUCTION. 
 
 The grand object, ne^ver to be lost sight of, in 
 
 every department of instruction, should be the 
 development of the iirtelU'Ctual faculties. Mathe- 
 matical studies have generally been thought to be 
 highly conducive to this gratad object; but, as ordi- 
 narily pursued, it may well be questioned whether 
 they do not exert an injurious rather than a beneficial 
 influence. The author hopes, by this "Primer," to 
 aid both teacher and pupil to draw the highest 
 possible intellectual benefit from these elementary 
 studies. 
 
 Machinery. — In the prosecution of this labor but 
 little machinery is necessary. A black board and 
 some chalk are great conveniences. An Abacus 
 may serve for a while to amuse, and may prove an 
 assistance. The author had one for some time, but 
 found it rather an incumbrance. A slate and pen- 
 cil from the beginning will be found indispensable. 
 
 Recitations. — Three features should characterize 
 every recitation, viz : absolute perfectness, great 
 promptness, and rigid attention. To state these 
 points may be suflicient. The author has been ac- 
 customed to consider a slip of the tongue, or the 
 
 P60750 
 
VI INTRODUCTION. 
 
 slightest hesitation in reciting the tables, a failure. 
 It requires a great deal of drilling to stimulate pu- 
 pils to this very high Standard of Excellence, but it 
 may be accomplished by gradual approaches, n<>t 
 only without annoyance, but with positive pleasure 
 to the pupil. 
 
 The Figures. — To teach the forms and names of 
 the figures, make the digits on the black-board in 
 any order whatever, thus: 
 
 1 
 
 9 
 
 4 
 
 
 
 5 
 
 3 
 
 6 
 
 5 
 
 7 
 
 2 
 
 8 
 
 I 
 
 Name them over in concert with the class several 
 times, and then call upon each pupil to point to any 
 number that may be named. A few lessons of from 
 ten to fifteen minutes each will be suflicient for the 
 instruction of a large class. The pupils should be 
 encouraged to write the figures with chalk upon the 
 black-board. The value of the figures may be 
 taught by making marks upon the black-board and 
 writing in connection the proper figures, thus: 1 = 1 
 11=2 111=3 1111=4 lllil 1111=9, and soon. 
 The pupils should, of course, write such exercises 
 both upon the board and upon the slates. 
 
 The same point may be further illustrated by an 
 
INTRODUCTION". Vll 
 
 Abacus, or by buttons, marbles, pencils, books or 
 anything else that may be convenient. 
 
 Counting. — This exercise should be performed 
 forwards and backwards to any required number in 
 concert at first, but afterwards by each pupil singly. 
 By a simple device, which will be found explained 
 at some length in the remarks before Multiplication, 
 the pupil will be enabled to count by any intervals 
 that may bo r« -quired. It may be done in the first 
 place by the odd numbers, 1, 3, 5, 7 and 9, and 
 afterwards by the even mrr. bers, 2. 4, 6 and K. As 
 this kind of counting facilitates the acquirement of 
 all the four fundamental operations of arithmetic, it 
 is suggested that it be put into practice as soon as 
 the pupils have a tolerable idea of the value of the 
 figures, and kept in daily exercise, forwards and 
 backwards, until the whole school can count thus 
 promptly and accurately. 
 
 The Sions. — The author prefers to use Algebraic 
 signs from the beginning. In the Addition fable two 
 signs are used -f-< plus; and =, equal. The name 
 of the first is plus — its meaning is " more, add or 
 and." In the table, the last meaning is used. The 
 = is the sign of equality, and may mean " are, 
 leaves or is," as the case may require. Thus, in 
 the Addition table for 1 + 1=2 read one, and one 
 aro two, and so on. 
 
 Iri the Subtraction Tubh on j additional sign is 
 
INTRODUCTION. 
 
 . viz: — , minus. It moans loss or from. Hence 
 rea 1 (6 — 1=4) thus : 1 from 5 leaves 4, & 
 
 In the ^fu J lti plication Tatje, anojbher sign is em- 
 ployed. It is formed thus x . and named tjhe sign 
 of multiplication. It may bo interpreted " times."' 
 The third line of the. table of six, which is written 
 thus (3 x 6 = 18.) may he read three times six is 
 eighteen. [See foot note Multiplication.) 
 
 In Division, still another si^n, made, thus ~, is 
 used. It is called the. sign of division, and may V)c 
 interpreted by "into." Thus in the table of nine 
 the sixth line, which is written (54 ~ d z= (».) may 
 be read nine into fifty-four six times* and so on. 
 
ADDITION. 
 
 Lesson First. — Increasing by Ones. 
 
 1. One boy is on a box, one more boy gets on ; how 
 many boys arc now on the box ? 
 
 2. Two hens are in a coop, one more is put in ; how 
 many hens are now in the coop ? 
 
 3. Three nuts are on a plate; if one nut more is put 
 on, how many will that mnke ? 
 
 4. John has four 1 talis and James has one ; how many 
 balls have both boys ? 
 
 5. Five girls are on a bench and one is on a chair; how 
 many girls are there in all ? 
 
 D. Six ducks are in the pond; if one more goes in how 
 many will that make V 
 
 7. 1 have .seven dimes in my right hand and one in my 
 left; how many dimes are in both hands? 
 
 8. Add eight yards to one yard; How many yards will 
 there be ? 
 
 9. Nine sticks of wood are in a pile ; if one more stick 
 is put in the pile, bow many will that make V 
 
 10. Ten hats are in a box ; put oik- mole hat in, and 
 how, many hats will there be? 
 
 
 
 THE TABLE 
 
 
 
 
 
 1 + 1 
 
 = 2 
 
 
 
 Q 
 
 + 
 
 1 
 
 = 7 
 
 2 1 
 
 3 
 
 
 
 7 
 
 
 1 
 
 8 
 
 3 1 
 
 4 
 
 
 
 8 
 
 
 1 
 
 9 
 
 4 1 
 
 5 
 
 1 
 
 
 9 
 
 
 1 
 
 10 
 
 5 1 
 
 6 
 
 1 
 
 
 10 
 
 
 1 
 
 11 
 
 EXERCISES. 
 
 5 and 1 ? 3 and 1 ? 7 and 1 ? 2 and 1 1 3 and 1 ? 
 8 and 1 ? 4 and 1 ? 2 and 1 ? 1 and 1 ? 5 and 1 ? 
 2 and 1 1 7 and 1 ? 3 and 1 1 9 and I? 10 and 1 1 
 
10 ARITHMETIC. 
 
 Lesson Second. — Increasing by Twos. 
 
 1. Mary lias put two pma in her dress and wants one 
 more; how man)' will that make? 
 
 2. One hen eats two g>-ains of corn and then eats twe 
 more groins ; how many grains did she eat ? 
 
 3. John puts two chairs to the table and Jane puts 
 three ; how many are theie at the table ? 
 
 4. If four books are in a pile, and two more are put in, 
 how many books will there be in the pile? 
 
 o. 
 
 George drives five nails into a board, and two into 
 another; how many nails did he drive? 
 
 6. There are six boxes on a dray, and two more are 
 put on ; how many does that make ? 
 
 7. Seven bells are in a store, and two moieare brought 
 in ; how many does that make ? 
 
 8. Eight hats are on a stand ; if two more are put on 
 how man)' will there be ? 
 
 9. James has nine old coats and two new ones ; how 
 many coats has he ? 
 
 10. Ten black birds and two red ones make how many? 
 
 
 
 THE TABLB. 
 
 
 1+2 = 3 
 
 
 + 2 = 
 
 8 
 
 2 
 
 2 4 
 
 
 7 2 
 
 9 
 
 3 
 
 2 5 
 
 
 8 2 
 
 10 
 
 4 
 
 2 6 
 
 
 9 2 
 
 11 
 
 5 
 
 2 7 
 
 
 10 2 
 
 - 12 . 
 
 
 
 EXERC1SE8. 
 
 
 4 and 2? 
 
 5 and 2? 
 
 4 and H 3 and 2? 
 
 7 and 21 
 
 6 and 2 ? 
 
 7 and 1 ? 
 
 10 and 2? 1 and 21 
 
 4 and 1 ? 
 
 7 and 2? 
 
 9 and 2 ? 
 
 8 and 2'? G and 1? 
 
 2 and 2? 
 
 3 and 1 1 
 
 2 and 2? 
 
 6 and 2? 5 and 2? 
 
 4 and 21 
 
 9 and 1? 
 
 8 and 2? 
 
 2 and 2 1 5 and 1 1 
 
 6 and 2 1 
 
 7 and 2? 
 
 5 and 2 1 
 
 9 an 
 
 d 2 % 4 and 2 ? 
 
 5 and 2? 
 
 £^£T" Many more such questions should be asked. 
 
ADDITION. 11 
 
 Lesson Third. — Increasing by Threes. 
 
 1. Three caps are in the drawer, and one more is pat 
 in ; how many will that make ? 
 
 2. Jane makes up three beds in one room and two in 
 another ; how many beds does she make up ? 
 
 3. Three large tigs and three small ones make how 
 many figs ? 
 
 4. If four jugs are full of milk and three full of wine, 
 how many jugs will that make? 
 
 5. Five bags are tilled with nuts and three with rice ; 
 how many bags does that make ? 
 
 6. There are six kegs in a row and three in another ; 
 how many kegs in both rows V 
 
 7. Seven axes with helves and three without, make 
 how many axes ? 
 
 8. Mary has eight dresses and Jane has three; how 
 many dresses have both? 
 
 i». Nine men are in the house and three in the street ; 
 how many men does that make? 
 
 10. There are ten maps in the book and three on the 
 wall ; how many maps are there in all ? 
 
 
 
 THE TABLE 
 
 
 
 
 14-3 = 4 
 
 | 
 
 
 
 + 3 : 
 
 = 9 
 
 o 
 
 3 5 
 
 j 
 
 7 
 
 3 
 
 10 
 
 3 
 
 3 6 
 
 1 
 
 8 
 
 
 11 
 
 4 
 
 3 7 
 
 
 i) 
 
 3 
 
 12 
 
 5 
 
 3 J 
 
 1 
 EXERCISES. 
 
 K) 
 
 3 
 
 13 
 
 7 and 3 ? 
 
 9 and 2? 
 
 "j and 3 ? 
 
 
 
 and 2? 
 
 8 and 3? 
 
 3 and 3 ? 
 
 (5 and 1 ? 
 
 7 and 2 ? 
 
 • > 
 
 a 
 
 and 3? 
 
 5 and 2? 
 
 5 and 2? 
 
 2 and 3 ? 
 
 9 and 3? 
 
 1 
 
 and 3 ? 
 
 2 and 3 ? 
 
 4 and I ? 
 
 7 and 2? 
 
 8 and 3 ? 
 
 7 
 
 and 1 ? 
 
 6 and 3 ? 
 
 4 and 2? 
 
 5 and 1 ? 
 
 3 and 1 1 
 
 2 and 5 ? 
 
 9 and 3 ? 
 
 7 and .3 ? 
 
 5 and 2 ? 
 
 2 and 1 ? 
 
 4 and 1 1 
 
 7 and 2? 
 
vz 
 
 AurniMKTir 
 
 Lesson Fourth. — Increasing by Fours. 
 
 1. Four palm-leaf fans and one silk one will make how 
 many fans ? 
 
 2. John brings in four logs and James brings 'in two; 
 how many logs do both bring in ? 
 
 5. Tlioiv arc tour glass mugs and three tin ones; how 
 many mugs does both make V 
 
 4. Mary lias four white and four red hair pins; how 
 many hair pins has she ? 
 
 o. J;me found five egi<s in one nest and four in another; 
 how many eggs did sin; lind ? 
 
 6. Sallie has four dolls and Mary has six; how many 
 dolls have both ? 
 
 7. George drew seven cats on one side of his slate and 
 four on the other; how many cats did ho draw ? 
 
 8. Eight birds are on one tree and four on another ; 
 how many birds on both trees ? 
 
 9. A boy ate nine cakes and a girl ate four; how many 
 did both cat ': 
 
 ID. Too blick eyes in five girls and four blue eyes in 
 two girls make how many eyes ? 
 
 
 
 THE ' 
 
 FABLE 
 
 
 
 
 1 -f- 4 = 5 
 
 
 
 6 
 
 + i = 
 
 = 10 
 
 o 
 
 4 G 
 
 
 
 7 
 
 4 
 
 11 
 
 *> 
 
 4 7 
 
 
 
 £ 
 
 4 
 
 12 
 
 4 
 
 4 8 
 
 
 > 
 
 
 
 4 
 
 13 
 
 5 
 
 4 9 
 
 
 
 10 
 
 4 
 
 14 
 
 
 
 exeuciseb. 
 
 
 
 
 and 4 ? 
 
 7 and 4? 
 
 3 and 3 } 
 
 G 
 
 and 21 
 
 8 and 4? 
 
 3 ami 4-1 
 
 4 and 4 \ 
 
 G and V. 
 
 4 
 
 and 3? 
 
 3 and 4 ? 
 
 5 ami 3-1 
 
 2 and 2> 
 
 9 ami I? 
 
 1 
 
 and 4'? 
 
 7 and 2 1 
 
 7 ami 2 ! 
 
 5 and 31 
 
 8 and -i'f 
 
 7 
 
 and 4 ? 
 
 4 and 3? 
 
 5 and 4 ? 
 
 ■> an 1 4? 
 
 2 a-nd 1? 
 
 7 
 
 and 3? 
 
 9 and 3? 
 
 G and 4 \ 
 
 7 and 4 ! 
 
 .9 an 
 
 d 4 1 
 
 2 
 
 and 4 ? 
 
 7 and 1 ? 
 
ADDITION. 13 
 
 Lesson Fifth. — Increasing by Fives. 
 
 1. A girl has five toys ; if one more be given her how 
 ninny toys will she have ? 
 
 2. There are two balls of white yarn in a box and five 
 of red ; how many balls are there ! 
 
 f. Five mules are in one team and three in another ; 
 how many mules in both teams? 
 
 4. Mary has five pet lambs and Kate has four; how 
 many lambs have both? 
 
 o." Five square bales and five round bales make how 
 many bales ! 
 
 t>. Six pinks are in bloom and six are not ; how many 
 pinks does that make P 
 
 7. Seven sheets are in the wash and six on the beds; 
 how many sheets in all ? 
 
 8. John jumps five times, Pete eight times; how many 
 times do both jump ? 
 
 if. Nine guns in one rack and five in another make 
 how many guns ? 
 
 10. James gave ten cents to a poor man and Charles 
 gave five ; how many cents did both give v 
 
 THE T.VHLK. 
 
 
 1 -f- 5 E 
 
 : G 
 
 
 6 
 
 + 
 
 5 r 
 
 = 11 
 
 
 y 
 
 5 
 
 7 
 
 
 < 
 
 
 5 
 
 12 
 
 
 3 
 
 5 
 
 8 
 
 
 8 
 
 
 5 
 
 13 
 
 
 # 4 
 
 5 
 
 9 
 
 
 <) 
 
 
 5 
 
 14 
 
 
 5 
 
 5 
 
 10 
 
 IXEUOUSS 
 
 10 
 
 
 5 
 
 15 
 
 7 
 
 an 1 5 \ 
 
 1 and 
 
 11 
 
 5 and 5 I 
 
 (5 
 
 and 5 ? 
 
 8 and 5 ! 
 
 3 
 
 and 4? 
 
 and 
 
 5 7 
 
 7 and 9 * 
 
 3 
 
 and 
 
 5* 
 
 5 and 4 1 
 
 i 
 
 ml i ? 
 
 2 and 
 
 5? 
 
 9 and 4 ? 
 
 1 and 5 ? 
 
 2 and 3* 
 
 G 
 
 and 3? 
 
 4 and 
 
 8? 
 
 3 and 1 } 
 
 4 
 
 and 
 
 £1 
 
 5 and 4 ? 
 
 :> 
 
 and 5 ? 
 
 7 and 
 
 5 .- 
 
 3 titui i % 
 
 9 
 
 and 
 
 51 
 
 7 and 5 ? 
 
 2 
 
 Mid 5'? 
 
 5 and 
 
 5? 
 
 9 and 5 I 
 
 10 and 
 
 5? 
 
 10 and 49 
 
It 
 
 ARITHMETIC 
 
 Losson Sixth. — Increasing by Sixes. 
 
 i. The babe had six teeth and one more has come; 
 how many teeth has it now ? 
 
 2. A boy had six fish hooks, he found two more; how 
 many did that make? 
 
 3. If three pies are done and six are not done; how 
 many pies will that be? 
 
 4. Four trees are in one, row and six in another; how 
 many trees in both rows ? 
 
 5. One knife has five blades, another has six; how 
 many blades have both knives? 
 
 0. There are six doors in the old house and six in the 
 new ; how many doors are th-^re in both houses? 
 
 7. If seven mills are on one stream and six on another; 
 how many will there be on both streams ? 
 
 8. Eight men are at work on that side of the house and 
 six on this ; now many men are there on both sides ? 
 
 9. If there are nine hens that have nests and six that 
 have not; how many hens Will that make ? 
 
 10. There are ten spools of white thread and six of black ; 
 how many spools of both ? 
 
 
 
 
 mi 
 
 : TABLE 
 
 
 
 
 1 + G 
 
 B= 7 
 
 
 
 
 G 
 
 + B ^ 
 
 : 12 
 
 2 
 
 G 
 
 8 
 
 
 
 
 7 
 
 6 
 
 13 
 
 3 
 
 G 
 
 9 
 
 
 
 
 8 
 
 6 
 
 14 
 
 4 
 
 G 
 
 10 
 
 
 
 
 9 
 
 G 
 
 15 ' 
 
 5 
 
 G 
 
 11 
 
 
 
 
 10 
 
 6 
 
 16 
 
 
 
 
 EXERCISES. 
 
 
 
 
 5 and G ? 
 4 and G ? 
 3 and 4? 
 7 and 5 ? 
 
 3 and G % 
 7 and G ? 
 1 and 6? 
 
 3 and G? 
 
 9 
 S 
 
 4 
 
 s 
 
 an 
 an 
 an 
 
 an 
 
 d 5? 
 d4? 
 el <i? 
 d G? 
 
 G and 1 ? 
 9 and 6? 
 6 and 3 1 
 6 and G 1 
 
 2 and 3? 
 f and 61 
 9 and 2? 
 9 and 5? 
 
 2 and 6? 5 and 4? 4 and 6? 7 and 3? 2 and 4? 
 
 3 and 3 1 7 and 5 ? 10 and 3 ? 10 and 5 ? 10 and G 1 
 
ADDITION. 15 
 
 Lesson Seventh. — Increasing by Sevens. 
 
 1. One loaf of bread is at the fire and seven are on 
 plates; bow many loaves does that make? 
 
 2. Two cars and seven cars will make a train of how 
 man)- cars ? 
 
 3. John has three balls, James gives him seven more ; 
 how many has he then ? 
 
 4. Seven pine posts are on this side of the fence and 
 four on that ; how many pine posts are there ? 
 
 5. Five plows and seven plows make how many? 
 
 6. Six boys have hoes and seven have guns; how many 
 boys does that make? 
 
 7. Ann has seven pins in one hand and seven in the 
 other; how many are there in both hands? 
 
 8. Btigh| boused are on one side of the road and seven 
 on the other, make how many houses? 
 
 9. Nine boys are in one room and seven in another; 
 how many hoys are there in both rooms ? 
 
 10. Ten cows and seven calves make how many cattle? 
 
 
 THE TABLE, 
 
 
 
 1+7 = 8 
 
 
 6 + 7 = 
 
 : 13 
 
 o 
 
 7 9 
 
 
 7 7 
 
 14 
 
 S 
 
 7 10 
 
 
 8 7 
 
 15 
 
 4 
 
 7 11 
 
 
 9 7 
 
 .16 
 
 5 
 
 7 12 
 
 
 10 7 
 
 17 
 
 
 EXERCISES. 
 
 
 
 6 and 7 1 
 
 5 and 7? 10 and 4? 
 
 4 and 5 ? 
 
 9 and 7 * 
 
 5 and 7 1 
 
 3 and 7 ? 6 and 6 1 
 
 5 and 4 1 
 
 2 and 5 ? 
 
 3 and 7? 
 
 1 and 3 1 4 and 7 ? 
 
 6 ami 5 ? 
 
 7 and 4? 
 
 9 and 7 ? 
 
 4 and 31 10 and 6? 
 
 8 and 1 1 
 
 6 and 4? 
 
 2 and 7 1 
 
 5 and 1 1 10 and 1 1 
 
 4 and 2? 
 
 3 and 51 
 
 4 and 6 1 
 
 1 and 1 1 9 and 4 ? 
 
 2 and 9? 
 
 1 and 81 
 
 7 and 6 1 
 
 Sand 3? 10 an 
 
 d9? 
 
 9 and 2? 
 
 7 and 8? 
 
 7 and 5 1 1 and 9 ? 6 and 1 ? 9 and 9 1 10 and 7 1 
 
16 
 
 ARITHMETIC. 
 
 Lesson Eighth. — Increasing by Eights. 
 
 1. Eight leaves have 1 »lnts on them and one leaf is torn; 
 how many leaven does that make? 
 
 2. Two trees are blown down and eight are dead; how 
 many trees ? . 
 
 3. Three sheep are in the fold and eight more are going 
 in ; how many will there be in ? 
 
 4. James has four books in his desk and John has eight 
 in his ; how many are there in both desks t 
 
 ti. Five snake.s are under one log and eight under an- 
 other ; how many snakes under both logs f 
 
 6. Three men have six spurs and four boys have eight; 
 how many spurs do they all have ? 
 
 7. There are seven blots on une page and eight on 
 another ; how many blots are there on both pag> . s I 
 
 8. There are eight wheels to this ear and eight wheels 
 to that; how many wheels to both ears? 
 
 9. If one boy makes eight rings on a slate and another 
 hoy makes nine, how many will both make? 
 
 10. Ten wet days and eight dry days ; make how many ? 
 
 THE TABLE. 
 
 1 + 8 
 
 2 8 
 
 3 8 
 
 4 8 
 
 5 8 
 
 9 
 10 
 11 
 12 
 13 
 
 8 mi 5? -land 8? 
 :. and 7? 6 and 8? 
 
 9 and 7 \ 5 and 6 ? 
 8 and 51 10 and 8 9 
 
 1 and (>? 10 and 1 '( 
 5 and ? ? 9 and 4 ? 
 P and 2? 10 and 5 1 
 
 EXERCISES. 
 
 3 and 5 ? 
 
 8 rind 8? 
 
 2 and 8 ? 
 
 9 *i ■ 
 
 7 and 5 ? 
 
 3 and 2? 
 7 and 7 % 
 
 C + 8: 
 
 7 8 
 
 8 8 
 8 
 
 10 8 
 
 7 and 4? 
 (3 and 8? 
 
 9 and 4 ? 
 3 and 7 % 
 5 and 8? 
 
 7 and (M 
 
 8 and 4 ? 
 
 : 14 
 15 
 16 
 17 
 18 
 
 f) and 6 ? 
 
 7 and 41 
 1 and 8 1 
 7 and 8? 
 3 and 8 ? 
 1 and 6 ? 
 3 and 1 
 
ADDITION. 
 
 17 
 
 Lesson Ninth* — Increasing by Nines. 
 
 1. Mary knows nine tunes; if she learns another how 
 lany will she know ? 
 
 2. Two hoys arc at the well and nine are playing town- 
 Vill ; how many hoys are there? 
 
 8. Three desks are of oak wood and nine of pine; how 
 many desks in all 1 
 
 4. Four goobers (ground nuts) are on the stove ; if 
 nhie more are put on how many will that make ? 
 
 5. Five frogs are in the well", hut nine have been taken 
 out; how many were, there in the well ? 
 
 6] How many corks do six large ones and nine small 
 ones make ? 
 
 7. There are seven rods for the girls ;-.nd nine for (lie 
 hoys; how many rods were there in all? 
 
 8. If to ei^ht pounds of rice you add nine pounds, how 
 many pounds will there he? 
 
 9. How many capes has Mary if she has nine of cloth 
 and nine of lace V 
 
 10. Ten rows of corn are on one ear and nine on another ; 
 how many rows are on both ears? 
 
 THE TABLE. 
 
 + 9 
 9 
 9 
 9 
 9 
 
 10 
 11 
 12 
 13 
 
 14 
 
 <> 
 7 
 8 
 9 
 10 
 
 9 
 9 
 9 
 9 
 
 15 
 16 
 
 17 
 18 
 19 
 
 4 and 9? 10 and 8? 
 7 and 9 ? 6 and 3 1 
 9 and 9? 6 and 4? 
 2 and 1 ? 6 and 9 % 
 1 and 9 ? 9 and 4 ? 
 
 5 and 9 ? 6 and 5 % 
 
 EXERCISES. 
 
 3 and 9? 6 and 9? 9 and T> ? 
 
 4 .-Mid 7? 7 and 9? 5 and 6? 
 4 and 8? 10 ; »ud 9.? 8 and 9? 
 
 8 and 9? 9 and 61 7 and 51 
 2 and 9? 5 and 1? 7 ar:d 81 
 
 9 and 4? 7 and %% 4 and 9 7 
 
18 ARITHMETIC. 
 
 Lesson Tenth. — Increasing by Tens. 
 
 1. One man owns one goat and another owns ten ; how 
 many do both own ? 
 
 2. John brings two yams to school and Mary brings 
 ten ; how many do both bring V 
 
 3. Three white beads and ten green beads make hov 
 many ? 
 
 4. Four Marys and ten Anns make how many girls ? 
 
 5. How many keys are there if five are in one bunoh 
 and ten in another I 
 
 6. There are six shell combs and ten horn combs ; how 
 many combs in all ? 
 
 7. If one girl is seven years old and another is ten, 
 what is the sum of their ages ? 
 
 8. Eight gnats are on my face and ten are on the wing; 
 how many gnats are there V 
 
 9. If there are nine red calves and ten black ones, how 
 many calves are there in all? 
 
 10. Ten birds are in one pie and ten in another; how 
 many birds are there in both pics ? 
 
 THE TABLE. 
 
 1 -f 10 = 11 I 6 -f 10 = 16 
 
 2 10 & 7 10 17 
 
 3 10 13 8 10 18 
 
 4 10 14 9 10 19 
 
 5 10 15 10 .10 20 
 
 EXERCISES. 
 
 1 and 10 ? 7 and 9 ? 5 and 4 1 3 and 10 % 5 and 6 ? 
 
 2 and 10 ? 7 and 4 ] 10 and 9 ? 8 and 10 ? 7 and 6 ? 
 
 3 and 10 1 9 and 7 % 10 and 8 1 4 and 10 ? 9 and 6 ? 
 (5 and 10 % 5 and 4 ? 10 and 4 % 6 and 1018 and 5 ? 
 9 and 10 % 3 and 7 % 7 and 4 ? 2 and 10 ? 8 and 5 1 
 5 and 10 ? 5 and 8 1 4 and 9 1 9 and 7 ? 2 and 9 1 
 9 and 6 ? 4 and 7 ? 5 and 9 ? 8 and 7 ? 8 and 5 1 
 
7- 
 ADDITION. 19 
 
 Lesson Eleventh. — Miscellaneous Questions. 
 
 1. Mary has one apple and George gives her three more; 
 how many has she then ? 
 
 | 2. In a box there are six marbles; John puts in four 
 more ; how many are there in the box ? 
 j 3. Seven cherries are on one stick and nine on another; 
 how many cherries are there on both sticks ? 
 
 4. Eight birds are sitting on one limb of a tree, and 
 nine inure are on another limb ; how many on both limbs ? 
 
 6. Nine houses are on this side the street and seven on 
 that ; how many houses are there on both sides ? 
 
 6. The speckled hen has eleven chickens and the black 
 hen seven ; how many have both ? 
 
 7. John has learned twelve verse? and little Kittie has 
 learned five; how many have they both learned 7 
 
 8. On one dish there are fourteen eggs and on another 
 six; how many on both dishes ? 
 
 9. Sallie has four kittens and Mary has three dolls ; 
 how many have both ? (If answered, ask "seven what?" 
 and state that things which are not alike cannot be added.) 
 
 10. Five boys and three boys and four boys ; are how 
 many ? 
 
 11. Three kites, two kites, and five kites; are how 
 many ? 
 
 .12. Six pens, three pens, and two pens ; are how many ? 
 
 13. One horse, six horses, and live horses; are how 
 many horses V 
 
 14. Three toes, five toes, and seven fingers; are how 
 many ? Why ? 
 
 15. Seven books, five books, and four books; are how 
 many V 
 
 16. Nine gloves, four gloves, and seven gloves ; are how 
 many ? 
 
 17. Eight chairs, six chairs, and nine chairs; are how 
 many ? N 
 
 18. Four birds, nine birds, and five birds ; are how many? 
 
 19. Six stars, eight stars; and nine stars ; are how many ? 
 
 20. Nine beds, three beds, two beds, and one bed ; are 
 how many ? 
 
20 .uuthmi.vk . 
 
 
 
 
 
 EXERCISES. 
 
 
 
 
 
 4+0+2? 
 
 9+2+3] 
 
 3+6+2'? 
 
 3+4+6+2? 
 
 6 2 
 
 3? 
 
 2 
 
 7 
 
 2? 
 
 
 
 4 
 
 3? 
 
 5 
 
 3 
 
 2 4? 
 
 7 2 
 
 4? 
 
 3 
 
 G 
 
 4? 
 
 7 
 
 G 
 
 2? 
 
 S 
 
 4 
 
 3 1? 
 
 3 7 
 
 5? 
 
 5 
 
 4 
 
 2 ! 
 
 G 
 
 5 
 
 3? 
 
 o 
 
 3 
 
 5 2? 
 
 1 8 
 
 2? 
 
 G 
 
 3 
 
 5? 
 
 4 
 
 3 
 
 0? 
 
 5 
 
 4 
 
 3 2? 
 
 5 4 
 
 3? 
 
 8 
 
 5 
 
 4? 
 
 5 
 
 4 
 
 8? 
 
 3 
 
 7 
 
 2 5? 
 
 3 2 
 
 61 
 
 2 
 
 3 
 
 6? 
 
 6 
 
 3 
 
 2 2 
 
 7 
 
 G 
 
 3 4? 
 
 <> 3 
 
 4? 
 
 9 
 
 1 
 
 3? 
 
 4 
 
 5 
 
 3? 
 
 8 
 
 4 
 
 5 3? 
 
 5 2 
 
 3? 
 
 8 
 
 4 
 
 2? 
 
 5 
 
 G 
 
 2? 
 
 5 
 
 3 
 
 8 4? 
 
 4 2 
 
 5? 
 
 7 
 
 5 
 
 G? 
 
 7 
 
 2 
 
 4? 
 
 9 
 
 5 
 
 4 2? 
 
 3 4 
 
 6? 
 
 
 
 4 
 
 3? 
 
 6 
 
 <> 
 
 5? 
 
 8 
 
 3 
 
 G 4 ? 
 
 7 3 
 
 2? 
 
 5 
 
 3 
 
 2 ? 
 
 3 
 
 2 
 
 5? 
 
 5 
 
 4 
 
 7 6? 
 
 Notk. — TheTeaeher should ask other ^u-stions of the sun- kind us 
 are written on these two list. |>:ijjfts. K > -< j >i re the answer to be?iven im- 
 ■!\- upon the completion "f the qaesijon., The object*)? thi%ia to 
 train the faculty oi act<.-ucL-j)i, and t> qniupcl the puull to use his 
 heacirathe^L' than his lingers in the Calculation. Lt-t. mc- ilhistr ill- this: 
 Suppose Hie toaehor says, (and he should always sneak somewhat slowly > 
 " niuo, live"' the pupil should he accustomed to i/(i'(h fourteen; then should 
 fcho teae.ier say, ana three, the pupil is re <(ty to answer seventeen. — 
 The auth >rhas sometimes had quite smsill children so w.ll trained that 
 the}- would tell accurately and pn m ;it ly npon the cmphnion of the 
 question, tho same of as many as a dozen a juros thus given out. 
 
V 
 
 SU DTK ACTION. 21 
 
 SUBTRACTION 
 
 Lesson Twelfth.— Decreasing by Ones. 
 
 1. A boy had one pencil, but he soon lost it ; what did 
 he have left ? 
 
 2. Mary had two yards of silk ; she cut oft' one yard 
 for a dress for her doll ; how much remained f 
 
 3. Three little boys stood up to recite, but one was sent 
 to his seat for talking ; how many remained ? 
 
 4. Four marbles were in a ring, but John knocked out 
 one; how many remained? 
 
 5. Sarah, having five apples, ate one ; how many re- 
 mained ? 
 
 0. A planter had six cows, one of which he sold; how 
 many were left. 
 
 7. Take one feather from a bunch of seven feathers ; 
 how many will remain ? 
 
 S. Eight birds were on a branch, but one rlcw away ; 
 how ma:iy we; e left * 
 
 9. A hen had nme little chickens, bnt the cat ate one 
 of them ; how many were left? 
 
 10. Ten books were in a pile, but George takes one off; 
 how many are left ? 
 
 TE1E TABLE. 
 
 1 -TT/1 =,,0 6 — 1 = 5 
 
 2 11 7 I <i 
 
 3 1 1 j j2 8 17 
 
 4 1 3 9 1 8 
 
 5 14 10 1 9 
 
 EXERCISES. 
 
 5 less 1 ? 7 less 1 '. less 1 ? 4 less 1 ? 
 
 9 U*M I ? « less ( 21 5 and 3? 7 less 1] 
 
 5 less 8? 8 less 11 8 and (? 9 less 8? 
 
 10 less 1 ? O hss 1 * 10 less ? 3 less 1 ? 
 
22 
 
 AKITflMKTIC 
 
 Lesson Thirteenth. — Decreasing by Twos, 
 
 1. Two vi.ils were standing on a shelf, but both were 
 knocked down ; what remained? 
 
 2. Three tapers were lighted, bui the wind blew two of 
 them out ; how many continued to burn ? 
 
 3. Four giants went out to war; two of them were 
 killed; how many returned? 
 
 4. Five basins were packed in a box ; two were broken ; 
 how many were whole? 
 
 5. Six spiders were in a corner; Jane swept two of 
 them clown ; how many were left. ? 
 
 0. Seven papers are lying together, but two of them are 
 torn ; how many are whole? 
 
 7. Eight pies were on the safe ; two of them were eaten 
 at dinner ; how many are left V 
 
 8. Mary has nine cherries, two of which are wormy; 
 how many are sound ? 
 
 0. Ten cows are in the field, but two of them are with- 
 out horns; how many have horns? 
 
 10. Eleven trees were standing in a row, but two have 
 been cut down ; how many remain ? 
 
 
 
 
 
 THE TABLE. 
 
 
 
 
 
 
 2 
 
 — 
 
 2 = 
 
 = 
 
 
 7 
 
 2 
 
 — 
 
 5 
 
 
 
 3 
 
 
 2 
 
 1 
 
 
 ■ 8 
 
 2 
 
 
 
 
 
 
 4 
 
 
 2 
 
 2 
 
 
 9 
 
 2 
 
 
 7 
 
 
 
 5 
 
 
 2 
 
 3 
 
 
 10 
 
 2 
 
 
 s 
 
 
 
 6 
 
 
 o 
 
 4 
 
 KXE1U 
 
 11 
 
 USES. 
 
 2 
 
 
 9 
 
 
 9 
 
 less 
 
 2? 
 
 9 
 
 less 
 
 1? 
 
 4 less 
 
 3? 
 
 5 
 
 less 
 
 2? 
 
 <; 
 
 less 
 
 21 
 
 4 
 
 less 
 
 1 1 
 
 7 less 
 
 2? 
 
 5 
 
 and 
 
 4? 
 
 o 
 
 less 
 
 2? 
 
 3 
 
 less 
 
 2 1 
 
 5 less 
 
 2? 
 
 8 
 
 and 
 
 ♦*> >. 
 
 i 
 
 and 
 
 71 
 
 4 
 
 less 
 
 21 
 
 9 and 
 
 41 
 
 t; 
 
 less 
 
 21 
 
 7 
 
 less 
 
 2! 
 
 3 
 
 less 
 
 11 
 
 7 and 
 
 SI 
 
 s 
 
 less 
 
 21 
 
 5 
 
 less 
 
 2? 
 
 10 
 
 less 
 
 2? 
 
 6 less 
 
 2? 
 
 9 
 
 less 
 
 21 
 
SUBTRACTION. 23 
 
 Lesson Fourteenth. — Decreasing by Threes. 
 
 1. Three balloons were sent up; if they all come down 
 will any remain up ? 
 
 2. There are four bottles of ink ; should three of them 
 be emptied, how many will still be lull ? 
 
 3. Five rabbits were in a cage; three got out ; how 
 many remained ? 
 
 4. A little girl who had six cents spent 'three ; how 
 many were left ? 
 
 5. Seven buggies are going by ; if three of them stop 
 how many will continue on ? 
 
 <>. Katie had eight peaches, but she give three of them 
 to her brother ; how many did she keep ? 
 
 7. Eildie, having nine chestnuts, gave three to George; 
 how many did he have left ? 
 
 8. When we eat three of the ten melons which father 
 bought, how many will remain ? 
 
 0. A merchant had eleven pitchers ; after three were 
 sold, how many remained ? 
 
 10. Twelve spools of cotton ore in a paper; how many- 
 will be left alter three are used V 
 
 THE TABLE. 
 
 3 — 
 
 3 = 
 
 = 
 
 
 
 8 
 
 
 a 
 
 = 5 
 
 4 
 
 3 
 
 1 
 
 
 
 9 
 
 
 3 
 
 6 
 
 r> 
 
 3 
 
 o 
 
 
 
 10 
 
 
 3 
 
 7 
 
 6 
 
 3 
 
 3 
 
 
 
 11 
 
 
 3 
 
 8 
 
 7 
 
 3 
 
 4 
 
 
 
 12 
 
 
 3 
 
 9 
 
 
 
 
 EXER 
 
 eiSKS. 
 
 
 
 
 7 less %\ 
 9 less 3 1 
 
 8 and 5? 
 
 9 less 6? 
 7 less 3 ? 
 
 13 less 
 
 5 loss 
 
 6 less 
 8 less 
 4 less 
 
 31 
 
 2 ? 
 21 
 3? 
 31 
 
 6 less 
 12 less 
 
 7 less 
 10 and 
 
 5 less 
 
 2? 
 3? 
 2 ] 
 4? 
 3? 
 
 5 and 4? 
 
 4 less 1 1 
 
 11 less 3? 
 
 7 and 3 1 
 
 8 and 6? 
 
 9 less 31 5 less 2? G less 3'? 9. less ,31 
 
24 ARITHMETIC. 
 
 Lesson Fifteenth. — Decreasing by Fours. 
 
 1. Henry had four £>et birds ; having given tnem away 
 
 Ik 1 granted to know how many won- left ? 
 
 9j A new house is to have live chimney$, but four of 
 which are finished ; how many art unfinished ? 
 
 8. A tanner sells four hides out of six; how many 
 remain ? 
 
 4. Sarah goes to school four days in the week ; how 
 many does she stay at home ? 
 
 5. Eight girls are sitting «.n the parlor; if four walk out, 
 how many remain V 
 
 '\ A drover has nine mutes, of which l:e sells a team of 
 four; how many does he keep? 
 
 7. Ten hogsheads of sugar arc at the depot; a dray 
 hauls off four; how many are left V 
 
 8. Eleven geese are swimming in the pond; if four 
 come out, how many wdl remain ? 
 
 9. Twelre shoes arc in a box ; if four are sold, how 
 many will there he in the box ? 
 
 10. Tf four grapes are taken from a bunch of thirteen, how 
 many will remain V 
 
 TUK T:\HI.K. 
 
 4 __ 
 
 4 
 
 — 
 
 
 9 
 
 — 
 
 4 
 
 
 S 
 
 
 5* 
 
 4 
 
 1 
 
 
 10 
 
 
 4 
 
 
 
 
 
 6 
 
 4 
 
 2 
 
 
 11 
 
 
 4 
 
 
 7 
 
 
 7 
 
 4 
 
 3 
 
 
 12 
 
 
 ■\ 
 
 
 8 
 
 
 8 
 
 4 
 
 4 
 
 KXER< 
 
 13 
 
 USES. 
 
 
 4 
 
 
 9 
 
 
 9 less 5? 
 
 4 
 
 and 
 
 3? 
 
 (> less 
 
 3? 
 
 
 5 
 
 iesa 
 
 2? 
 
 7 less 5? 
 
 3 
 
 and 
 
 3? 
 
 5 loss 
 
 4? 
 
 
 gf 
 
 less 
 
 2 % 
 
 6 less 3 ? 
 
 3 
 
 less 
 
 1 ? 
 
 10 less 
 
 4? 
 
 
 s 
 
 and 
 
 61 
 
 <) loss <\ 1 
 
 7 
 
 less 
 
 4? 
 
 11 le-s 
 
 3? 
 
 
 (> 
 
 1 ess 
 
 4? 
 
 7 and 6 ? 
 
 8 
 
 less 
 
 4? 
 
 13 Jess 
 
 4? 
 
 
 5 
 
 and 
 
 t? 
 
 4 and 9 % 
 
 5 
 
 less 
 
 3? 
 
 10 less 
 
 8? 
 
 
 V2 
 
 less 
 
 4? 
 
SUUT K ACTION. 96 
 
 Lesson Sixteenth.— Decreasing by Fives. 
 
 1. Five pitchforks were in the tool house, but Jim 
 threw their all out; how many remained.? 
 
 2. There are six padlocks, live of which have keys ; 
 h isv many are without kcysr 
 
 3. A ladder has seven rounds, five of which are painted; 
 how many are not painted? 
 
 ■1. Eight |jilfls are out walking; five have pink scarfs ; 
 how many have not? 
 
 5. A large mouth ate five out of nine dumplings; how 
 many were left ? 
 
 t>. Mary had ten strings .of chinquepins ; she gave five 
 to Sarah ; how many were left ? 
 
 7. Eleven boys are playing town ball ; if five are on 
 one side how many are on the other ';' 
 
 8. Twelve bags of iiour ; after five* were sold, how many 
 remained ? 
 
 i>. Thirteen hands arc sent to work on the road; five 
 of them lie down in the shade; how many work ? 
 
 10. Five men out of fourteen are six feet high; how 
 many are less ? 
 
 THE TABLE. 
 5 _ 5 ~ 10 — 5 = f) 
 
 b r> l ii r> G 
 
 7 5 2 12 5 7 
 
 8 5 3 13 5 8 
 
 9 5 4 14 5 9 
 
 EXEKCI8ES. 
 
 14 less 5 % 10 less 5 ? 15 less 5 \ 6 less 3 ? 
 
 ti and i% 13 less 5? 7 and 3'? 9 less 4? 
 
 11 Jess 5 I 9 and 8? 12 less 5? 7 less 5: 
 
 9 less 5 ] 7 less (> ? 6 less 5 ? 4 less 3 ? 
 
 tj and 5 ? S le^ 5 .' 10 less 5? 7 less f> ? 
 
 4 u-:.. 9 * 10 less 4 ! 3 and li 1 2 an.! 8? 
 
2fl 
 
 AUITIIMETIC. 
 
 Lesson Seventeenth. Decreasing by Sixes. 
 
 1. Six rats made their nests tinder a stack of fodder; 
 the c;it caught them all ; how many were left? 
 
 2. If we work six days out of seven, on how many do 
 we rest P 
 
 .'5. Eight pigs are in the pen ; if six are spotted, how 
 many are not spotted ? 
 
 4. Of nine beehives six are filled with honey; how 
 many are not filled V 
 
 5. Lizzie has painted ten pictures ; six- have frames ; 
 how many have not ? 
 
 6. Birdy is playing with eleven keys ; if he keeps six, 
 how many will be lose? 
 
 7. Twelve soldiers are inarching ; if there are six in the 
 front rank, how many will there be in the rear rank? 
 
 8. ff six flowers are pulled from a boquet of thirteen, 
 how main- remain V 
 
 9. Fourteen cows are in the pea field ; six are lying 
 down ; how many are standing? 
 
 10. Fifteen servants are dancing to the banjo; six are 
 men ; how many are women ? 
 
 
 THE TABLE. 
 
 
 
 
 6 — 
 
 6 = 
 
 11 
 
 
 6 
 
 = 5 
 
 7 
 
 1 
 
 12 
 
 
 6 
 
 <> 
 
 8 
 
 6 2 
 
 VA 
 
 
 6 
 
 7 
 
 9 
 
 6 i 
 
 14 
 
 
 6 
 
 8 
 
 10 
 
 KXKIt 
 
 15 
 
 OISES. 
 
 
 b 
 
 9 
 
 9 loss '? 
 M less 8 ? 
 7 less 4 ? 
 7 less 6 ? 
 1 and 8 ? 
 :rlld 5 I 
 
 11 less 6l 
 
 10 less 6? 
 
 10 less 5? 
 
 6 and 9? 
 
 9 less 6? 
 13 uss ! 
 
 7 and 6 
 5 and 6 
 
 8 less 3 
 14 less 6 
 12 less 5 
 
 7 iind 5 
 
 | 
 \ 
 
 ? 
 
 2 
 2 
 
 13 less 5? 
 12 less 6 ? 
 
 6 less 6? 
 
 6 and 6? 
 
 15 less 6? 
 9 k-,S $ * 
 
SUBTRACTION. 27 
 
 Lesson Eighteenth. — Decreasing by Sevens. 
 
 1. Seven cakes were on, a plate; John ate them up; 
 how many remained ? 
 
 •J. Eight pine trees grow together; seven are boxed for 
 turpentine ; how many are not ? 
 
 81 Nine servants are picking cotton ; if seven are wo- 
 men, how many are men ? 
 
 i. Ten sta.-ks of fodder are in the field; seven arc 
 fenced around ; how many are not? 
 
 5 Out of eleven large yams seven have been cut with 
 tli.' hoe; how many are uncut? 
 
 6. Seven out of twelve cabins arc double ; how many 
 are single ? 
 
 7. In a family of thirteen children seven are boys; how 
 many are girls ? 
 
 8. Fourteen loads of wood have been hauled, of which 
 seven were light-wood knots; how many were not? 
 
 9. Fifteen martin gourds are upon a pole; seven are 
 empty ; how many are occupied ? 
 
 10. Of sixteen bales of cotton, if seven are hauled at 
 one load, how many would he left for another ? 
 
 
 THE TABLE. 
 
 
 
 7 — 
 
 7 = 
 
 12 
 
 — 7 
 
 m 5 
 
 8 
 
 7 1 
 
 13 
 
 7 
 
 6 
 
 9 
 
 7 2 
 
 14 
 
 7 
 
 7 
 
 10 
 
 7 3 
 
 15 
 
 7 
 
 8 
 
 11 
 
 7 4 
 
 EXER< 
 
 16 
 
 hises. 
 
 7 
 
 9 
 
 .6 less 7 ? 
 
 15 less 6? 
 
 10 less 
 
 5? 
 
 4 and 9? 
 
 9 less 7 ? 
 
 17 less 7 ? 
 
 13 less 6 
 
 6 and 8? 
 
 5 and 6 ? 
 
 8 less 1% 
 
 9 less 
 
 5? 
 
 12 less 7 ? 
 
 9 and 4 1 
 
 7 and 7 ? 
 
 16 less 7? • 
 
 14 less 4? 
 
 8 and 4 % 
 
 10 less 7? 
 
 12 less 
 
 7? 
 
 7 and 9? 
 
 6 and 7 1 
 
 15 less 7? 
 
 11 less 
 
 71 
 
 13 less 7? 
 
28 
 
 ARITHMETIC. 
 
 Lesson Nineteenth. — Decreasing by Eights. 
 
 1. A boy who bad eight jackets hunt had worn thorn all 
 out; how many were left V 
 
 2. Nine bacon aides were hanging in the smoke house; 
 eight have been given out ; bow many are left.? 
 
 3. James bought let) plugs ol tobacco; after chewing 
 eight how many were hi. V 
 
 4. Bought eleven dozen egg* ; eight dozen only were 
 fresh ; how many wore spoiled: 
 
 5. Take eight bales ol' cotton from twelve bales, and 
 how many will be left? 
 
 0. Thirteen girls were in two classes; if eight are in 
 one how many are there in the. other? 
 
 7. Fourteen spinning wheels are at the shop ; when 
 eight are sold how many will be left ? 
 
 8. Sarah has fifteen books; eight of them contain pic- 
 tures; how many do not V 
 
 0. Sixteen hogs are- in the pen ; if eight are killed how 
 many will be left ? 
 
 10. Seventeen dead trees were in the field, but the wind 
 blew down eight; how many are standing ? 
 
 
 THE TAHLE. 
 
 
 
 8 — 
 
 8 = 
 
 13 
 
 — 8 
 
 = 5 
 
 9 
 
 8 1 
 
 14 
 
 8 
 
 
 
 10 
 
 8 2 
 
 15 
 
 8 
 
 7 
 
 11 
 
 8 3 
 
 10 
 
 8 
 
 8 
 
 12 
 
 8 4 
 
 EXER 
 
 17 
 
 CI6ES. 
 
 8 
 
 9 
 
 16 less-8? 
 
 9 less 4? 
 
 13 less 
 
 8? 
 
 15 less 7? 
 
 15 less 8 ? 
 
 7 and 1) ? 
 
 14 less 
 
 7? 
 
 12 less %% 
 
 10 loss 8 1 
 
 13 leys 7? 
 
 and 9? 
 
 11 less 8? 
 
 6 and 8 1 
 
 • 9 less 5? 
 
 13 less 
 
 7? 
 
 17 loss 8? 
 
 15 loss 8 ? 
 
 10 leas 8? 
 
 12 less 7? 
 
 9 less 8? 
 
 12 less 6 ] 
 
 7 an-d 9 % 
 
 10 less 
 
 3? 
 
 14 less 8? 
 
sen nt actio*:. 
 
 20 
 
 Lesson Twentieth. — Decreasing by Nines. 
 
 1. Nim* piles of brush are burning; when they are ali 
 out, how many will remain ? 
 
 i, Nine out of tew jars of iard have been used; how 
 many remained ? 
 
 3. If n fence is eleven rails high and nine of them arc 
 old, hew many are new 7 
 
 4. Twelve chairs are in a room ; if nine are split bot- 
 tomed, how many are not ? 
 
 5. At my quarters there are thirteen chimnevs, nine of 
 which are built with sticks ; how many are not V 
 
 o\ Fourteen shuck ]>ens stand in a row ; nine are full; 
 how many have been emptied? 
 
 7. Out of fifteen days John rode to school nine times ; 
 how often did he walk ? 
 
 8. Sixteen plows are at the shop; nine are scooters ; 
 how many are not ? 
 
 9. Seventeen plates were in a tray ; Sallie upset the 
 tray and nine were broken ; how many were not ? 
 
 10. Eighteen sacks of salt were on the wagon ; nine 
 have been carried into the smoke house ; how many are 
 left I 
 
 THE TABLE. 
 
 9 
 10 
 11 
 12 
 13 
 
 14 
 15 
 16 
 17 
 
 18 
 
 9 = 5 
 
 9 6 
 
 9 7 
 
 9 8 
 
 9 9 
 
 EXERCISES. 
 
 15 lew 9? 16 less 8? 8 less 2? 9 less 9? 
 
 5 and 4(1 12 less 9? 9 and 5? 11 less 9? 
 
 17 less 81 36 lees 9? 19 less 9? 15 less 0? 
 
 12 less 8? 18 less 9? 4 and 6 % 10 less 9? 
 
 13 less 9? 9 and 5? 17 less 9? 7 and 6? 
 
no 
 
 ARITHMETIC. 
 
 Lesson Twenty-first. — Decreasing l>y Tens. 
 
 1. Ten boys were playing ball ; when they all stopped 
 how many were .still playing? 
 
 2. Eleven pigeons have alighted on their house; if ten 
 fly off, how many will be left ? 
 
 .'3. Twelve wagons are on the road ; if ten of them have 
 loads how many have not? 
 
 4. Thirteen shawls are hanging in a row ; if ten of them 
 are removed, how many will remain ? 
 
 5. Take ten pods of pepper from a string of fourteen 
 pods, how many will remain ? 
 
 0. A girl who has fifteen dimes spends ten ; how many 
 are left ? 
 
 7. John is sixteen years old; Henry is ten years; re- 
 quired the difference of their ages ? 
 
 8. If ten pupils stay at home from a class of seventeen, 
 how many will be present? 
 
 9. Eighteen fruit trees are in the garden; ten of them 
 are in bloom ; how many are not? 
 
 10. The distance between two places is nineteen miles; 
 if we have traveled ten, how many more must we travel ? 
 
 
 
 
 THE TABLE. 
 
 
 
 
 10 
 
 — 
 
 10 ~ 
 
 
 
 
 15 
 
 — 10 =s 
 
 5 
 
 
 11 
 
 
 10 
 
 1 
 
 
 16 
 
 10 
 
 6 
 
 
 12 
 
 
 10 
 
 2 
 
 
 17 
 
 10 
 
 7 
 
 
 13 
 
 
 10 
 
 3 
 
 
 18 
 
 10 
 
 8 
 
 
 14 
 
 
 10 
 
 4 
 
 
 19 
 
 10 
 
 9 
 
 
 
 
 
 EXERCISES. 
 
 
 
 
 18 less 
 
 10? 
 
 15 1 
 
 ess 
 
 9? 12 less 
 
 6? 17 less 10? 
 
 9 and 
 
 7? 
 
 15 less 
 
 8? 16 less 
 
 10? 18 less 
 
 9? 
 
 14 less 
 
 7? 
 
 17 less 
 
 9? 13 less 
 
 10? 10 less 
 
 7? 
 
 12 less 10? 
 
 19 1 
 
 ess 
 
 6? 14 less 10? 10 1 
 
 3SS 
 
 4? 
 
 8 and 
 
 6? 
 
 13 less 
 
 9? 17 less 
 
 8? 19 1 
 
 ess 
 
 10? 
 
 10 less 
 
 10? 
 
 17 1 
 
 fcas 
 
 9? 
 
 12 less 
 
 6M5 1 
 
 JSS 
 
 8? 
 
SUBTRACTION. itt 
 
 Lesson Twenty-second. — Miscellaneous Questions. 
 
 1. Henry had eight peaches, but he gave three to his 
 sister ; 'now many did he have left? 
 
 '2. Mary had ten dunes in her purse, but she lost four 
 of them ; how many had she left ? 
 
 3. The dog had nine puppies, but six of them were 
 drowned ; bow many had she left ? 
 
 4. The hen had fourteen chickens, but she raised only 
 six of them ; how marly did she lose ? 
 
 5. Katie had thirteen chestnuts, of which eight were 
 roasted ; how many were not roasted? 
 
 (5. Ei^hteeri girts went up to recite, but seven were sent 
 to their seats for not knowing tlvoir lessons; how many 
 remained ? 
 
 7. Sarah has twelve apples; she gives two to George 
 and two to Rirdy ; how many has she for herself? 
 
 ,8. Carrie had nine pencils ; she lost three and gave one 
 each to her two little brothers; how many are left? 
 
 0. Twelve eggs are boiling ; four are taken out by James 
 and three by John ; how many are left? 
 
 10. Mary has three pies, but gives away two peaches; 
 what has'she left ? Why? 
 
 11. John found six marbles and his mother gave him 
 three more ; but he owed fifteen marbles ; how many did 
 he still need ? 
 
 12. There are fourteen sheets oi paper on the table; two 
 of them are yellow, five are brown, and the rest are 
 while; how many are white ? / 
 
32 
 
 AllITHMETiC. 
 
 6+4+3—2? 
 5-f-<5 + 4 — 2? 
 
 4+7+3-4? 
 5 + 2+4— 31 
 3 + 7_2+4? 
 8 + 5—44-3? 
 5 + 5—3+4? 
 6+9—2—4? 
 9+3— 5+2? 
 8+6—3—4? 
 9_|_4_2_5? 
 8—3+4+6? 
 7__4+5+8 ? 
 0—6+4— 3? 
 8—3+4+5? 
 7+5_3_4? 
 
 S+6— 5+6 ? 
 
 EXERCISES. 
 
 12—3—2—4? 
 
 14_5_:j + g? 
 
 15. |-3-9— 2? 
 13+0—4+8? 
 12—5+4—2? 
 11+0—2—3? 
 14_3+9—2? 
 16—2—3+4? 
 
 5+4+6+3? 
 
 7+9+3+6? 
 
 4 + 9_2+5 ? 
 13_4+6— 7? 
 12+6—4—2 ? 
 15+4—3—4? 
 
 8+9+4—5 ? 
 
 9+8+7—3? 
 
 4„9+o+4? 
 
 4+2+1+5+3? 
 
 5+3+2+3+4? 
 3+^+4+1+3? 
 2+4+3+2+1 ? 
 8+1+3+4+2? 
 3+5+2+5+4? 
 5+2+3+4+5? 
 3+4+2+5+6? 
 2+2+4+4+3? 
 5+4+3+6+2? 
 4+5+3+5+2? 
 6+3+2+4+1? 
 8+2+1+3+2? 
 9+3+4+5+3? 
 3+4+2+4+3 ? 
 6+3+2+4+5 ? 
 4+5+3+6+2? 
 
 Notk.— Lotnot the Teacher bo alarmed at this array of figures, or lay 
 it asido without faithful trial. The author, in thin little Prime*, merely 
 indicates the outline of his ooriroe. A great many additional examples 
 .should bV mtide bv the Teacher at every step iu the progress of his class. 
 
MtTLTIPLlCATIOK. 
 
 tt 
 
 MULTIPLICATION. 
 
 To the Teacher. 
 
 Multiplication consists in successive additions of the 
 same number. Availing himself of this fact, the author 
 has adopted, with great success, the following plan for 
 teaching the multiplication table to young children : 
 
 The floor of the room is supposed to be divided into 
 nine compartments, thus: 
 
 l_i. ...£_: 
 
 I i t 
 
 I i 
 
 H ; 
 
 A tenth compartment is supposed to be on the ceiling 
 directly over the middle one on the floor. 
 
 In each of these compartments a digit is to be written 
 with chalk. The cypher being supposed to be written in 
 the compartment on the ceiling, thus : 
 
 lj 
 
 ! 1 
 l| 
 
 2 
 
 3 ! 
 
 ! * 
 
 5 
 
 « 1 
 
 L 7 _ 
 
 8 
 
 
 
 » 1! 
 
 Every thing is now ready. Begin by counting. The 
 class may be placed on the line indicated by the figures 
 2, 5, 8, with their faces toward the line 3, 6, 9. Pointing 
 to each figure as they advance, the class repeats, in cons 
 cert, as follows : 3, 6, 9, 12, 15, 18, 21, 24, 27, 30. Care 
 2 
 
34 
 
 ARITHMETIC. 
 
 must be taken to make the pupils understand that, when 
 adding by threes, they cannot go from 9 to 2 , that the 2 
 is only the final figure and the number becomes 12 ; so, 
 from 18 to 1, the 1 becomes 21, and so on. 
 
 It is neither desirable nor necessary to stop the process 
 at thirty. Continue thus: 33, 36, $9, 42, &c, at the 
 teacher's pleasure. Ahodyscdun U from whatever 
 
 number you may have ascended to. 
 
 What has been stated above as to counting by threes, 
 holds good for the other odd numbers, except five. Ar- 
 range the class always ^o front towards the line in which 
 the number they are to increase by is found. The num- 
 ber five is so simple a one to count by that no directions 
 are necessary for it. 
 
 To count by the even numbers, let the class face the 
 number, and five motions of the arm will always point out 
 the proper unit figure in the number required. These five 
 motions are: first, to the front ; second, to the left ; third, 
 to the right ; fourth, to the rear ; and fifth, to the 0. 
 
 Illustration: Suppose it is required to count by twos. 
 The diagram on the lloor may then be represented thus: 
 
 1 
 
 * 
 
 3 
 
 
 5 
 
 6 [ 
 
 s 
 
 9 
 
 9 
 
 The exercise will proceed : front, 2 ; left, 1 ; right, 6 ; 
 rear, 8; overhead, 10; front, 12; left, li; right, 16; 
 rear 18; overhead 20, and so on. Practice counting for- 
 wards and backwards. 
 
 It may be required to begin with an odd number and 
 increase by an even number. Five motions of the arm 
 are again sufficient, viz : Two in front, one underfoot, 
 
MULTIPLICATION. 35 
 
 and (wo in the rear, (first, front left ; second, front right; 
 third, downwards ; fourth, rear left ; fifth, rear right.) 
 These movements describe the letter Z. 
 
 These exercises should proceed daily until each pupil 
 can readily count forwards and backwards to the number 
 of twenty additions without the motion of the arm. These 
 motions and the numbers on the floor being mere scaffold- 
 in-', should be dispensed with as soon as possible. 
 
 Tint what has all this to do with multiplication? Eve- 
 rything with multiplication and everything with division. 
 Instead ol c Hinting 4, S, 12. 1G, 20, and so on, let the 
 class begin in concert to add the multiplication formula,* 
 which is .-ill that is required; thus: ')nce four is four; 
 two times four are 8 ; three times four are 12, and so on. 
 
 Instead of counting backwards thus: :J0, 24, 18, 12, (5, 
 add trie division formula thus: (5 into 80, five times ; 6 
 into 24, t'o.ur times; 6 into 18, three times; u into 12 
 two times; 6 into 6, once. 
 
 The slate and the blackboard should be brought into 
 frequent requisition in all this training. If the pupil 
 frequently recites out the columns (2, 3, 4, &c.,) he will 
 become much more perfectly acquainted with them than 
 by any other process. 
 
 *The formula is elliptical : expressed fully it ln'couien four taken five 
 Jiiues becomes (are) twenty. That is, abbreviated, five times four are 
 twenty. 
 
36 
 
 ARITHMETIC. 
 
 MULTIPLICATION. 
 
 Le«son Twenty-third. — Increasing by Twos. 
 
 1. At one cent each what will be the cost of two apples ? 
 
 2. At two cents each required the cost of two peaches. 
 
 3. If one cap costs two dollars, how much will three 
 caps cost ? 
 
 4. If one gun costs two dollars, what will four gun* 
 cost? 
 
 5. Required the cost of five pencils at two cents each. 
 
 6. Required the cost of six books at two dollars each. 
 
 7. How much will seven buckles cost at two cents each? 
 
 8. One pair of shoes cost two dollars ; required the 
 cost of eight pairs. 
 
 9. One hammer costs two dimes ; what will nine ham- 
 mers cost? 
 
 10. Ten tops will cost how much, if one cost two cents ? 
 
 
 
 
 THE TABLE. 
 
 
 
 I 
 
 x 2 
 
 = 2 
 
 
 6 
 
 x 2 = 
 
 = 12 
 
 a 
 
 2 
 
 4 
 
 
 7 
 
 2 
 
 14 
 
 8 
 
 2 
 
 6 
 
 
 8 
 
 2 
 
 16 
 
 4 
 
 2 
 
 8 
 
 
 9 
 
 2 
 
 18 
 
 5 
 
 2 
 
 10 
 
 
 10 
 
 2 
 
 20 
 
MtTLTTPLICATION. 
 
 EXEKOISES. 
 
 2 times a? 4 times 2? 
 
 4 times 21 
 
 2 times 11 
 
 3 times 2? 
 10 times 21 
 13 less 6? 
 
 4 times 2? 
 
 8 times 1 1 
 
 9 times 2] 
 6 times 2 1 
 8 times 2? 
 2 times 6 ? 
 8 times 2? 
 
 7 times 6 ? 
 2 times 7 ? 
 5 times 2? 
 4 times 2 ? 
 2 times 7 ? 
 
 and 
 and 
 
 8? 
 
 11 
 
 Lesson Twenty-fourth.—- Increasing 
 
 37 
 
 2 times 9 1 
 8 times 21 
 
 3 times 21 
 
 6 and 9? 
 12 less 9? 
 
 3 times 2 1 
 
 7 times 2? 
 by Threes. 
 
 3 6 
 
 9 
 
 i o 
 
 8 
 
 1 4 
 
 7 
 
 1. What cost three marbles at one cent each ? 
 
 2. How much will two pens cost at three cents each? 
 
 3. If. three boys each recite three lessons, how many 
 will they all recite? 
 
 4. Four girls have each three dolls ; how many have 
 they all.? 
 
 5. Three bottles of ink at five cents each will cost how 
 much ? 
 
 6. There are three nests, each containing six eggs ; how 
 many eggs in all three ? 
 
 7. If there are seven pounds of butter in each of three 
 boxes, how many pounds will that make ? 
 
 8. Eight boys have each three cents ; how manv have 
 they all ? 
 
 9. Three oranges at nine cents apiece will cost how 
 much ? 
 
 10. In one dime there are ten centg ; how many cents in 
 three dimes ? 
 
38 
 
 ARITHMETIC. 
 
 
 
 
 
 TIIE TABLE. 
 
 
 
 
 1 X 
 
 3=3 
 
 6 
 
 X 
 
 3 
 
 = 18 
 
 25 
 
 3 6 
 
 7 
 
 
 3 
 
 21 
 
 3 
 
 3 9 
 
 8 
 
 
 3 
 
 24 
 
 4 
 
 3 12 
 
 9 
 
 
 3 
 
 27 
 
 5 
 
 3 15 
 
 10 
 
 
 3 
 
 30 
 
 
 EXERCISES. 
 
 
 
 
 3 times 3? 
 
 5 ;md 0? 
 
 1 times 
 
 
 ? 
 
 4 times 3 ? 
 
 9 times 21 
 
 2 times 3? 
 
 8 times 
 
 a 
 
 ? 
 
 1 and 7 \ 
 
 7 limes 3? 
 
 8 rim.s 3* 
 
 12 i'SS 
 
 9 
 
 ? 
 
 6 times 3? 
 
 16 and 91 
 
 4 times 2 * 
 
 5 times 
 
 3 
 
 ? 
 
 9 times 31 
 
 [Q less 8? 
 
 3 times 9? 
 
 4 times 
 
 3 
 
 > 
 
 7 times 3? 
 
 1 and 7'? 
 
 9 times 3? 
 
 11 less 
 
 5 
 
 ? 
 
 8 less 3? 
 
 3 times 2? 
 
 9 times 4? 
 
 5 times 
 
 3 
 
 £ 
 
 5 times 8 ? 
 
 Lesson Twenty-fifth.— Increasing by Fours. 
 
 1 7 
 
 1 
 
 4 
 
 i 
 
 i 
 
 ! 9 
 
 5 
 
 2 
 
 9 
 
 6 
 
 3 
 
 1. Four tumblers each holding one pint would contain 
 how much ? 
 
 2. Two rooms each contain lour windows, have how 
 many in all ? 
 
 3. Three cats have each four legs ; how many legs have 
 they all ? 
 
 4. Four vests are each to have four buttons ; how many 
 will be required ? 
 
MULTIPLICATION. 
 
 39 
 
 5. How many pencils will there be in five boxes if each 
 box contains four? 
 
 6. How many horses are there in four teams if each 
 team consists of six horses ? 
 
 7. Seven trees are in a row, .-urn there are four rows ; 
 how many trees will that make? 
 
 8. What is the joint age of four girls who are each eight 
 years old? 
 
 Q, A four sided pig-pen has nine rails in each side ; how 
 many rails ? 
 
 ten dimes 
 
 10. In a dollar there arc- 
 are there in four dollars ? 
 
 THE 
 
 how many dimes 
 
 TAKLK. 
 
 4 
 
 8 
 
 12 
 10 
 20 
 
 8 
 
 9 
 
 10 
 
 li 
 
 times 4 I 
 less 91 
 5 times 4 \ 
 9 times 4 1 
 2 times 1 ? 
 
 exercises. 
 times, 3 ? 3 times 4 ? 
 
 
 
 4 times 4? 
 
 9 times 3 i 
 
 4 times 4 % 
 
 5 times 4? 
 
 1 times 4? 
 8 times 4? 
 
 5 ana 91 
 
 6 times 4'? 
 
 = 24 
 
 28 
 32 
 36 
 40 
 
 4 times 6? 
 
 7 times 4? 
 9 and 7? 
 9 times 6? 
 
 8 times 5? 
 
 Lesson Twenty-Sixth— Increasing by Fives. 
 
40 
 
 ARITHMETIC. 
 
 1. At one dollar each what will five capes cost ? 
 
 2. At five dollars each two bonnets will cost how much ? 
 
 3. If cotton thread costs five cents a spool, how much 
 will three spools cost? 
 
 4. If four plates contain each five potatoes, how many 
 do they all contain ? 
 
 5. What cost five oranges at five cents each ? 
 
 6. Required the cost of five sheep at six dollars apiece? 
 
 7. How much will seven guns cost at five dollars each ? 
 
 8. Every boy ought to have eight fingers ; how many 
 ought five boys to have ? 
 
 9. Five clusters each contain nine pods ; how many 
 pods will the five contain? 
 
 10. Five piles each contain ten dollars ; how many dol- 
 lars in all V 
 
 
 THE 1 
 
 WBLE. 
 
 
 1 X 
 
 5=5 
 
 6x5 
 
 = 30 
 
 2 
 
 5 10 
 
 7 5 
 
 35 
 
 8 
 
 5 15 
 
 8 5 
 
 40 
 
 4 
 
 5 20 
 
 9 5 
 
 45 
 
 5 
 
 5 25 
 
 EXER< 
 
 10 5 
 
 3ISES. 
 
 50 
 
 2 times 2? 
 
 4 times 5 1 
 
 9 times 5 ? 
 
 7 times 5 1 
 
 8 times 4? 
 
 8 times 3 % 
 
 7 times 4 ? 
 
 1 times 5 ? 
 
 5 times 5 ? 
 
 2 times 5 ? 
 
 3 times 5? 
 
 5 times 4? 
 
 4 times 4? 
 
 8 times 5? 
 
 6 times 5 ? 
 
 9 times 4 ? 
 
 6 times 5? 
 
 7 times 5 1 
 
 4 times 5 ? 
 
 9 times 5? 
 
 4 and 91 
 
 6 times 4? 
 
 3 times 4 ? 
 
 7 times 5 ? 
 
 4 times 5 ? 
 
 9 times 5? 
 
 13 less 2? 
 
 15 less 6? 
 
 5 times 5 1 
 
 8 times 6 ? 
 
 10 times 3? 
 
 2 times 6? 
 
 3 times 4? 
 
 9 times 9 ? 
 
 8 times 9 ] 
 
 3 times 2? 
 
 8 times 31 
 
 7 times 4? 
 
 5 times 4? 
 
 8 times 4? 
 
 3 and 9? 
 
 4 times 3 % 
 
 16 less 9? 
 
 9 times 4 1 
 
MULTIPLICATION. 
 
 41 
 
 Lesson Twenty-Seventh—Increasing by Sixes. 
 
 1. Required the cost of six screws at one cent apiece. 
 
 2. At two dollars each what will six handkerchiefs cost? 
 
 3. If six boys can sit on a bench, how many can sit on 
 three benches ? 
 
 4. How much must I pay for four pounds of soap at 
 six cents per pound ? 
 
 5. One spool costs five cents ; required the cost of six 
 spools. 
 
 6. Six balls will cost how much at six cents apiece? 
 
 7. What number of yards in six dresses if there aie 
 seven yards in each ? 
 
 8. In each wagon are six barrels ; how many are there 
 in eight wagons ? 
 
 9. John gave nine marbles to each ot six little boys; 
 how many did he give away ? 
 
 10. Ten mills make a cent ; how many mills in six cents? 
 
 / 
 
 THE 1 
 
 'ABLE. 
 
 
 
 1 X 6 r 
 
 = 6 
 
 6x6 = 
 
 ^ 36 
 
 2 6 
 
 12 
 
 7 
 
 6 
 
 42 
 
 3 6 
 
 18 
 
 8 
 
 6 
 
 48 
 
 • 
 
 4 6 
 
 24 
 
 9 
 
 6 
 
 54 
 
 5 6 
 
 30 
 
 10 
 
 6 
 
 60 
 
42 
 
 ARITHMETIC. 
 
 EXERCISES. 
 
 5 times (5 ? 
 i) times 5 ? 
 ! time 6 ? 
 7 times 4 * 
 5 times 6 ? 
 
 4 times 6 ? 
 9 times 2 ? 
 
 3 times 5 .' 
 6 times 6 ? 
 
 4 times 4 \ 
 
 5 times 6 ? 
 ■Slimes 4? 
 11 less SI 
 3 times 6 ? 
 (') times 6? 
 
 9 and 5? 
 7 times 6 1 
 6 times 6 ? 
 4 times 5 ? 
 2 times 6 ? 
 
 Lesson Twenty-Eighth.— Increasing by Sevens. 
 
 7 4 
 
 1 
 
 II S 5 
 
 1 
 
 ii 
 
 3 
 
 Ii 
 
 9 6 
 
 J __ 
 
 1. What will seven sticks of candy cost at one cent a 
 stick? 
 
 2. How much will two suits of clothes cost at seven 
 dollars a suit ? 
 
 8. Three little girls had each seven ehinquepins ; how 
 many did all have? 
 
 4. At the carriage shop are seven buggies, each with 
 four wheels ; how many wheels have they all ? 
 
 5. There are seven days in one week ; how many days 
 in five weeks ? 
 
 6. The merchant has seven boxes of ink, each contain- 
 ing six bottles ; how many bottles has he? 
 
 7. Seven buttons on seven coats make how many? 
 
 8. If eight boys have each seven books, how many have 
 they all ? 
 
 9. How much will seven barrels of flour cost at nine 
 dollars a barrel ? 
 
 10. Ten dollars makes one eagle ; how many dollars in 
 seven eagles ? 
 
MULTIPLICATION. 
 
 43 
 
 
 
 THE TABLE. 
 
 
 
 
 1 X 
 
 7 
 
 — 7 
 
 6 
 
 X 
 
 7 
 
 = 42 
 
 o 
 
 
 14 
 
 * 
 
 
 7 
 
 49 
 
 Q 
 O 
 
 7 
 
 21 
 
 8 
 
 
 7 
 
 50 
 
 4 
 
 7 
 
 28 
 
 
 
 
 7 
 
 63 
 
 5 
 
 7 
 
 35 
 
 10 
 
 
 7 
 
 70 
 
 
 
 EXERCISES. 
 
 
 
 
 6 times 7 ? 
 
 7 
 
 times 7 1 
 
 5 times 
 
 7? 
 
 
 9 times 7 ? 
 
 o times 6 ? 
 
 1 times 7 ? 
 
 3 times 
 
 7? 
 
 
 4 times 6 ? 
 
 9 times 6 ? 
 
 5 
 
 times 7 ? 
 
 14 less 
 
 5? 
 
 
 6 times 7 ? 
 
 i times 7 * 
 
 9 
 
 times 5 1 
 
 8 times 7 '? 
 
 
 7 titnes 71 
 
 4 times 6 ? 
 
 7 times 8 ? 
 
 2 times 
 
 7? 
 
 
 4 times 7 ? 
 
 ^ times 9 1 
 
 8 times 7? 
 
 5 times (S ? 
 
 
 3 times 7? 
 
 5 times 7 ? 
 
 2 times 7? 
 
 7 times 
 
 7? 
 
 
 4 times 7 ? 
 
 Lesson Twenty-Ninth.— Increasing; by Eights. 
 
 !; o 
 
 8 
 
 it 
 
 ; j 
 
 ii w 
 
 
 
 1; 
 4 
 
 ii 3 
 
 $ 
 
 1 
 1 
 
 1. Eight cakes cost how much at one cent apiece ? 
 
 2. Two legs to each pair of tongs ; how many legs to 
 eight pairs ? 
 
 3. What will eight penknives cost at three dollars 
 j. piece? 
 
 4. If one cedar pencil costs eight cents, what will four 
 cost ? 
 
 5. Required the cost of eight calves at five dollars each. 
 
44 
 
 ARITHMETIC. 
 
 6. How much must T pay for six pumpkins at eight 
 cents apiece ? 
 
 7. There are seven rows of trees and eight in a row ; 
 how many trees ? 
 
 8. On a checker-board there are eight rows of squares 
 and eight in a row ; how many squares ? 
 
 9. A train of nine cars, and each car has eight wheels ; 
 required the whole number of wheels? 
 
 10. What will be the cost or' eight brass clocks at ten 
 dollars each ? 
 
 
 THE 
 
 TABLE. 
 
 
 
 1 X 
 
 8 = 8 
 
 6 x 
 
 8 
 
 = 48 
 
 '2 
 
 S 10 
 
 i 
 
 8 
 
 56 
 
 3 
 
 8 24 
 
 8 
 
 8 
 
 64 
 
 4 
 
 8 32 
 
 9 
 
 8 
 
 72 
 
 5 
 
 8 40 
 
 10 
 
 S 
 
 SO 
 
 
 EXERCISES. 
 
 
 
 7 times 8 '? 
 
 9 times 8 ? 
 
 3 times 8? 
 
 
 4 times 8 ? 
 
 9 times 8 ? 
 
 4 times 8 ? 
 
 1 times 8 ? 
 
 
 6 times 8 ? 
 
 5 times 7 ? 
 
 6 times 7 "? 
 
 8 times 7 1 
 
 
 9 times 7 ? 
 
 4 times 7 I 
 
 4 times 8 ? 
 
 5 times 8 ? 
 
 
 9 times 8 ? 
 
 2 times 8 ? 
 
 6 times 8 ? 
 
 9 times 8 ? 
 
 
 5 times 7? 
 
 b times 8 ? 
 
 8 times 7 ? 
 
 3 times 8 ? 
 
 
 2 times 7? 
 
 Lesson Thirtieth.— -Increasing by Nines. 
 
 1 7 
 
 9 
 
 8 
 
 ll 
 7 
 
 6 
 
 5 
 
 4 
 
 1 i 
 
 3 
 
 2 
 
MULTIPLICATION, 
 
 45 
 
 1 . Nine girls have each one cent ; how many have they 
 all? 
 
 2. If one urn costs nine dollars, how much will two 
 urns cost ? 
 
 8. One bottle of medicine costs three dollars ; how much 
 will nine bottles cost? 
 
 4. Four buckets contain each nine quarts of milk ; how 
 much do all the buckets contain ? 
 
 5. Nine long words each of five syllables, contain how 
 many syllables ? 
 
 6. How much will six papers of needles cost at nine 
 cents a paper ? 
 
 7. Seven yards of trimming at nine cents per yard will 
 cost how much ? 
 
 8. What must I pay for nine cords of wood at eight 
 dollars a cord ? 
 
 9. Nine girls each learn nine hymns ; how many did 
 all learn ? 
 
 10. Required the weight of ten lumps of butter, each 
 weighing nine pounds. 
 
 
 THE TABLE, 
 
 
 1 4- 
 
 9= 9 
 
 6 + 9 
 
 = 54 
 
 2 
 
 9 18 
 
 7 9 
 
 63 
 
 3 
 
 9 27 
 
 8 9 
 
 72 
 
 4 
 
 .9 3(5 
 
 9 9 
 
 81 
 
 5 
 
 9 45 
 
 BXER 
 
 10 9 
 
 CI8ES. 
 
 90 
 
 7 times 9 ? 
 
 5 times 8 ? 
 
 3 times 9 1 
 
 8 times 8 ? 
 
 3 times 8 ? 
 
 8 times 9 ? 
 
 5 times 7? 
 
 4 times 9 ? 
 
 6 times 7 ? 
 
 9 times 7 ? 
 
 6 times 8 ? 
 
 9 times 9 ? 
 
 4 times 9 ? 
 
 2 times 9 ? 
 
 4 times 9 1 
 
 7 times 7 ? 
 
 5 times 9 ? 
 
 6 times 9 ? 
 
 9 times 7 ? 
 
 8 times 7 ? 
 
 3 times 7 ? 
 
 4 times 8 ? 
 
 6 times 7 ? 
 
 9 times 8 1 
 
 7 times 9 ? 
 
 3 times 8 1 
 
 5 times 9 ? 
 
 8 times 7 ? 
 
46 ARITHMETIC. 
 
 Lesson Thirty-first.— Miscellaneous Questions. 
 
 1. Three little girls have each four fingers on each 
 hand ; how many lingers have they all ? 
 
 •2. How many legs have seven horses ? 
 
 i 7 !. I have three rakes with eight teeth each, how many 
 teeth have they all V 
 
 4. How many hands and feet have six little girls V 
 
 5. There are four windows in my room, each with two 
 sash and six panes of glass in each sash. How in my 
 panes of glass are there in the room ? 
 
 6. Eight flies have how many feci ' J . 
 
 7. How many horns and feet ought eight cows io 
 have? 
 
 8. A railroad car has four wheels on each side ; how 
 many wheels have eight cars ? 
 
 9. In my house there are two pictures on each wall of 
 each room ; how many pictures are there in four rooms? 
 
 10. Two meeting-houses are lighted by four chan Lei' 
 icrs, each supporting three lamps ; how many lamps in 
 both? 
 
 11. I have five jackets each with seven buttons on a 
 side; how many buttons on all the jackets V 
 
 12. Mary bought three boxes each with four cards con> 
 taining six hooks and eyes ? how many in all ? 
 
 EXERCISES. 
 
 4x0+2?* 2x2 x 3f 6x5—2 
 
 8x7+3? 2x2x4' 5x4—3 
 
 9x5+1? 2x2x5 7x0—4 
 
 8x4+5? 3x2x4 Sx?— 2 
 
 6x2+8? 2x3x4 6x8—3 
 
 8x2+3? 4x2x3 9x5—6 
 
 4x6+5? 6x2x4 8x9—3 
 
 8x3+4? 0x2x3 9x9—2 
 
 * Either 4 timea 9 mhI 2 to carry, or 4 times 9 ami 2, or 4 times ;» and 
 two ninths of nine, 
 t Bead two times 2 times 8, (the last times pronounced tims.) 
 
DIVISION. 
 
 47 
 
 DIVISION. 
 
 Lesson Thirty-second.— Increasing by Twos. 
 
 1 
 
 5 
 
 3 
 
 II 4 
 
 it 
 
 « i 
 
 I " 
 
 8 
 
 9 | 
 
 1. How often can two apples be taken from two ap- 
 ples ? 
 
 2. How often will two go into two ? 
 
 3. Four apples are to be divided between two boys, 
 how many will each one get ? 
 
 4. Six cents .will buy how many pencils at two cents 
 apiece ? 
 
 5. How many cakes at two cents apiece can I buy for 
 eight cents? 
 
 6. Ten dollars to be divided between two persons; 
 how much will each receive ? 
 
 7. Twelve girls sit on two benches ; how many are 
 there on each ? 
 
 8. Divide fourteen books between two boys ; how 
 many will each receive ? 
 
 9. Sixteen finger rings are to be divided between two 
 girls ; how many will each receive ? 
 
 10. Eighteen lights of glass in two sashes ; how many 
 in each ? 
 
 11. Twenty dollars in two equal notes ; how many in 
 each note ? 
 
48 
 
 ARITHMETIC. 
 
 2 
 4 
 
 6 
 
 8 
 10 
 
 THE TABLE. 
 1 12 
 
 14 
 
 8 16 
 
 4 18 
 
 5 20 
 
 EXERCISES. 
 
 2 = 6 
 2 7 
 2 8 
 2 9 
 2 10 
 
 2 into 6 ? 2 into 2 ? 3 times 9 ? 2 into 6 ? 
 
 2 into 4 ? 2 into 10 ? 2 into 12 ? 2 into 8 ? 
 
 5 times 4 1 5 times 7? 5 times 8 ? 2 into 14? 
 
 9 times 5 ? 2 into 18 ? 3 times 9 1 2 into 16 ? 
 
 7 times 9 ? 5 times 8 ? 9 times 7 ? 2 into 14 1 
 
 5 times 6 ? 2 into 14 ? 9 times 8 ? 5 into 15 ? 
 
 Lesson Thirty-third. — Increasing by Threes. 
 
 3 
 
 6 
 
 * 
 
 2 
 
 5 
 
 8 1 
 
 1 
 
 4 
 
 * 1 
 i 
 
 1. Ilow often will three go into three ? 
 
 2. If you divide six hair-pins between three girls, how 
 many will each one receive ? 
 
 3. A father wants to distribute nine books among his 
 three children ; how many will each child receive? 
 
 4. Twelve cherries will make\how many bunches of 
 three each ? 
 
 5. Three squirrels eat fifteen nuts ; how many does 
 each one eat ? 
 
DIVISION. 
 
 49 
 
 6. Eighteen boys are to be seated on three benches; 
 how many should sit on each bench ? 
 
 7. Twenty-one days make three weeks; how many 
 days in one week ? 
 
 8. Twenty-four wheels are to three cars; how many 
 w heels is that to ea'ch ? 
 
 9. Three men shoot each the same number of birds ; 
 together they have twenty-seven. How many did each 
 man shoot ? 
 
 10. Thirty dimes are in three piles ; how many are 
 there in eneh ? 
 
 THE TABLE. 
 
 
 3 : 
 
 3 
 
 = 1 
 
 
 18 ~ 
 
 3 = 6 
 
 
 
 6 
 
 3 
 
 2 
 
 
 21 
 
 3 7 
 
 
 
 9 
 
 o 
 •> 
 
 a 
 
 
 24 
 
 3 8 
 
 
 
 12 
 
 3 
 
 4 
 
 
 27 
 
 3 9 
 
 
 
 i:> 
 
 3 
 
 5 
 
 KXER( 
 
 218 
 
 30 
 
 ES. 
 
 3 10 
 
 
 • > 
 
 3 
 3 
 2 
 
 iuto 9? 
 
 into (5? 
 into 9? 
 into 8 : 
 into 4? 
 
 3 
 3 
 3 
 
 •> 
 
 into 15? 
 into 3 \ 
 into 18? 
 into 301 
 into 18? 
 
 3 
 3 
 3 
 2 
 2 
 
 into 27 \ 
 into 24 ? 
 into 30? 
 intu 18? 
 into 12 ? 
 
 4 times 
 9 times 
 3 times 
 
 5 times 
 5 times 
 
 5? 
 
 11 
 9? 
 
 9? 
 
 8 ? 
 
 Lesson Thirty-fourth. — Increasing by Fours. 
 
 7 
 
 4 
 
 1 i 
 
 1 
 
 1 s 
 
 5 
 
 
 
 
 6 
 
 3 
 
60 ARITHMETIC. 
 
 1. Four boys divide four balls between themselves ; 
 how many is that to each t 
 
 2. Eight wheels are sufficient for how many carria- 
 ges ? 
 
 8 Divide twelve marbles among four boys ; required 
 each one's share ? 
 
 4. Sixteen legs are sufficient to make how many tables, 
 each with four legs ? 
 
 5. Divide twenty dollars equally between four poor 
 families ; what amount will each receive ? 
 
 6. Four wagons haul twenty-four bales of cotton ; 
 how many bales to each wagon? 
 
 7. Twenty-eight soldiers are marching in ranks of 
 four each ; how many soldiers in each rank ? 
 
 8. Thirty-two pounds of sugar will till how many f<>ur 
 pound bags? 
 
 9. Four houses have thirty-six rooms ; how many 
 rooms in eacja house? 
 
 10. Forty quarters are equal to how many dollars? 
 
 THE TABLE. 
 
 4 + 4=1' I 24 ~ 4 = 6 
 
 8 4 2 28 4 7 
 
 12 4 3 32 4 8 
 
 16 4 4 36 4 9 
 
 20 4 5 40 4 10 
 
 EXERCISES. 
 
 4 into 4? 7 into 28? 4 into 12? 2 into 16? 
 
 3 into 3? 3 into 24? 4 into 16? 4 into 12? 
 
 4 into 8? 3 into 15? 4 into 24? 2 into 18? 
 4 into 20? 3 into 18? 4 into 30? 4 into 
 
 3 into 27? 3 into 15? 4 into 40? 4 into 36? 
 
 4 into 32? 2 into 20? 6 into 18? 5 into 50? 
 4 into 28? 5 into 30? 9 into 81,? 7 into 56? 
 
DIVISION. 
 
 51 
 
 Lesson Thirty-fifth. — Increasing by Fives. 
 
 ; i > I 
 
 lj . L 
 
 i 
 
 ji — — — 
 
 It 1_ ; . 
 
 1. Five boys have five canes ; how inany have each ? 
 
 2. Five cows have ten horns; how many have each ? 
 
 3. Divide fifteen pencils among five scholars ; how 
 many will each get ? 
 
 4. Twenty dollars will buy how many hats at five 
 dollars each ? 
 
 5. Twenty-five cents are exchanged for five equal 
 change bills ; required the value of each ? 
 
 6. Distribute thirty cords of wood equally between 
 6ve poor families; how many cords to each ? 
 
 7. At five cents a skein, how many skeins of silk will 
 :hirty-five cents buy ? 
 
 8. Forty chairs are to be carried in one trip by five 
 nen ; how many chairs must each one carry ? 
 
 9. Five drays are to haul forty-five barrels in one trip; 
 how many to each dray ? 
 
 10. Exchange a fifty dollar note for five equal smaller 
 notes; required the value of each? 
 
 5 
 
 -s- 5 ± 
 
 = 1 
 
 LAU.L..&.. 
 
 30 - 
 
 r- 5 = 
 
 G 
 
 10 
 
 5 
 
 2 
 
 35 
 
 5 
 
 7 
 
 15 
 
 5 
 
 3 
 
 40 
 
 5 
 
 8 
 
 20 
 
 5 
 
 4 
 
 45 
 
 5 
 
 9 
 
 25 
 
 5 
 
 5 
 
 50 
 
 5 
 
 10 
 
52 
 
 ARITHMETIC 
 
 5 into 15? 
 
 4 into 24? 
 
 5 into 35 ? 
 5 into 45? 
 4 into 36? 
 
 
 
 EXERCISES. 
 
 
 
 
 
 3 
 
 into 
 
 27? 
 
 5 into 
 
 30? 
 
 ."> 
 
 into 
 
 :>? 
 
 5 
 
 into* 
 
 25? 
 
 5 into 
 
 10? 
 
 5 
 
 into 
 
 10? 
 
 5 
 
 into 
 
 15? 
 
 4 into 
 
 12? 
 
 3 
 
 into 
 
 24? 
 
 5 
 
 into 
 
 20? 
 
 3 into 
 
 18? 
 
 5 
 
 into 
 
 25 % 
 
 2 
 
 into 
 
 10? 
 
 3 into 
 
 24? 
 
 3 
 
 into 
 
 30? 
 
 Lesson Thirty-sixth. — Increasing by Sixes. 
 
 3 
 
 6 
 
 9 
 
 ! » 
 
 5 
 
 8 • 
 
 1 
 
 4 
 
 7 
 
 1. How often will six go into six ? 
 
 2. Six boys have twelve thumbs; how many have 
 each ? 
 
 3. Eighteen garments are to be divided between six 
 men ; how many to each ? 
 
 4. Six silver forks have twenty-tour tines ; how many 
 has each fork? 
 
 5. Thirty dollars pay (or six pairs of boots ; required 
 the price of one pair ? 
 
 6. Thirty-six chairs are in six rows ; how many are 
 in each row ? 
 
 7. The joint ages of six girls of equal age was forty- 
 two years ; what was the age of each ? 
 
 8. Forty-eight lots of land are to be divided equally be- 
 tween six heirs ; how many does each one receive? 
 
 9. Fifty-four legs are sufficient to furnish how many 
 rlies ? 
 
 10. Sixty acres of land are to be laid off in six lots ; how 
 many acres will each contain? 
 

 
 
 DIVISION. 
 
 
 
 53 
 
 
 
 
 THE TABLE. 
 
 
 
 
 
 6 -r- 
 
 6 = 1 
 
 
 36 
 
 --:- 6 
 
 
 = 6 
 
 
 12 
 
 6 2 
 
 
 42 
 
 6 
 
 
 7 
 
 
 18 
 
 6 3 
 
 
 48 
 
 6 
 
 
 8 
 
 
 24 
 
 6 4 
 
 
 54 
 
 6 
 
 
 9 
 
 
 30 
 
 6 5 
 
 
 60 
 
 6 
 
 
 10 
 
 
 
 
 EXERCISES. 
 
 
 
 
 6 
 
 into 24? 
 
 2 into 
 
 16? 
 
 6 into 
 
 12? 
 
 3 
 
 into 21 ? 
 
 ♦'> 
 
 into 30? 
 
 6 into 
 
 18? 
 
 6 into 
 
 6? 
 
 6 
 
 into 24? 
 
 5 
 
 into 35? 
 
 3 into 
 
 18? 
 
 6 into 
 
 42? 
 
 5 
 
 into 45? 
 
 •4 
 
 into 24? 
 
 3 into 
 
 9? 
 
 6 into 
 
 48? 
 
 3 
 
 into 27? 
 
 4 
 
 into 16? 
 
 5 into 
 
 50? 
 
 6 into 
 
 54? 
 
 <; 
 
 into 48? 
 
 A 
 
 into 12? 
 
 3 into 
 
 21? 
 
 5 into 
 
 45? 
 
 
 
 into 42? 
 
 Lesson Thirty-seventh.— Increasing by Sevens. 
 
 jj' 7 
 
 4 
 
 1 
 
 8 
 
 5 
 
 2 
 
 9 
 
 6 
 
 3 
 
 1. How many sevens are contained in seven ? 
 
 2. A dress may be made of seven yards of homespun ; 
 how many dresses will fourteen yards make? 
 
 3. Twenty-one days make how many weeks ? 
 
 4. Seven men divide twenty-eight mules equally among 
 themselves ; how many does each man receive? 
 
 o. Thirty-five acres are to be plowed by seven men ; 
 what should be the task of each, supposing each to plow 
 the same number of acres ? 
 
54 
 
 ARITHMETIC. 
 
 8. If seven pupils sit on one bench, how many benches 
 will forty-two pupils need? 
 
 7 Forty-nine dinners should be eaten in ihow many 
 weeks ? 
 
 8. In seven hymns of equal length are fifty-six verses ; 
 how many verses have each ? 
 
 ( .) In digging over seven hills, I found sixty-three 
 large yams ; how many was that to the hill ? 
 
 10. Seven boys shoot seventy squirrels ; how many was 
 that apiece ? 
 
 7 
 
 U 
 21 
 28 
 35 
 
 into 21 ? 
 into 35? 
 into 49? 
 into 63? 
 into 21 ? 
 G into 48? 
 
 THE TABLE. 
 
 42 
 49 
 50 
 63 
 70 
 
 EXERCISE8. 
 
 into 42? 7 into 63? 
 7 into 7? 
 7 into 21? 
 7 into 35? 
 7 into 49 ? 
 3 into 27 ? 
 
 = 1 
 2 
 3 
 4 
 5 
 
 7 
 
 7 into 56? 
 
 6 into 30 ? 
 
 7 into 14? 
 7 into 28? 
 4 into 36? 
 
 = 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 into 24? 
 into 28? 
 into 42? 
 into 36? 
 into 70 ? 
 into 45? 
 
 lesson Thirty-eighth.— Increasing by Eights. 
 
 9 
 
 8 
 
 1 
 7 
 
 O 
 
 | 
 
 5 
 
 4 
 
 3 
 
 2 
 
 1 
 
 ■ ■■ ■:-:■ ■::■■:;:■< 
 
DIVISION. 
 
 55 
 
 1. Fow many times does eight contain eight ? 
 
 2. There are sixteen blades in eight knives ; how 
 many has each ? 
 
 3. Twenty-four tierces of rice will make how many 
 loads, eight tierces being a load? 
 
 4. Suppose a rake has eight teeth; how many rakes 
 would thirty-two teeth furnish ? 
 
 5. A flute has eight keys; how many such flutes 
 would forty keys furnish ? 
 
 G. Sixty four books arc to be placed upon shelves that 
 hold eight books each ; how many shelves will be filled ? 
 
 7 If there are eight horses to a team ; how many teams 
 would f]ft} - -six horses make? 
 
 8. On a draughts board there are sixtj'-four squares, 
 and eight squares in a row ; how many rows are there V 
 
 U. Seventy-two wheels will suffice for how many cars; 
 eight wheels being to one car? 
 
 10. Eighty dollars aro in eight gold pieces ; required 
 the value of each ? 
 
 THE TABLE. 
 
 8 -*- 8 
 
 16 8 
 24 8 
 32 8 
 40 8 
 
 48 
 56 
 64 
 
 72 
 80 
 
 6 
 
 7 
 8 
 9 
 10 
 
 EXERCISES 
 
 8 into 32? 
 
 7 into 631 
 
 8 into 64? 
 
 7 into 35 ? 
 
 8 into 56? 
 
 3 into 27? 
 
 4 into 28? 
 
 into 36? 
 into 24? 
 into 48? 
 into 27? 
 into 32? 
 into 45? 
 into 64? 
 
 into 24? 
 ato 40? 
 nto 161 
 
 nto 64? 
 
 nto 49? 
 
 nto 30? 
 
 into 49? 
 
 into 8 ? 
 into 72? 
 into 80? 
 into 48? 
 into 48? 
 into 72? 
 into -60? 
 
56 
 
 ARITHMETIC. 
 
 Lesson Thirty-Ninth—Increasing by Nines. 
 
 9 
 
 I 3 
 
 8 7 
 
 5 4 
 
 1 
 
 1. How many times is nine contained in nine ? 
 
 2. Place eighteen chairs, nine in a row ; how many 
 rows will be made ? 
 
 3. Nine families have twenty-seven children ; how 
 many is that for each ? 
 
 4. Thirty -six spools of cotton are to be divided be- 
 tween nine women ; how many are given to each ? 
 
 5. Forty-five kegs of powder are to be distributed to 
 nine regiments ; how many kegs is that to each ? 
 
 6. Fifty-four bales of cotton are hauled to market by 
 nine wagons ; how many bales to the wagon ? 
 
 7. If board is nine dollars a week ; how many weeks 
 will sixty-three dollars pay for ? 
 
 8. Nine merchants buy seventy-two hogsheads of su- 
 gar ; how many apiece ? 
 
 y. Eighty-one trees stand in 
 trees are there in each row ? 
 10. How many cents in one c 
 tain ninety* cents ? 
 
 THE TABLE. 
 
 9 - 
 
 ~ 9 = 
 
 : 1 
 
 18 
 
 9 
 
 o 
 
 27 
 
 9 
 
 3 
 
 36 
 
 9 
 
 4 
 
 45 
 
 9 
 
 5 
 
 ine 
 
 rows ; 
 
 how many 
 
 le, 
 
 if nine 
 
 dimes con- 
 
 54 
 
 — 9 
 
 = 6 
 
 63 
 
 9 
 
 7 
 
 72 
 
 9 
 
 8 
 
 81 
 
 9 
 
 9 
 
 90 
 
 9 
 
 10 
 
DIVISION. 57 
 
 EXERCISES. 
 
 9 into 18? 3 into 27? 6 into 36 ? 9 into 15? 
 
 8 into 64? 9 into 63? 8 into 321 9 into 811 
 
 9 into 90? 9 into 9? 7 into 21? 9 into 72? 
 7 into 63? 9 into 54? 7 into 35? 8 into 56? 
 9 into 27 ? 8 into 48 ? 7 into 49 ? 8 into 32 ? 
 9 into 81? 9 into 63? 6 in*© 24? 9 into 45? 
 
 DIVISION, 
 
 Lesson Fortieth. — Miscellaneous Questions. 
 
 1. A father bought sixty-three marbles to divide among 
 his seven boys ; how many should each one receive ? 
 
 2. Nine girls agree to knit seventy-two pairs of gloves 
 for poor children ; how many must each one knit ? 
 
 3. Henry brought home eighteen chestnuts ; how many 
 burrs must he have cracked to get them, if he found two 
 chestnuts in each burr ? 
 
 4. A cruel boy had forty-twc fly legs; how many flies 
 must he have killed to get them ? 
 
 5. One dray can haul seven barrels of Hour ; how many 
 such drays will be required to haul fifty-six barrels at one 
 trip ? 
 
 6. I see sixty-four fingers ; how many girls must they 
 belong to ? How many hands ? 
 
 7. My wagons require six mules to the team ; thirty 
 mules will be sufficient for how man}^ wagons ? 
 
 8. At nine lights of glass to a sash, how many sash 
 will seventy-two lights fill ? 
 
 9. Forty-five toes belong to how many feet? 
 
 10. Eighty-one soldiers will make how many ranks of 
 nine each ? 
 
 11. If there are seven yards in a dress, how many 
 dresses will a piece of cloth measuring forty-two yards 
 make V 
 
58 ARITHMETIC. 
 
 12. Sixty four fruit trees are to be planted in an orchard; 
 how many rows will they make if there are eight trees in 
 a row ? 
 
 13. [Tow often will four so into 12? 86? 28? 24? 8? 
 IG? 
 
 14. 5 into 25? 40? 851 20? 15? 35? 45? 
 
 15. 6 into 42? 30? 18? 54? 3(3? 48? 24? 12? 
 
 16. 3 into 15 ? 6? 21 ? 27 ? 9 ? 18 ? 12 ? 24 ? 
 
 42— 2-:-4 ? * 13 +3—2 x 2 ? f 
 
 57— 3-f-6 ? 9 x 4£-3 x 2 ? 
 
 454-4-J-7 1 8x5-2x2?. 
 
 32+4-4-9? 2x9—3x3? 
 
 54+2—8? 5x4—2x5? 
 
 75_3_^-9? 6x4—4x2? 
 
 8?_6—9? 6x6-3x3? 
 
 48+6 + 6? 8x6—2x2? 
 
 70—6—8? 23+5—2x2? 
 
 * Maybe read two from forty-two leases how many times foar. 
 t May be read, divido two tirnos two into thirteen and three. 
 
MISCELLANEOUS TABLES. 59 
 
 MISCELLANEOUS TABLES. 
 
 TABLE OF UNITED STATES CURRENCY. 
 
 10 Mills mako 1 Cent, marked c. 
 
 1<> Cents " 1 Dime, " d. 
 
 10 Dimes " 1 Dollar, " $. 
 
 10 Dollars " 1 Eagle, " E. 
 
 TABLE OF ENGLISH MONEY. 
 
 4 Farthings ir.ake 1 Pennv, marked d. 
 
 12 Pence " 1 Shilling, " s. 
 
 2" Shillings " 1 Pound, " £. 
 
 21 Shillings sterling " 1 ( ; uinea, " G. 
 
 28 Shillings N. E. " 1 Guinea, *■ G. 
 
 Note.— One pound Sterling is equal to $4.44 4-9 exchange 
 ralue. 
 
 TABLE OF TROY WEIGHT. 
 
 24 Grnin8 make 1 Pennyweight, marked pwt, 
 
 20 Pennyweights " 1 Ounce, * 4 oz. 
 
 12 Ounces " 1 Pound, " lb. 
 
 TABLE OF APOTHECARIES' WEIGHT. 
 
 20 Grains make ' 1 Scruple. 
 
 3 Scruples *.* 1 Dram. 
 
 8 Drains *' I Ounce. 
 
 12 Ounces " 1 Pound. 
 
 Apothecaries mix their medicines by this weight; but buy 
 and sell by Avoirdupois. The pound and ounce of this weight 
 are the same as in Troy Weight. 
 
 TABLE OF AVOIRDUPOIS WEIGHT. 
 
 16 Drams 
 
 make 1 Ounce, marked oz. 
 
 16 Ounces 
 
 1 Pound, " lb. 
 
 28 Pounds 
 
 " 1 Quarter, « qr. 
 
 4 Quarters 
 
 " 1 Hundred Weight, * cwt. 
 
 20 Hundred Weight 
 
 " 1 Ton, " ton. 
 
60 
 
 ARITHMETIC. 
 
 By this weight are weighed almost every kind of goods, aud 
 all metals except gold and silver. By a late law of .Massachu- 
 setts, the cwt. contains 100 lbs. instead of 112 lbs. 
 
 A ton is reckoned at the custom-houses of the United States 
 at '2240 lbs. 
 
 TABLE OF CLOTH MEASURE. 
 
 2% Inches 
 
 Nails 
 
 Quarters 
 Quarters 
 Quarters 
 Quarters 1 
 Quarters 
 
 make 
 
 1-;; inch 
 
 1 Nfcll, 
 
 1 Quarter of a vard, 
 
 1 Yard, 
 
 1 Ell Flemish, 
 
 1 Ell English, 
 
 1 Ell Scotch, 
 
 1 Ell French, 
 
 marked na. 
 
 " q J- 
 
 yd. 
 
 " E. F. 
 
 '• E. E. 
 
 " E. S. 
 
 " E. Fr. 
 
 TABLE OF LONG MEASURE. 
 
 3 Barley-corns (be.) make 1 Inch, 
 
 marked 
 
 12 Inche, 
 
 8 Feet 
 
 r>}. 2 \ ards, or lok. Feet 
 40 " Rods, or 220 Yds. 
 
 8 Furlongs 
 
 3 Miles 
 tio Geographic, or | 
 C'J 1 .; Statute Miles f 
 360 Degt'ees. 
 
 1 Foot, 
 
 1 Vard, 
 
 1 Rod or Role, 
 
 1 Furlong, 
 
 1 Mile, 
 
 1 League, 
 
 rd. 
 
 in. 
 ft. 
 
 yd. 
 
 or po. 
 
 fur. 
 
 mi. 
 
 le. 
 
 deg. or 
 
 1 Degree, 
 
 the circumference of the earth. 
 TABLE OF LAND OR SQUARE MEASURE. 
 
 144 Square In. (sq. in.) make 1 Square Foot, marked 
 
 9 Square feet 
 BOX Sq. Yds., or 272^ ft., 
 
 Sq. Rods or Poles < 
 
 Roods 
 
 Acres 
 
 Square Poles 
 
 Square Chains 
 
 40 
 
 4 
 
 040 
 
 16 
 
 10 
 
 1 Square 'Yard, 
 
 1 Sq. Rod or Pole, 
 
 1 Rood, 
 
 1 Acre, 
 
 1 Sauare Mile, 
 
 1 Square Chain, 
 
 1 Acre, 
 
 sq 
 
 sq. ft. 
 >q. yd. 
 rod. 
 
 R. 
 
 A. 
 sq. M. 
 
 ch. 
 
 A. 
 
 TABLE OF MEASURING DISTANCES. 
 
 7 92-100 Inches 
 25 Links 
 100 Links 
 10 Chains 
 S Furlongs 
 
 make 
 
 1 Link. 
 1 Pole. 
 1 Chain. 
 1 Furlong. 
 1 Mile. 
 
MISCELLANEOUS TABLES. ftl 
 
 TABLE OF SOLID OR CUBIC MEASURE 
 
 1728 Solid In. (sol. in.) makeJ Solid Foot, 
 27 Solid Feet *' 1 Solid Yard, 
 
 £ 
 
 >URE. 
 
 marked so 
 " iOl. 
 
 . ft. 
 
 yd. 
 
 
 a 
 
 T. 
 
 
 C 
 
 . ft. 
 
 cd. 
 
 4 
 
 feet high, 
 
 is a 
 
 make 1 Pint, 
 
 marked pt. 
 
 " 1 Quart, 
 
 " qt. 
 
 11 1 Gallon, 
 
 " sral. 
 
 " 1 Barrel, 
 
 11 bbl. 
 
 " 1 Tierce, 
 
 " tee. 
 
 " 1 Hogshead, 
 
 " hhd. 
 
 " 1 Puncheon, 
 
 " pun. 
 
 " 1 Pipe, 
 
 " pi. 
 
 s." 1 Tun, 
 
 T. 
 
 40 ft. round tim., or \ <( 1 Ton 
 50 ft. hewn timber \ ' 
 
 16 Solid feet " 1 Cord foot, 
 
 aaass"} - * <*#«.*>* 
 
 A pile of wood S feet long, 4 feet wide, and 
 cord. 
 
 TABLE OF WINE MEASURE. 
 
 4 Gills {gi) 
 
 2 Pints 
 
 4 Quarts 
 
 313^ Gallons 
 
 42 Gallons 
 
 63 Gallons, or 2 barrels 
 
 2 Tierces 
 
 2 Hogsheads, (126 gals.) 
 
 2 Pipes, 4 hhds., or 252 gals." 
 
 N^ote. — The "Wine Gallon contains 281 cubic inches. Water- 
 wine, and spirits, are measured and sold by this measure. 
 
 A cubic foot of distilled water weighs 1,000 ounces Avoirdu- 
 pois. 
 
 The English Imperial Gallon contains 277 '4 cubic inches, and 
 weighs 10 lbs. Avoirdupois, or 12 lbs. 1 oz. 10 dwt. 16 gr. Troy. 
 There is no legal measure in the United States for tierce, hogs- 
 head, puncheon, pipe, or butt. 
 
 TABLE OF DRY MEASURE. 
 
 2 Pints make 1 Quart, marked qt. 
 
 4 Quarts " 1 Gallon, " gal. 
 
 2 Gallons " 1 Peck, " pk. 
 
 4 Pecks " 1 Bushel, " bu. 
 
 36 Bushels " 1 Chaldron, " ch. 
 
 Note. — This measure is applied to all goods that are not 
 liquid and are sold by measure, as corn, fruit, salt, coals, etc. 
 A Winchester Bushel is 18% inches in diameter, and 8 inches 
 deep. The standard Gallon, Dry Measure, contains 268 4-5 
 cubic inches. 
 
62 
 
 ARTTHMRTIC. 
 
 TABLE OF ALE AND BEER MEASURE. 
 
 2 Pints make 1 Quart, • marked qt 
 
 4 Quarts " 1 Gallon, " gal 
 
 82 Gallons * " 1 Barrel, " bbl 
 
 54 Gallons u 1 Hogshead, '.' hhd 
 
 2 Hogsheads « 1 Butt, * butt 
 
 2 Butts " 1 Tun, " tun 
 
 Note. — By a law of Massachusetts, the barrel for cider and 
 
 beer shall contain 32 gallons, but in some other States it is of 
 
 different capacity. The Ale Gallon contains 282 cubic or solid 
 
 inches. 
 
 TABLE OF TIME. 
 
 60 Seconds (sec.) 
 
 make 1 Minute, 
 
 
 marked m. 
 
 60 Minutes 
 
 
 " 1 Hour, 
 
 
 hr. 
 
 24 Hours 
 
 
 " 1 l»ay, 
 
 
 d. 
 
 7 Days 
 
 
 " 1 Week, 
 
 
 " w. 
 
 4 Weeks 
 
 
 " 1 Month, 
 
 
 '' mo. 
 
 12 Calendar months 
 
 " 1 Year, 
 
 
 yr. 
 
 52 Weeks 
 
 
 " 1 Year, 
 
 
 yr. 
 
 S65 Days 
 
 
 " 1 Common Year, " jr. 
 
 366 Days 
 
 
 " 1 Leap Year, 
 
 yr. 
 
 100 Years 
 
 
 " 1 Century 
 
 , 
 
 C. 
 
 The following table exhibits the divisions 
 
 of the year, the 
 
 names of the months, and the number of days 
 
 in each : 
 
 Winter. J 
 
 1st month, 
 
 January, has 
 
 S3 
 
 days. 
 
 2d 
 
 February, f 
 
 2b, 
 
 in leap year 29. 
 
 i 
 
 3d 
 
 March, U 
 
 31 days. 
 
 Spring. J 
 
 4th " 
 
 April, " 
 
 30 
 
 " 
 
 I 
 
 5th 
 
 May, 
 
 81 
 
 " 
 
 
 6th " 
 
 June, 
 
 30 
 
 " 
 
 Summer. 4 
 
 7 th 
 
 July, 
 
 31 
 
 44 
 
 I 
 
 8 th 
 
 August, " 
 
 3i 
 
 44 
 
 
 mh " 
 
 September, " 
 
 30 
 
 44 
 
 Autumn. •< 
 
 10th 
 
 October, " 
 
 81 
 
 *' 
 
 I 
 
 1 1 th 
 
 November, " 
 
 30 
 
 " 
 
 Winter. 
 
 1 2th 
 
 December, " 
 
 31 
 
 " 
 
 The following lines will help to remember the number of 
 days in each month : 
 
 " Thirty days hath September, 
 April, June, and November; 
 AM the rest have thirty -one, 
 Except February alone, 
 Which hath but twenty-eight, in fine, 
 Till leap year gives it twenty-nine." 
 
MISCELLANEOUS TABLES. 
 
 6$ 
 
 TABLE OF CIRCULAR MOTION. 
 
 60 Seconds, or 60 ' make 1 Prime minute, marked 
 
 60 Minutes " 1 Degree, " 
 
 30 Degiees " 1 Sign, 
 
 12 Signs, or 860 Degrees, the whole great circle of the zodiac. 
 
 MISCELLANEOUS TABLE. 
 
 A gallon of train oil 
 
 weighs 
 
 7}4 pounds. 
 
 A stone o'' butcher's meat 
 
 " 
 
 8 
 
 a 
 
 A gallon of molasses 
 
 u 
 
 11 
 
 iri 
 
 A stone of iron 
 
 u 
 
 14 
 
 M 
 
 A tod 
 
 ** 
 
 28 
 
 tt 
 
 A firkin of butter 
 
 ** 
 
 56 
 
 tt 
 
 A firkin of soap 
 
 it 
 
 94 
 
 tt 
 
 A quintal of fish 
 
 " 
 
 100 
 
 1 1 
 
 A weigh 
 
 " 
 
 182 
 
 a 
 
 A sack 
 
 " 
 
 364 
 
 n 
 
 A nuncheon of foreign prunes 
 
 it 
 
 1120 
 
 44 
 
 A last 
 
 a 
 
 4368 
 
 " 
 
 A fother of lead 
 
 u 
 
 19# cwt. 
 
 A bbl. of flour 
 
 *' 
 
 196 
 
 pounds. 
 
 A " anchovies 
 
 a 
 
 30 
 
 " 
 
 A " raisins 
 
 ** 
 
 112 
 
 a 
 
 A " pork or beef 
 
 44 
 
 200 
 
 44 
 
 A " soap 
 
 44 
 
 256 
 
 44 
 
 A " Bhad or salmon in Connee 
 
 } " 
 
 200 
 
 tt 
 
 ticut or New York 
 
 
 A " fish iu Massachusetts 
 
 '8 
 
 30 
 
 gallons. 
 
 A " cider and beer 
 
 is 
 
 82 
 
 a 
 
 A " herrings in England 
 
 is 
 
 82 
 
 44 
 
 A " salmon or eels do. 
 
 is 
 
 42 
 
 44 
 
 S bushels of salt, measured on 
 
 \ . 
 
 
 hogshead. 
 
 board the vessel, 
 
 S ls 
 
 1 
 
 7% do. measured ou shore, 
 
 is 
 
 1 
 
 u 
 
 5 hoops 
 
 make 
 
 1 
 
 cast. 
 
 40 casts 
 
 M 
 
 1 
 
 hundred. 
 
 10 hundred 
 
 U 
 
 1 
 
 thousand. 
 
 12 units, or things, 
 
 " 
 
 1 
 
 dozen. 
 
 1 2 dozen 
 
 tt 
 
 1 
 
 gross. 
 
 144 dozen 
 
 • « 
 
 1 
 
 great gross. 
 
 24 sheets of paper 
 
 « 
 
 1 
 
 quire. 
 
 20 quires 
 
 <• 
 
 1 
 
 ream. 
 
 55 pounds 
 
 « 
 
 1 
 
 bush. corn. 
 
 60 pounds 
 
 tt 
 
 1 
 
 bush, wheat 
 
64 ARITHMETIC. 
 
 BOOKS. 
 
 \ sheet folded in 'J leaves is called a FbHo. 
 
 A sheet folded in 4 leaves is called a Quarto, or Ato. 
 
 A sheet folded in 8 leaves tiled an Octavo, or 8ro. 
 
 \ sheet folded in 12 leaves is called a Duodecimo, or 12mo. 
 
 A sheet folded in IS leaves is called an 18mo. 
 
 A sheet folded in c li leaves is called a 24mo. 
 
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 YOUNG- C HI LDREN. 
 
 BY S. SOOT. 
 THIRD EDITION, REVISED, ENLARGED AND JWPRO^ Blip. 
 
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 many of the largest Sabbath Schools without, denominational 
 restrictions, in Georgia and Alabama. 
 
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 Single copies 30 cents. 
 
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AND 
 
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