UC-NRLF B 3 mt, DSS in \*\ il»t /•tticfitr KiftAtY 1 ^ k N i^yv ^^^ xxmu^ %xxt\xmttu, EMBRACING MENTAL AND WEITTEN EXEEOISES, FOU BEGINNERS BY BENJAMIN , GREENLEAF, A.M. -ooX»o PREFACE. 6D--p -•o*- 'HE object of this primary book is to teach ttie pupil how to think, and to enable him, by an almost im- perceptible gradation of thought, to advance from the simplest forms of reasoning to the more vigor- ous exercises of the mind. Hence, no arbitrary rules have been introduced, and only such hints and suggestions, with occasional formulae of reasoning, as were considered absolutely necessary for the profitable study of the lessons. In order that the reasoning of some of the principal processes might be the more apparent to the beginner, pictures of objects have been, to some extent, introduced. After these, counters are employed, as unit marks; and then follow lessons without any such aids, that the learner may early acquire the habit of depending upon mental resources alone for the solution of problems. The numerous Pictorial Illustrations of the present edition have been designed and engraved, by skilful ai • tists, especially for this work. In this edition, the exercises in Written Arithmetic have been extended, and other improvements introduced, with a view of fully adapting the work to the present demands of the best primary schools. 3 088 TO TEACHERS. -»o*- % t/Jr HE lessons assigned to the learner should never be longer than will admit of being thoroughly prepared for recitation. The better to secure the attention of each member of the class, and elicit earnestness of thought, the questions should be read to the whole class, and each pupil taught to be in readiness, in whatever order called upon, to give promptly the solution required. The solutions should be uniformly according to such forms as are deemed by the teacher the neatest and best. The greatest care should be observed to have them always expressed in language entirely accurate, and pronounced in a clear and distinct manner. Frequent reviews, especially of the tables, will alone give thoroughness. In general, with a lesson in advance, it will be advantageous to assign some portion pre\dously gone over, as a review. Every term, or process, connected with any of the lessons, which the beginner may be likely not readily to understand, the intelligent teacher will not need to be reminded, should be clearly explained to the pupil, before assignincr the lesson. 4 NEW Primary Arithmetic. LESSOR I. How many thumbs have you on each hand? How many hands have you? How many eyes? If you wish to know how many fingers you have, what must you do? I must count them. What, then, is counting? Counting is finding how many there are of things. In counting, what is a single thing called? One. What is a number ? A . Number is one, or more than one. 5 PRTMAKT LESSON II. Count the pears in each row^ from left to right, and tell the number. One. One, two. One, two, three. One, two, three, four. One, two, three, etc. 6 %^ %a/ C-/ ^^ ^^ 66666 6 One. Two. Three. Pour. Five. Six. Seven. Eight. Nine. Ten. d O o Eh o o u • o • o .a EH ^ Ph CQ o o +3 © o Eh Count the pears in each row, from the top downward. How many pears are there in the second row from the top? How many pears are there in the next to the lowest row? ARITHMETIC. LESSON III. &^i;s*i«^g^>~S5S^?^^^.ig^sJSSKsS^ Answer the in the picture How many How many How many How many How many How many How many How many How many Count from Count from Count from following questions by counting the balls of the Numeral Frame : — balls are one ball and one ball? balls are two balls and one ball? balls are three balls and one ball? balls are four balls and one ball? balls are five balls and one ball? l)alls are six balls and one ball ? balls are seven balls and one ball? balls are eight balls and one ball? balls are nine balls and one ball? one to five. From two to six. one to seven. From three to seven, seven to ten. From one to ten. 8 PRIMARY LESSON lY. Count ten books. Count ten chickens. What do one, two, three, etc., express? Numbers. How, then, can you express numbers? By words. AVhat is another method of expressing numbers? By certain marks called Figures. How many different figures are used in expressing numbers ? Ten. Make on the slate the figure 1 for one ; 2 for two , 3 for three : 4 for four : 5 for five. Make on the slate the fio-ure 6 for six : 7 for seven ; 8 for eight; 9 for nine. Make on the slate for no number. AVhat is the called? Cipher, Zero, or Naught. Write on the slate and read the following figures : — 2, 3, 6, 7, 0, 4. Write on the slate and read the following figures : — 8, 9, 1, 0, 5, 6. What is one of any kind called ? A Unit. How many ones or units are one ten? Ten. How can you express one ten by figures? By writ- inor the fio-ure 1 with on the ricrht : thus, 10. For what, then, does the fio;ure 1, with at the right, stand? One ten, or ten. Write on the slate and read, — 9, 8, 7, 10, 6, 3. ARITHilETIC LESSON V. 1. Here is a picture of some bees; count the number of bees about each hive. 2. How many bees are there about both hives? 3. If there are ten bees about each hive, and twenty about both, how many, then, are two tens? 4. How can you express twenty by figures? By writing the figure 2 with on the right: thus, 20. 5. How many roses are ten roses and one rose? 6. Make the figures 11 for eleven ; 12 for twelve ; 13 for thirteen: 11 for fourteen; 15 for fifteen. 7. How many are fourteen and one? fifteen and one? sixteen and one? seventeen and one? eighteen and one? nineteen and one? 8. Make the fiofures 16 for sixteen: 17 for seven- teen; 18 for eighteen; 19 for nineteen. 9. Write and read the following figures : — 11, IS, 17, 14, 1^, 18. xo PRIMARY LESSOIf VI. 1. 1 horse and 1 horse are how many horses? How many are 1 and 1 ? 2. 1 vessel and 2 vessels are how many vessels? How many are 1 and 2? 3. A cat caught 1 mouse in the cellar and 3 mice in the pantry. How many mice did she catch in all? 4. Jane put 1 cup on the table, and her sister put on 4 more. How many cups did they both put on the table? How many are 1 and 4? 5. John set out 1 tree, and James set out 5. many did they both set? How many are 1 and 5? How £-?*■ ARITHMETIC. 11 6. Here is a picture of some acorns. How many acorns are 1 acorn and 6 acorns? How many are 1 and 6? 7. Henry has 1 acorn and Edward has 7. How many acorns have they both? How many are 1 and 7? 8. Ellen and 8 other girls are at play. How many girls are at play? How many are 1 and 8? 9. 1 snow-bird and 9 yellow-birds are sitting on a branch. How many birds are there in all? How^ many are 1 and 9? 10. Recite the table : — 1 and 1 are 2. 1 afid 2 are 3. 1 and 3 are 4. * 1 and 4 are 5. 1 and 5 ai*e 6. 1 and 6 are 7. 1 and 7 are 8. 1 and 8 are 9. 1 and 9 are 10. 1 and 10 are 11. 12 PRIMARY LESSON YII. 1. George had 2 clusters of grapes, and his father gave him another. How many clusters had he then? How many are 2 and 1 ? 2. In one yard there are 2 pigs, and m another there are 2. How many pigs are in both yards? How many are 2 and 2? 3. 2 baskets and 3 baskets are how many? How many are 2 and 3 ? 4. A merchant sold 2 pitchers at one time, and 4 pitchers at another time. How many did he sell in all? How many arc 2 and 4 ? 5. 2 apples and 5 apples are how many? How many are 2 and 5? ARITHMETIC. 13 6. Edwin has 2 tops, and George has 6. have they both? How many are 2 and 6 ? How many 7. 2 flowers and 7 flowers are how many flowers? How many are 2 and 7? # ^ 8. How many are 2 parasols and 8 parasols? How many are 2 and 8 ? 9. How many are 2 soldiers and 9 soldiers? How many are 2 and 9 ? w J 10. Recite the table : — 2 and 1 are 3. 2 and 2 are 4. 2 and 3 are 5. 2 and 4 are 6. 2 and 5 are 7. 2 and 6 arc 8. 2 and 7 are 9. 2 and 8 arc 10. 2 and 9 are 11. 2 and 10 are 12. 14 PEIMARY LESSOIT YIII. 1. Arthur had 3 lambs, and his brother gave him 1 more. How many lambs had he then? How many are 3 and 1? 2. 3 sloops began to sail on the lake, and soon after 3 more. How many were then sailing? How many are 3 and 3? 3. 3 tumblers and 5 tumblers are how many tum- blers ? How many are 3 and 5? e 4. 3 bees and 7 bees are how many bees? How many are 3 and 7? J^i ^ ^^Z- 'j ■^4^ ^ 5. Becitc the table : — 3 3 3 3 3 and and and and and 1 2 3 4 5 are are 4. 5. are 6. are 7. are §. 3 and 6 are 9. 3 and 7 are 10. 3 and 8 are 11. 3 and 9 are 12. 3 and 10 are 13. ARITHMETIC. 15 LESSON IX. 1. 4 rabbits are in one place, and 2 in another, /nany in all ? , ,** How many are 4 and 2 ? ^ Ho^ 2. Frank has 4 pears, and Charles has 4 more. Hov many pears have both ? How many are 4 and 4 ? 3. 4 locks and 5 locks are how many locks ? How many are 4 and 5 ? 4. Henry has 4 flags, and Charles has 6. How many flags have both ? ^ How many are 4 and 6 ? 5. Recite thVtabl*: — 4 and 1 are 5. 4 and 2 are 6. 4 and 3 ara J. 4 am 4 are 8. 4 and 5 are 9. J4 and 6 are 10. r^J'^aiJ^ 7 are 11. 4 and '^Itre- 12. 4 and 9 are 13. 4 and 10 are 14. 16 PRIMARY LESSON X. 1. James has caught 5 trouts. If he should catch 1 more, how many trouts would he have caught ? How many are 5 and 1 ? 2. Five trouts and 2 trouts are how many trouts ? How many are 5 and 2? 3. How many peaches are 5 peaches and 4 peaches? How many are 5 and 4? 4. There are 5 peaches in one plate and 6 in another. How many are there in both? ^ How many ^ re,^ -and 6? 5. There are 5 peaches in one plate and 7 in another J3ow many are there in both? How many are 5 and 7? 6. Recite the table : — 5 and 1 are 6. 5 and 2 are 7. 5 and 3 are 8. 5 and 4 are 9. 5 and 5 are 10. 5 and 6 are 11. 5 and 7 are 12. 5 and 8 are 13. 5 and 9 are 14.' 5 and 10 are 15. ARITHMETIC. LESSON XI. 1. Six girl^ and 2 girls are how many girls? How many are 6 and 2 ? 2. John caught 6 fishes, and Daniel caught 5 fishes. How many fishes did both catch ? How many are 6 and 5 ? 3. In one place there are 6 birds and in another 10. How many are there in both places ? How many are 6 and 10? '£S^ 4. Recite the table 6 and 1 are 7. 6 and 6 are 12 6 and 2 are 8. 6 and 7 are 13 6 and 3 are 9. 6 and 8 are 14 6 and 4 are 10. 6 and 9 are 15 6 and 5 are 11. 6 and 10 are 16 WRITTEN EXERCISES. Write and read : — (5.) (6.) 0') (8.) (9.) (10.) 6 11 10 3 16 7 9 16 17 U 6 8 12 13 2 15 1 20 19 4 18 9 18 PRIMARY LESSON XII. 1. How many bees are 7 bees and 2 bees? How many are 7 '^ ^'^i 1^^^' ^v^ ^V ^^^ 2 ? 2. How many bees are 7 bees and llyyj ^^^ 4 bees? How many are 7 and 4? 8. Recite the table : — 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. 2. chairs LESSOl^ XIII. 1. Albert paid 8 dollars for a globe, and 3 dollars for taking lessons on it. How much did he pay in all? How many are 8 and 3 ? Paid 8 dollars for a table, and 9 dollars for some . How many dollars did both cost? How many are 8 and 9? Recite the table : — 8 and 1 are 9. 8 and 2 are 10. 8 and 3 are 11. 8 and 4 are 12. 8 iind 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. ARITHxMETIC. VJ LESSON XIY. 1. Rufus one day rode 9 miles, and the next day 7 miles. How many miles did he ride both days? IIow many are 9 and 7 V 2. Susan found on one rose-bush 9 roses, and on another 10 roses. How many did she find on both bushes ? How many are 9 and 10? Recite the table : — 9 and 1 are 10. 9 and 2 are 11. 9 and 3 are 12. 9 and 4 are 13. 9 and 5 are 14. 9 and 6 are 15. 9 and 7 are 16. 9 and 8 are 17. 9 and 9 are 18. 9 and 10 are 19. LESSON XV. 1. Alice saw 10 butterflies in the fore- noon, and 6 in the afternoon. How many butterflies did she see in all? 2. Edwin had 10 marbles, and bought 10 more. How many then had he? 3. Recite the table : — 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 arc 19. 10 and 10 are. 20. 20 PRIMARY LESSON XVI. 3 and 5? 7 and 4 ? 6 and 5 ? 9 and 1 ? Why 14? 1. How many are 2 and 5 ? 2. How many are 4 and 7 ? 3. How many are 5 and 6 ? 4. How many are 8 and 2 ? 5. How many are 10 and 4 ? Ans. Because fO and 4- make /4. 6. A car containing 7 persons took in 5 more. How many did the car then contain? Why? 7. How many peaches are 9 peaches and 8 peaches ? Why? 8. What is the finding of a number equal to two more numbers called? Addition. 9. What is the number which is equal to two or more numbers called? Their Sum. 10. What is the sum of 4 and 3? Of 7 and 5? 11. What is the sum of 5 and 4 ? Of 6 and 2 ? 12. Add 4 and 3. 5 and 4. 7 and 6. WRITTEN EXERCISES, Write and add : — - (13.) (14.) (15.) (16.) (17.) (18.) 6 7 4 9 6 U 2 1 3 1 3 3 um, 7 10 17 (19.) (20.) (21.) (22.) (23.) (24.) 6 9 7 8 6 13 1 5 3 6 4 ARITHMETIC. H LESSON XYII. 4 and 5? 4 and 7? 5 and 1? 5 and 2? 6 and 2? 7 and 0? 1. 2 pigs are eating their supper, and 1 has had his and gone away. How many pigs are theie in all? 2. How many are 3 and 0? 3 and 6? 3 and 3? 3 and 5? 3 and 8? 3. How many are 4 and 4? 4 and 6? 4 and 10? 4. How many are 5 and 5? 5 and 8? 5 and 6? 5. How many are 6 and 1? 6 and 8? 6 and 9? 6. How many are 7 and 2? 7 and 5? 7 and 8? 7 and 10? 7. How many are 8 and 1 ? 8 and 2 ? 8 and 8? 8 and 10? 8. How many are 9 and 3 ? 9 and 5 ? 9 and 7? 9 and 6? 9 and 10? 9. How many are 10 and ? 10 and 1 ? 10 ani 2? 10 and 5? 10 and 10? 10. Levi had 6 cents, and his father gave him 6 more. How many cents then had he? Why? 11. Charles has in one pocket 7 chestnuts, and in the other 9 more. How many has he in both? 12. In a park there were seen 4 squirrels running on the ground, and 10 on the trees. How many squirrels were there in all? 6 and 7? 7 and 3? 8 and 4? 9 and 8? 22 P R I :M A R Y LESSOl^' XYIII. 1. Here is a picture of a lively scene. See what a collection of bii'ds. both on the ground and on the fence. Count and tell how many there ai^e on the ground. 2. Count and tell how many there are on one of the rails. 3. Count and tell how many there are on the two rails. 4. Count and tell how many there are on the gi^ound and on one of the rails. 5. Count and tell how many there are on the ground and on both rails. 6. How can you express thirty by figures ? By writ- ing the figure 3 with on the right of it: thus, SO- 7. What, then, does the figm*e 3, with on its right, represent? Three tens, or thii'ty. 8. Write the figures which stand for thirty. ARTTH.METIC. 23 9. How can you express thirty-two by figures? By u-ritiiig 3 and 2, side by side; thus, 32. 10. What do the figures thus written expres? "* Three tens and two, or thirty-two. 11. Write the figures which stand for thirty-two. 12. How can you express thirty-three by figures? By writing 3 and 3, side by side; thus, 33. 13. What do the figures thus written express? Three tens and three, or thirty-three. 14. Write the figures which stand for thirty-three. 15. How can you expi'ess forty by figures ? By writ- ing 4 and 0, side by side ; thus, 40- 16. What do the figures thus written express? Four tens and no ones or units, or forty. 17. Write the figures Avhich stand for forty. 18. Write and read the figures of the following ta- ble : — Nrnnber. rnntea figures. w ritcen figures. Number. rrmxea figures. writi figure Twenty-one, 21 21 Thirty-one, 31 31 Twenty-two, 22 22 Thirty-two, 32 32 Twenty-three, 23 23 Thirty-tkree, 33 33 Twenty-four, 24 24 Thirty-four, 34 34 Twenty-five, 25 25 Thirty-five, 35 35 Tv/'enty-six, 26 26 Thirty-six, 36 36 TAventy-seven, 27 27 Thirty-seven, 37 37 Twenty-eight, 28 28 Thirty-eight, 38 38 Twenty-nine, 29 29 Thirty-nine, 39 39 Thirty, 30 30 Forty, 40 40 24 PRIMARY LESSON XIX. 1. Two ducks were standing near a pool : but 1 of them has gone into it. =^^8iK. How many remain out of the pool ? 1 from 2 leaves how many? 2. Farmer Jones had 3 wheelbarrows, but has sold 1. How many has he left? 1 from 3 leaves how many? :^3E3EI 1^ 3. Mary had 4: walnuts, but has given her sister 1. How many has she left? 1 from 4 leaves how many? 4. There are 5 pitchers upon a table ; 1 of them con- tains milk, and the others water. How many contain water ? 1 from 5 leaves how many? 5. There are 6 flowers ; 1 of them is a tulip, and the others are pinks. How many are pinks ? ARITHMETIC. 26 6. A merchant had T chests of tea, but has sold 1 chest. How many chests has he left? 1 from 7 leaves how many? o rri CT fq fa CT •Vma ao^ 1l^ 7. Lucy had 8 flowers, but has given^ 1 of them to her sister. How many has Lucy left ? 1 from 8 leaves how many? 8. 9 flags were standing in a row, but 1 has been taken away. How many flags remain? 1 from 9 leaves how many? 9. John has 10 chickens. If he should sell 1 of them, how many would he have left? 1 from 10 leaves how many? 10. Recite the table : — 1 from 1 leaves 0. 1 from 2 leaves 1. 1 from 3 leaves 2. 1 from 4 leaves 3. 1 from 5 leaves 4. 1 from 6 leaver 5. 1 from 7 leaves 6. 1 from 8 leaves 7. 1 from 9 leaves 8. 1 from 10 leaves 9. 26 PRIMARY LESBOIT XX. 1. George found 3 eoro;s in a nest, and took away 2 of them. How many did he ? eo^2:s trom leave 2. Two 6 ecrofs leaves how many? Two eggs and how many eggs are 6 eggs 3. "^ 3. Two from leaves how many? Two from 9 leaves how many? 4. Recite the table : — 2 from 2 leaves 0. 2 from 3 leaves 1. 2 from 4 leaves 2. 2 fi'om 5 leaves 3. 2 from 6 leaves 4. 2 from 7 leaves 5. 2 from 8 leaves 6. 2 from 9 leaves 7. 2 from 10 leaves 8. 2 from 11 leaves 9. 8 WMITTEX JEXEJRCISES. ^^rite and read: — (5.) (6.) ('•) (8.) (9.) (10.) 22 21 25 37 23 24 31 39 28 22 26 29 32 40 36 27 20 33 (11.) (12.) (13.) (14.) (15.) (16.) 30 39 17 25 18 21 38 22 26 13 27 38 34 19 35 11 19 40 ARITHiMETIC 27 LESSON XXI. 3. Recite the table : — 3 from 3 leaves 0. 3 from 4 leaves 1. 3 from 5 leaves 2. 3 from 6 leaves 3. 3 from 7 leaves 4. 1. Six squirrels less 3 squirrels are how many? 2. Eight ships were at sea. and 3 of them were lost in a storm. How many- were left? 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. LESSON XXII. 1. Four flowers from 7 flowers leave how many? 2. Ten chickens less 4 chickens are how many ? Recite the table : — 4 from 4 leaves 0. 4 from 5 leaves 1. 4 from G leaves 2. 4 from 7 leaves 3. 4 from 8 leaves 4. 4 from 9 leaves 5. 4 from 10 leaves 6. 4 from 11 leaves 7. 4 from 12 leaves 8. 4 from 13 leaves 9, 28 PRIMARY LESSOIT XXIII. 1. A boy had 6 rabbits, and lost 2 of them. Hotv many had he left? 2. Laura had 9 sheets of paper, but has used 5 of them in writing letters. How many sheets has she left': Recite the table : — 5 from 5 leaves 0. 5 from 6 leaves 1. 5 from T leaves 2. 5 from 8 leaves 3. 5 from 9 leaves 4. 5 from 10 leaves 5. 5 from 11 leaves 6. 5 from 12 leaves 7. 5 from 13 leaves 8. 5 from 14 leaves 9. LESSOI^T XXIY. 1. Ten peaches were upon a table, but 6 of them have been put in a plate. How many remain on the table? 2. In two plates are 13 peaches, but in one of the plates are 6. How many are there in the other plate ? 3. Recite the table : — 6 from 6 leaves 0. 6 from 7 leaves 1. 6 from 8 leaves 2. 6 from 9 leaves 3. 6 from 10 leaves 4. 6 from 11 leaves 5. 6 from 12 leaves 6. 6 from 13 leaves 7. 6 A'om 14 leaves 8. 6 from 15 leaves 9. ARITHMETIC. 29 LESSON XXY. Recite the table : — 7 from 7 leaves 0. 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. 1. Emma bought a muff for 13 dollars, and sold it for 7 dollars. How much did she lose ? 7 from 13 leaves how many.?. 2. Eliza planted 16 seeds, but only 7 came up. many seeds failed to come up ? 7 from 16 leaves how many? How LESSON XXVI. Recite the table : — 8 from 8 leaves 0. 8 from 9 leaves 1. 8 from 10 leaves 2. 8 from 11 leaves 3. 8 from 12 leaves 4. 8 from 13 leaves 5. 8 from 14 leaves 6. 8 from 15. leaves 7. 8 from 16 leaves 8. 8 from 17 leaves 9. 1. William earned 8 dollars, but paid them all away for a dog. How many dollars had he then left? 8 from 8 leaves how many? 2. Robert caught 11 squirrels, but 8 of them ran away. How many remained? 3* 30 PRIMARY LESSON XXVII. 1. Recite the table: — 9 from 9 leaves 0. 9 from 10 leaves 1. 9 from 11 leaves 2. 9 from 12 leaves 3. 9 from 13 leaves 4. 9 from 14 leaves 5, 9 from 15 leaves 6. 9 from 16 leaves 7. 9 from 17 kaves 8. 9 from 18 leaves 9. 2. Julia rode at one time 15 miles, and at another time 9 miles. How many more miles did she ride at the one time than at the other? 'frop^ ' -^ leaves how many ? 3. From a chest of tea that contained 18 pounds there have been sold 9 pounds. How many pounds re- main unsold? LESSOIT XXYIII. 1. Recite the table: — 10 from 10 leaves 0. 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. 2. A man sold bird cages, that cost him 15 dollars, for 10 dollars. How many dollars did he lose ? 10 from 15 leaves how many ? 3. A farmer has 17 sheep and 10 lambs. How many more sheep has he than lambs? ARITHMETIC. 31 LESSON XXIX. 1. The children represented in the picture are en- gaged in play, during recess. In one group are 16 children : in the other there are 10. How manj more are there in the one group than in the other? 2. In one group there are 9 girls and 7 boys. How many more girls are there than boys? 3. How many are 8 less 1 ? 10 less 3 'i 4. How many are 6 less 2? 12 less 4? 5. How many are 11 less 5?'- 14 less 8? 6. How many are 19 less 10? 10 less 9? 7. How many are 17 less 10 ?^ 13 less 7 ? 8. How many are 16 less 8 ? /.. 15 less 6 ? 9. How many are 14 less 9 ? - 16 less 7 ? 10. How many are 17 less 7?/r?15 less 6? 11. llow many are 19 less 8? 17 less 9? 82 PRIMARY LESSON XXX. 1. From a brood of 16 chickens 9 have been carried away by a hawk. Hew many remain ? Why ? Ans. Because .9 taken frotn /6 leaves 7. 2. Lucy had 11 books, but has given 10 of them away. How many has she left? Why? 3. A lady had in her purse 13 dollars, but has spent 7 of them. How many dollars has she left? Why? 4. What is the taking of one number from another called ? Subtraction. 5. What is that left after taking one number from another called? Their Difference. 6. What is the difference between 13 and 7? 9 and 2? 15 and 8? 16 and 9? 7. What is the difference between 13 and 6 ? 14 and 7? 16 and 6? 17 and 9? WJRITTEX EXERCISES, Write and subtract : — (8.) (9.) (10.) (11.) (12.) (13.) (14.) (1.3.; 89769,889 54327135 Difference, 3 (IC.) (17.) (18.) (19.) (20.) (21.) (22.) (23.) 459 789 79 23868329 ARITH3IETIC, 33 .-^n?^ LESSON XXXI. There were 6 butterflies on the ground, but 5 have flown away. How many remain ? Five from 6 leaves how many? Five and how many are 6 ? 2. Two from 2 leaves how many ? 2 fi-om 6 ? 2 from 4 ? 2 from 10? 3. Three from 4 leaves how many ? 3 from 5? 3 from 10? 3 from 9? 4. Four from 7 leaves how many ? from 9 ? 4 from 5 ? 4 from 8? 4 5. Five fi'om 9 leaves how many ? 5 from 6 ? 5 from T ? 5 from 8 ? 5 from 10 ? 6. Six from 7 leaves how many ? 6 from 8 ? 6 from 9? 6 from 11? 6 from 12? 7. Seven from 8 leaves how many? 7 from 13? 8 from 15? 8 from 17? 10 from 16? 8. Andrew is 19 years old, and Jason is 10. How much older is Andrew than Jason ? 9. Mary has 15 cents, and Lucy 9. How many have both? Nine from 1'5 leaves how many? 34 PRIMARY LESSOIT XXXII. 1. Count from one to forty. Write the figures, which express forty. JfO. 2. Count from forty to fifty Write the figures, which express fifty. 50. 3. Count from fifty to sixty. Write the figures, which express sixty. 60. 4. Count from sixty to seventy. Write the figures, which express seventy. 70- 5. Write and read the figures of the table : — Numberi Forty-one, Eorty-two, Forty-three, Forty-four, Forty-five, Forty-six, Forty-seven, Forty-eight, Forty-nine, Fifty, Fifty-one, Fifty-two, Fifty-three, Fifty-four, Fifty-five, Printed figures. 41 Written figures. 42 Jf2 43 43 44 u 45 45 46 46 47 47 48 48 49 49 50 50 51 51 52 52 53 53 54 54 55 ^55 Number. rrinxea figures. w ntte figures Fifty-six, m 56 I'ifty-seven, 57 57 Fifty-eight, 58 58 Fifty-nine, 59 59 Sixty, 60 60 Sixty-one, 61 61 Sixty-two, 62 62 Sixty-three, 63 63 Sixty-four, 64 64 Sixty-five, ^^ 65 Sixty-six, m 66 Sixty-seven, 67 67 Sixty-eight, 68 68 Sixty-nine, 69 69 Seventy, 70 70 ARITHMETIC. 35 LESSOIT XXXIII. 1. Count from one to seventy. Write the figures, which express seventy. 70. 2. Count from seventy to eighty. Write the figures, which express eighty. 80. 3. Count from eighty to ninety. Write the figures, which express ninety. 90. 4. Count from ninety to one hundred. Write the fig- ures, which express one hundred. 100 5. Write and read the figures of the table : — Numter. Seventy-one, Seventy-two, Seventy-three, Seventy-four, Seventy-five, Seventy-six, Seventy-seven, Seventy-eight, Seventy-nine, Eighty, Eighty-one, Eighty-two, Eighty-three, Eighty-four, Eighty-five, Printed figures. 71 Written figures, 71 72 72 73 73 74 74 75 75 76 76 77 77 78 78 79 79 80 80 81 81 82 82 83 83 84 84 85 85 Number. Eighty-six, Eighty-seven, Eighty-eight, Eighty-nine, Ninety, Ninety-one, Ninety-two, Ninety-three, Ninety-four, Ninety-five, Ninety-six, Ninety-seven, Ninety-eight, Ninety-nine, Printed Written figures, figures. 86 86 87 88 89 90 91 92 93 94 95 96 97 98 99 87 88 89 90 91 92 93 94 95 96 97 98 99 One Hundred, 100 100 36 PRIMARY LESSON XZXIY. 1. If John should see 1 vessel every time he should go down to the sea-side, how many would he see on going down to the sea-side twice? 2. If a cabinet-maker can finish 1 table in a day, how many tables can he finish in 3 days? 3 times 1 table are how many tables? 3. 5 times 1 tree are how many trees? 4. 1 turkey was taken from a poultry-yard every night for 6 nights. How many were taken in all? 6 times 1 turkey are how many turkeys? 5. Recite the table : Once 1 is 1. 2 times 1 are 2. 3 times 1 are 8. 4 times 1 are 4. 5 times 1 are 5. 6 times 1 are 6. 7 times 1 are 7. 8 times 1 are 8. 9 times 1 are 9. 10 times 1 are 10. ARITHMETIC. 37 LESSON XXXV. 1. If 1 butterfly has 2 wings, how many wings have 2 butterflies? 2 times 2 are how many? 2. 3 pairs of skates are how many skates? 3 times 2 are how many? J «^ ^-^ 3. A boy has 2 hands. How many hands have 4 boys? 4 times 2 are K)W many? 4. A merchant sold 2 umbrellas every day for 7 .iaya How many umbrellas did he sell ? 7 times 2 are how many? X X X X X X 6. Recite the table : — Once 2 is 2. 2 times 2 are 4. 3 times 2 are 6. 4 times 2 are 8. 5 times 2 are 10. 6 times 2 are 12. 7 times 2 are 14. 8 times 2 are 16. 9 times 2 are 18. 10 times 2 are 20 38 PRIMARY LESSON XXXVI. 1. How man J cherries in 2 clusters of 3 cherries each? 2. How many marbles are 5 times 3 marbles? 3. Recite the table : — Once 3 is 3. 2 times 3 are 6. 3 times 3 are 9 4 times 8 are 12 5 times 3 are 15. 6 times 3 are 18. 7 times 3 are 21. 8 times 3 are 24. 9 times 3 are 27. 10 times 3 are 30. WRITTEN HXXlixCISES. Write and read: — (4) (5.) (6.) 0) (8.) 6 23 61 16 76 8 U 77 43 67 10 65 S4 32 17 12 61 43 17 53 (9.) (10.) (11.) (12.) (13.) 86 9 11 33 91 19 25 4'o 47 12 22 54 78 5 21 76 63 49 73 82 ARITHMETIC. 39 LESSON XXXVII. 1. Recite the table : — 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 4 are 28. 8 times 4 are 32. 9 times 4 are 36. 10 times 4 are 40. 2. If a cat can catch 4 mice in 1 day, how many can she catch in 4 days ? 4 times 4 are how many? 8. At 4 cents each, what will cost 6 pencils? LESSON XXXYIII. 1. Recite the table : — Once 5 is 5. 2 times 5 are 10. 3 times 5 are 15. 4 times 5 are 20. 5 times 5 are 25. 6 times 5 are 30. 7 times 5 are 35. 8 times 5 are 40. 9 times 5 are 45. 10 times 5 are 50. 2. When 1 vase costs 5 dollars, how many dollars must be paid for 3 vases? ' 3 times 5 are how many? 3. If a boat will sail 5 miles in 1 hour, 'low far will it sail in 6 hours? 6 times 5 are how many? 40 PRIMARY LESSON XXXIX. Recite the table : — Once 6 is 6. 2 times 6 are 12. 3 times 6 ai^e 18. 4 times 6 are 24. 5 times 6 are 30. 6 times 6 are 36. 7 times 6 are 42. 8 times 6 are 48. 9 times 6 are 54. 10 times 6 are 60. 2. In a garden there are 6 rose-bushes, and on each bush there are 2 roses. • How many roses are there in all? 2 times 6 are how many? 3. If 1 barrel of flour cost 6 dollars, how many dol- lars will 9 barrels cost? 9 times 6 are how many? w LESSON 1. Recite the table : — Once 7 is 7. 2 times 7 are 14. 8 times 7 are 21. 4 times 7 are 28. 5 times 7 are 35. XL. 6 times 7 are 42. 7 times 7 are 49. 8 times 7 are 56. 9 times 7 are 63. 10 times 7 are 70. 2. When 7 cents are paid for 1 dove, K^w many cents must be paid for 5 doves? 3. If 1 basket will contain 7 apples, kow many apples will 8 baskets contain ? 8 times 7 are how many ? ARITHMETIC 41 LESSON 1. Recite the table : — Once 8 is 8. 2 times 8 are 16. 3 times 8 are 24. 4 times 8 are 32. 5 times 8 are 40. XLI. 6 times 8 are 48. 7 times 8 are 56. 8 times 8 are 64. 9 times 8 are 72. 10 times 8 are 80. 2. If 8 bales will make 1 load, how many bales will make 6 loads ? 6 times 8 are how many? 3. If it take 9 men to row 1 boat, how many will it take to row 8 boats? LESSON XLII. Recite the table : — Once 9 is 9. 6 t 2 times 9 are 18. 7 t 3 times 9 are 27. 8 t 4 times 9 are 36. 9 t 5 times 9 are 45. 10 t mes 9 are 54. mes 9 are 63. mes 9 are 72. mes 9 are 81. mes 9 are 90. 2. "When 9 cents are paid for 1 cluster of grapes, how many cents must be paid for 3 clusters ? 3 times 9 are how many? 3. At 9 cents a pound, what will 10 pound? of sugar cost? 42 PRIMARY LESSON XLIII. 1. Recite the table : — Once 10 is 10. 2 times 10 are 20. 3 times 10 are 30. 4 times 10 are 40. 5 times 10 are 50. 6 times 10 are 60. 7 times 10 are 70, 8 times 10 are 80. 9 times 10 are 90. 10 times 10 are 100. 2. If a house have 10 windows in front, how, many windows in front will 4 houses of the same kind have? 4 times 10 are how many ? 3. If a wi'iting-book cost 10 cents, what will 9 writ- ing-books cost? 9 times 10 are how many? WniTTEN BXEJtiCISES. Write and addi- - ct) (5.) (6.) a-) (8.) (9.) 2 s 4 3 5 7 2 2 3 3 1 1 1 1 2 1 3 1 Sum, 5 (10.) (11.) (12.) (13.) (14.) (15.) 6 7 8 9 5 8 3 4 5 3 6 6 (16.) (17.) (18.) (19.) (20.) (21.) U 17 10 31 43 16 i 2 12 37 26 30 ARITHMETIC. 4B LESSON XLIY. 1. Three dogs while hunting caught 4 rabbits each. How many rabbits did they catch in all? 3 times 4 are how many ? 2. "What will 2 lemons cost, at 2 cents apiece? 2 times 2 are how many ? 3. At 5 cents apiece, what will 7 oranges cost? 5 times 7 are how many ? 4. Joseph went a fishing 6 times, and caught 8 fishes each time. How many fishes did he catch? 3 times 6 are how many ? 5. What will 4 sheep cost, at 3 dollars each? 4 times 3 are how many ? 6. What will 6 tops cost, at 7 cents apiece? 6 times 7 are how many ? 44 PRIMARY LESSON XLY. 1. If a cow give 6 quarts of milk a day, how manj quarts of milk will she give in 8 days? 6 times 8 are how many? Emily bought 10 combs, at 10 cents apiece. How did she pay for them? 10 times 10 are how many? "Wiijt will 7 barrels of vinegar cost, at 6 dollars 6 times 7 are how many ? At 9 cents a pound, what will 4 pounds of sugar 9 times 4 are how many ? 8 times 6 are how many? 4 times 9? LESSON XLYI. 1. What cost 4 plows, at 10 dollars apiece? Why 40 dollars? Ans. Since one ploiv cost 10 dollars, Jf plows ivill cost Jf times 10 dollars, or JfO dollars. 2. Oliver bought 6 melons, at 9 cents each. How much did he pay for all ? Why ? 8. 5 pear-trees have on each of them 8 pears. How many pears are on them all? Why? 4. Caroline has 8 classmates, and she gave to each 2 apples. How many apples did she give them ? Why ? 5. What is the cost of 7 hats, at 3 dollars apiece ? Why? 2. much 3. each? 4. cost? 5. ARITHMETIC. 45 LESSON XLYII. 1. If 1 ball cost 9 cents, what will 5 balls cost? Wbj? How many cents are 5 times 9 cents? 2. What is the cost of 4 pairs of boots, at 4 dollars a h pair ? AVhy ? How many dollars are 4 times 4 dol- lars ? Why ? 3. If a man can make 6 pairs of shoes in a day, how many pairs can he make in 6 days? Why? 4. What is the cost of 8 pounds of sugar, at 10 cents a pound? Why? 5. Bought 9 cords of wood, at 7 dollars a cord. What was the, cost ? Why ? 6. What is the cost of 5 pounds of cheese, at 10 cents a pouud? Why? T. If James earns 8 dollars in 1 month, how many dollars will he earn in 10 months? 8. How many dollars are 8 times 8 dollars? Why? 9. What will 9 pounds of rice cost, at 10 cents a pound ? Why ? 10. What will 10 pounds of beef cost, at 10 cents a pound ? Why ? 46 PRIMARY LESSON XLYIII. 1. How many are 6 times 7 ? 4 times 3 ? 2. How many are 7 times 6 ? 3 times 4 ? 3. How many units or ones are 8 times 5 ? 4. How many units or ones are 9 taken 3 times/ How many are 9, 9, and 9 ? 5. What is a short way of taking a number a cer- tain number of times called? Multiplication. 6. If 8 be multiplied by 5, what is the result ? 7. If 6 be multiplied by 6, what is the result? 8. What is the result of the multiplication of one number by another called? Their Product. 9. What is the product of 7 by 3 ? Of 8 by 4 ? WRITTEN JEXERCISJES. Write and multiply : — (10.) (11.) (12.) (13.) (U.) (15.) 6 5 7 9 4 8 2 4-3676 Product, 12 (16.) (17.) (18.) (19.) (20.) (21.) 11 12 12 14 14 13 3 S 4 2 3 2 . (22.) (23.) (24.) (25.) (26.) (27.) 31 22 23 24 33 44 2 3 3 2 3 2 ARITHMETIC. 47 LESSON XLIX. 1. A father has given his 2 sons 4 gold pens. How many pens are there to each of the sons? 2 in 4 how many times? 2. A fi^rmer has 6 pigs, which he wishes to put in pens that shall contain only 2 pigs each. How many pens must he have? 3. If it takes 2 skates to make a pair, how many pairs will 8 skates make? 2 in 8 how many times? ^-^' 4. How many pairs of gloves are there in 10 gloves? 2 in 10 how many times? * SI (1 Si ei 5. Recite the table : — 2 in 2, once. 2 in 4, 2 times. 2 in 6, 3 times. 2 in 8, 4 times. 2 in 10, 5 times. 2 in 12, 6 times. 2 in 14, 7 times. 2 in 16, 8 times. 2 in 18, 9 times. 2 in 20, 10 times. 48 PRIMARY LESSOIT L. 1^ 1. Albert gave his. 3 brothers 9 marbles, to be shared equally be- tween them. How many did each receive ? 2. How many times 3 marbles are 15 marbles ? 3. Recite the table : — 3 3 3 3 in 3, once, in 6, 2 times. m in 12 9, 3 times. 3 m 15, 4 times. 5 times. 3 in 18, 6 times. 3 in 21, 7 times. 3 in 24, 8 times. 3 in 27, 9 times. 3 in 30, 10 times. LESSON LI. 1. Sixteen marbles are how many times 4 marbles ? 4 in 16 hoAV many times? 2. Recite the table : — 4 in 4, once. 4 m 8, 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. -*> ARITHMETIC. 49 LESSON Kecite the table : — 5 in 5, once. 5 in 10. 2 times. 5 in 15, 3 times. 5 in 20, 4 times. 5 in 25, 5 times. LII. 5 in 30, 6 times. 5 in 35, 7 times. 5 in 40, 8 times. 5 in 45, 9 times. 5 in 50, 10 times. 2. If 5 men are required to row one boat, how many boats can 30 men row? 5 in 30 how many times? 3. Thomas divided 45 peaches equally among 5 of his schoolmates. How many peaches did each receive? 5 in 45 how many times ? LESSON LIII. 1. Recite the table : — 6 in 6, once. 6 in 12, 2 times. 6 in 18, 3 times. 6 in 24. 4 times. 6 in 30, 5 times. 2. If one ear of corn is required to feed 6 chickens, how many ears of corn will it take to feed 42 chickens? 6 in 42 how many times ? 3. At 6 cents each, how many melons can be bought for 24 cents? 6 in 24 how many times? 6 in 36, 6 times. 6 in 42, 7 times. 6 in 48, 8 times. 6 in 54, 9 times. 6 in 60, 10 times. 50 PRIMARY LESSON LIV. Recite the table : — 7 in 7, once. 7 in 14, 2 times. 7 in 21, 3 times. 7 in 28, 4 times. 7 in 35, 5 times. 7 in 42, 6 times. 7 in 49, 7 times. 7 in 56, 8 times. 7 in 63, 9 times. 7 m 70, 10 times. 2. If 28 roses are divided equally between 7 children, how many will each receive? 4 in 28 how many times? 3. At 7 cents a pound, how many pounds of rice can be bought for 56 cents? i 7 in 56 how many times ? N WRITTEN EXEJtCISES, Write and subtract • (4.) (5.) (6.) 0) (8.) (9.) u 17 10 31 43 96 4. 2 2 7 26 30 (10.) (11.) (12.) (13.) (U.) (15.) 17 16 17 25 42 56 4 c 18 8 15 19 36 (16.) (17.) (18.) (19.) (20.) (21.) 40 51 21 10 42 62 20 12 13 1 24 11 ARITHMETIC. 51 LESSOR 1. Recite the table: — 8 in 8, once. 8 in 16, 2 times. 8 in 24, 3 times. 8 in 32, 4 times. 8 in 40, 5 times. LY. 8 in 48, 6 times. 8 in 56, 7 times. 8 in 64, 8 times. 8 in 72, 9 times. 8 in 80, 10 times. 2. If one quart of cherries cost 8 cents, how many quarts of cherries may be bought for 32 cents ? 8 in 32 how many times ? 3. Francis bouo;ht 8 writino;-books for 80 cents. How much were the writing-books apiece ? 8 in 80 how many times ? LESSON LYI. 1. Recite the table : — 9 in 9, once. 9 in 18, 2 times. 9 in 27, 3 times. 9 in 36, 4 times. 9 in 45, 5 times. 9 in 54, 9 in 63, 9 in 72, 9 in 81, 6 times. 7 times. 8 times. 9 times. 9 in 90, 10 times. lars? 2 If a soldier can buy a gun for 9 dollars, how many guns can he buy for 18 dollars? , 9 in 18 how many times? 3. If 9 dollars will buy a barrel of flour, how many barrels of flour can be bought for 63 dol- 9 in 63 how many times? D'Z PRIMARY LESSON LVII. 1. Recite the table : — 10 in 10, once. 10 in 20, 2 times. 10 in 30, 3 times. 10 in 40, 4 times. 10 in 50, 5 times. 10 in 60, 6 times. 10 in 70, 7 times. 10 in 80, 8 times. 10 in 90, 9 times. 10 in 100, 10 times. I 2. When one fish costs 10 cents, how many fishes can be bought for 40 cents? 10 in 40 how many times? 3. At 10 cents a yard, how many yards of cloth can be bought for 90 cents? 10 in 90 how many times? LESSON LVIII. 1. How many dogs, at 5 dollars each, can be bought for 25 dollars ? Why ? Ans. Since 5 dollars will buy one dog, as many dogs can he bought for 25 dollars as 5 %s contained times in 25^ or 5. Therefore, at 5 dollars each, 5 dogs can he honght for 25 dol- lars. 2. How many toy-books, at 3 cents each, can be bought for 18 cents ? Why ? 3. How many marbles, at 1 cent apiece, can be bought for 9 cents ? Why ? 4. If 8 books cost 24 cents, ^what Avill 1 book colst? Why? 5. Arthur walked 36 miles in 9 days. How many miles did he walk each day ? Why ? ARITHMETIC. 53 LESSON LIX. 1. A sportsman in shooting 6 times shot 30 ducks, killing the same number at each shot. How manj ducks did he kill at a shot? Why? ' 2. At 7 cents a quart, how many quarts of nuts can be bought for 49 cents? Why? 8. At 10 cents a pound, how many pounds of sugar can be bought for 50 cents? Why? 4. Alfred gave 24 apples for 6 oranges. How many apples did he give for 1 orange? Why? 5. How many skeins of silk, at 5 cents a skein, can be bought for 35 cents? Why? LESSON LX. 1. How many times 2 in 4 ? In 8 ? In 6 ? In 10? In 2? 2. How many times 3 in 9 ? In 6 ? In 12 ? In 15? In 27? 3. How many times 4 in 4? In 16? In 20? In 32? In 40? 4. How many times 5 in 10 ? In 25 ? In 30 ? In 40? In 5? ^In 50? 5. How many times 6 in 12? In 18? In 6 r" In 42? In 60? 6. How many times 7 in 14 ? In 21 ? In 35 ? Id 49? In 03? 7. How many time3 8 in 24 ? In 40 ? In 64 ? In 72? 54 PRIMARY 1. How 2. 45? 3. 10? 4. 5 6. 7. 8. 9. 10. 11. 12. 13. 14 LESSON LXI. Edward had 7 doves, and sold 3 for 30 cents, much did he get apiece for them? How many times 9 in 18? In 36? In 9? In 63? In 90? How many times 10 in 20? In 50? In 90? In 100? How many times 2 in 18? How many times 3 in 3? How many times 5 in 35? How many times 6 in 24? How many times 8 in 32? How many times 9 in 27? How many times 10 in 40 ? How many times 7 in 28 ? How many times 8 in 64? How many times 9 in 45? How many times 10 in 80? In 54? In In 30? In 70? In In 12? In 21? In 45? In 54? In 80? In 72? In 70? In 56? In 72? In 81? 9 i.i 63? ARITHMETIC. 55 LESSON LXII. 1. How man J times are 4 cents contained in 24 cents ? 2. How many times 6 in 24 ? 8 in 24 ? 3. What is the finding of the number of times one number is contained in another called? Division. 4. What is the result of 15 divided by 3? Of 21 divided by 7? 5. What is the result of the division of one number by another called? The Quotient. 6. What is the quotient of 30 divided by 5 ? Of 49 divided by 7? 7. How many times 4 dollars in 17 dollars, and how many dollars over? 8. What is the number which is sometimes left after dividing called? The Remainder. 9. Divide 63 days by 10, and what will be the re- mainder ? WRITTEN EXERCISES. ^ Write and divide : — (10.) (11.) (12.) (13.) 2)8 4)12 3)18 5)25 Quotient, 4 (U.) (15.) (16.) (17.) (18.) (19.) 3)36 4US 3)69 3)39 4)44 5)55 (20.) (21.) (22.) (23.) (24.) (25.) 6)42 6)72 7)84 7)49 6)36 4)64 56 PRIMARY LESSON LXIII. 1. In a store-room 4 mice are on the shelves and 6 on the floor. How many in all? Why? 2. A man bought a load of wood for 6 dollars, and a barrel of flour for 9 dollars. How much did both cost? 3. In one field there are 5 oxen feeding, and in an- other 7. How many oxen are there in both fields? 4. 3 years ago George was 8 years old. How old is he now? 5. Flora recited 5 perfect lessons yesterday, and 5 more to-day. How many did she recite both days? 6. In a cage are 4 old bii'ds, and 8 young birds. How many birds are in the cage? 7. A man boucrht a chair for 7 dollars, and a desk for 8 dollars. How many dollars did both cost? ARITHMETIC. 67 LESSON LXIY. 1. Jane spent 3 cents for candy, and 9 cents for a book. How much did she spend in all? 2. Albert rode 8 miles in the morning, and 9 in the afternoon. How many miles did he ride in all? 3 Caleb, having spent 9 cents, found he had 10 re- maming. How piany cents had he at first? 4. A farmer sold to one man 3 sheep, to another 3, and then found he had 7 remaining. How many had he at first? 5. Henry received 4 merit-marks, Rollo 5, and Sam- uel 7. How many merit-marks did they all receive? 6. Jasper has 4 marbles, Peter 3, and Ezra 6. How many marbles have they all? 7 James is 4 years old, Arthur 2 years, and Edward 1 year. "What is the sum of their ages? 8. Jane had 9 cents, Mary 8, and Lydia 5. How many cents had they all? 9. ]Maria gave her sister 3 apples, lost 2, and had 9 left? How many had she at first? 10. A lady bought a dress for 8 dollars, a bonnet for 9 dollars, and a pair of gloves for 1 dollar. How much did they all cost ? 11. If you give 10 cents for an inkstand, 5 for a pen, and 3 for a pencil, how much will they all cost ? 12. Eva paid 8 cents for a comb, 4 cents for thread, and had left 2 cents. How much had she at first? y 58 PRIMARY LESSON LXV. 1. John has 3 apples, and William has 3. ^|y How many more has John than William? Why? 2. Samuel caught 8 birds, but let 7 of them escape. How many had he left? I 3. Isabel is 13 years old, and Susan only 3. How many years older is Isabel than Susan? /,< 4. 12 black-birds were on a fence, but 3 of them have flown away. How many then remain ?«>/ 5. James had 11 figs, and ate 4 of them. How many has he left? 7 6. Walter bought 10 slate-pencils, and gave 9 of them away. What number then remained? 7. Gave 11 dollars to Emily, and 7 to Betsey. How many more dollars were given to Emily than to Bet- sey? • 8. Sold a cloak for 14 dollars, and received as part pay 9 dollars. How many dollars remained due? 9. Gave 10 cents for apples, and 12 cents for peaches. How much more was given for the peaches than for the apples ? 10. Andrew had 9 chickens, but the hawks have taken 4 of them. How many remain? 11. Edwin had 20 cents, but has given away 10 in charity. How many cents has he left? 12. James is 18 years old, and John is 10 years old. How much older is James than John? ARITHMETIC. 59 LESSON LXVI. 1. Ellen has 9 chickens; 7 of them are light-colored, a/id the remainder dark. How many of them are dark- colored ? 2. In a class of 9 boys, only 2 had got their lessons. How many failed to have their lessons? 3. Ell rode 12 miles and walked 6. How much further did he ride than walk? 4. Paid for a coat 13 dollars, and for a pair of pants 7. How many dollars did the coat cost more than the pants ? 5. Nathan bought a slate for 8 eents, and sold it for 13 cents. How much did he gain? 6. A man bought a gun for 11 dollars, and sold it for 9. How much did he lose? 7. From a bucket of water containing 14 quarts there have been taken out 7 quarts. How much is left in the bucket ? 8. 16 swallows light on a barn, and 10 of them fly off again. How many remain? 9. Henry is 18 years old, and Willie 9 years. How many years older is Henry than Willie? 10. John . answered 19 questions, and Charles only 10. How many more questions did John answer than Charles ? 11. If you have 20 dollars, and should lose 10 of them, how many dollars would you have left? 60 PRIMARY LESSOI^ LXYII. 1. John's clocr cauo;ht 19 rabbits in two weeks; 8 of them the first week, and the remainder the second week. IIow many did he catch the second week? Why? 2. Helen found in the orchard 15 apples. After she had given 4 of them to Mary, and 5 to Sarah, how many had she left? 3. Jonathan had 6 marbles, and Peter gave him 3 more; but on the way to school he lost 4 of them. How many had he then left? Why? 4. From a flock of 18 sheep the dogs killed 8, and 1 died. How many remained? 5. Jacob picked 6 quarts of berries one day, and the next day 8 quarts, and sold 9 quarts. How many quarts of berries did he keep ? 6. 17 pigeons were flying together; 6 of them were shot at one time, and 2 at another. How many of the pigeons escaped? 7. Edgar had 13 chestnuts, but gave Edwin 3, George 2, and Jane 4. How many had he left? 8. James gathered 16 quarts of berries, and sold 6 quarts to one man, and 2 quarts to another. How many then had he left? 9. Edwin earned 18 dollars. After giving his mother 7 dollars, and his sister 1 dollar, how many dollars had he left? 10. Bou2i;ht a hat for 5 dollars and a. vest for 5 dol- lars. and gave in payment a 20-dollar bill. IIow many dollars should be paid back ? ARITHMETIC. 61 J Dies LESSOIT LXVIII. 1. 2 boys are coasting and 3 times iS many are skating. Ho-^' many are skating? ,/ 2. How many are 2 times 2? 2 timfs 3? 2 times 5? 2 times 4? 2 times 7? 3. How many are 3 times 1? 3 tinieSj-'i? 3 ti 6? 3 times 8? 3 times 10? % 4. How many are 4 times 3? 4 times 5? 4 time 4? 4 times 9? 4 times 1? 5. IIow many are 5 times 3 ? 5 times 6 ? 5 times 7? 5 times 0? 5 times 10? '^ G. How many are 6 times 2 ? 6 times 4 ? G times 6 ? G times 7 ? G times 9 ? 7. How many are 7 times 3 ? 7 times 4 ? 7 times 7? 7 times 8? 7 times 10? 8. How many are 8 times 2? 8 times 5? 8 times 7? 8 times 8? 8 times 10? \ 62 PRIMARY LESSON LXIX. 1. How many are 8 times 1 ? 8 times 2 ? 8 times 4? 8 times 6? 8 times 9? 2. How many are 9 times 2 ? 9 times 3 ? 9 times 7? 9 times 6? 9 times 10? 3. How many are 10 times 1? 10 times 2? 10 times 6? 10 times 4? 10 times 10? 4. How many are 2 times 6 ? 3 times 4 ? 5 times 8? 4 times 7? 6 times 3? 9 times 9? 5. How many are 6 times ? 6 times 1 ? 2 times 10 ? 4 times 10 ? 5 times 2 ? 7 times 2 ? 7 times 9? 6. When sugar is sold at 8 cents a pound, how much must be paid for 3 pounds? Why? WRITTEN EXERCISES. Write and divide : — \ ['.) (8.) (9.) (10.) 6)90 8)88 8)96 9)90 Quotient, 15 (11.) (12.) (13.) (14.) (15.) 9)99 4)56 7)77 3)81 (?;7^ (IG.) (17.) (18) (19.) (20.) 3)72 2)94 5)75 p>><5i 8)96 (21.) (22.) (23.) (24.) (25.) 7)84 5)85 6)84 8)96 ^;5>^ ARITHMETIC. 63 LESSOIT LXX. 1. Ellen saw in a pool 2 frogs, and in a pond 7 ^ times as many. How many did she ^^^^m see in the pond? 2. A farmer raised 5 bushels of peas, and 7 times as many bushels ^ of beans. How many bushels of beans did he raise? 3. If one cord of wood cost 8 dollars, how many dol- lars will 6 cords cost? 4. How many cents must be paid for 9 pounds .oi cheese, at 10 cents a- pound? 5. There are on the lake 6 boats, and 10 persons in each boat. How many persons are in all the boats? 6. If 8 apples will buy 1 ruler, how many apples will it take to buy 7 rulers? 7. How many roses are on 9 bushes, if there are 6 on each bush? 8. What will cost 9 yards of cloth, at 2 dollars a yard ? Why ? 9. What will cost 6 pairs of boots, at 4 dollars a pair ? Why ? 10. If Robert can walk 8 miles in 1 hour, how many miles can he walk in 7 hours? Why? 11. What will cost 6 loaves of bread, at 8 cents a loaf? Why ? 12. How many cents must be paid for 8 slates, at 10 cents each? 64 PRIMARY LESSO:tT LXXI. 1. What cost 9 lambs, at 3 dollars each? Why? 2. If there are 8 panes of glass in 1 window, how many panes are there iu/^ ^^= windows ? ^- g ^^ -^Q cents an hour, how manv cents may be earned in 10 hours? 4. Augustus picked 9 quarts of berries. If he gets 9 cents a quart for them, how many cents will he ob- tain ? 5. If a scholar can perform 9 examples in one hour, how many can he perform in T hours? 6. If Samuel should recite 6 perfect lessons m one day, how many perfect lessons would he recite in 10 days ? LESSON LXXII. 1. John has 5 marbles, and James has 6 times as many as John. How many has James? Why? 2. At 4 dollars apiece, what cost 8 sheep? Why? 3. At 5 cents a quart, how much must be paid for 3 quarts of milk? 4. Charles found 3 eggs, and Alfred 6 times as many. How many did Alfred find? 5. If Henry write 7 lines a day, how many will he write in 6 days? 6. If 1 pound of starch cost 8 cents, what will 5 pounds cost? ARITHMETIC. 67 -LESSON LXXV. 1. If an apple, or any thing, be divided into two equal parts, what will one of those parts be? One Half. 2. How many halves make one whole? Two. 3. If an orange be divided into three equal parts, what will one of those parts be? One Third. 4. How many thirds make one whole? Three. 5. If a melon be divided into four equal parts, what will one of those parts be ? ^ One Fourth. 6. How many fourths make one whole ? Four. 7. If a cake be divided into five equal parts, what will one of those parts be? ' One Fifth. 8. How many fifths make one whole ? Five. 9. If a line be divided into six equal parts, what is one of those parts called? One Sixth. 10. How many sixths make one whole? Six. 68 PRIMARY LESSON LXXVI. 1. When any thing is divided into seven equal parts, what is one of those parts? One SeveiJih. 2. How many sevenths make a whole one? 3. What is meant by one eighth of any thing ? Ans. One of the eight equal parts into which a thing ts di- vided. 4. How many eighths make a whole one? 5. What is meant by one ninth of any thing ? 6. How many ninths make a whole one? 7. What is meant by one tenth of any thing? 8. How many tenths make a whole one? 9. James had 2 fourths of a dollar, and his mother gave him one fourth more. How many fourths of a dollar then had he? 10. 2 fifths of an acre are planted with beets, and 2 fifths with carrots. What part of an acre is planted with both? 11. 3 eighths and 4 eighths are how many eighths? 12. George gave 2 sixths of a melon to his brother, and to his sister 3 sixths. What part did he give away in all? 13. Bought a book for 2 fourths of a dollar, and sold it for 3 fourths of a dollar. How much is gained by the sale? 14. If you should have 5 sevenths of a pound of candy, and should give away 3 sevenths of a pound, how much would you have left? 15. 8 ninths less 6 ninths are how many ninths? ARITHMETIC. 69 LESSOIT LXXVII. 1. IIow many halves are there in one orange ? 2. How many halves in 2 oranges? Why ? . Axs. Since there are 2 halves in one orarige, in 2 oranges there are 2 times 2 halves, or Jf halves. 3. How many halves in 3 oranges? In 4 oranges? In 5 oranges? In 6 oranges? 4. How many thirds in 1 orange? In 2 oranges ? Why ? 5. How many thirds in 3 oranges? In \ 4 oranges ? 6. How many fourths in one melon? In 2 melons? Why? 7. How many fourths in 3 pears? In 5 pears? 8. If one half of a melon cost 6 cents, how much will 2 halves, or a whole melon, cost? Why? Ans. Since one }Lalf cost 6 cents, 2 halves, or a whole one, will cost 2 times 6 cents, or 12 cents. 9. If one third of a pie cost 4 cents, how much will a whole pie cost? 10. 4 is one third of what number? Why? 11. If one fifth of an acre of land is worth 6 dol- lars, how much is 2 fifths worth? Why? 12. If one fourth of a yard of cloth cost 8 cents, how much will 2 fourths cost? 3 fourths? A whole yard? 70 PRIMARY LESSON LXXVIII. 1. In 4 halves of a dollar, how many dollars? Why? Ans. Since there are 2 halves in one dollar, in Jf halves of a dollar there are as many dollars as 2 halves is contained times in Jf halves, or 2 dollars. 2. In 6 halves of an orange, how many oranges? In '8 halves? In 10 halves? 3. In 6 thirds of an apple, how many apples ? 4. How many whole ones in four fourths ? In 8 fourths? In 12 fourths? In 16 fourths? 5. How many whole ones in 10 fifths ? Why ? 6. How many whole ones in 12 sixths? Why? 7. If a yard of ribbon cost 4 cents, how much will one half of a yard cost? Why? Ans. Since a whole yard cost Jf cents, one half of a yard will cost one half of Jj. cents, or 2 cents, 8. If a melon is worth 10 cents, how much is half a melon worth? Why? 9. One half of 10 is how many ? 10. If a cord of wood is worth 8 dollars, how much is one fourth of a cord worth ? 11. One fourth of 8 is how many? 12. At 10 dollars a barrel, what will one fifth of a barrel of flour cost ? Two fifths ? 13. One third of twelve is how many ? 14. A man is 35 years old, and his son is one sev- enth as old. How old is his son? 15. At 63 cents a yard, what is one ninth of a yard of cloth worth ? Four ninths ? ARITHMETIC. 71 LESSON LXXIX. 1. What is United States money? United States Money is that used in the United States. Recite the table : — are 1 cent, 1 dime, 1 dollar, u ii a 1 eagle. 10 mills 10 cents, 10 dimes, 10 dollars 2. How many mills make 1 cent? 2 cents? 3. How many cents make 1 dime? 2 dimes ? 3 dimes ? 4. How many cents are 1 dime and 3 cents ? 1 dime and 4 cents ? 5. How many dimes in 1 dollar ? 2 dollars ? 6. How many cents in 10 dimes, or 1 dollar? 7. How many dollars in 1 eagle ? In half of an eagle ? In a fourth of an eagle? 8. How many eagles in 50 dol- lars? In 60 dollars? 9. At half a dollar each, how many dollars wiU 6 oooks cost? 72 PRIMARY LESSON LXXX. 1. How man J dollars" will 2 barrels of flour cost at 10 dollars a barrel? 2. At 10 dollars a barrel, how many barrels of flour can be bought for 20 dollars? 3. What is the sign of dollar or dollars ? The Sign of Dollar or Dollars is $. 4. In §31, what does the sign denote? It denotes that the 31 expresses that number of dollars. 5. What then does $25 express? $43 express? 6. When dollars and cents are expressed together by figures, how are the figures expressing the cents sep- arated from those expressing the dollars? By the Decimal Point (.). 7. What does $25.10 express? It expresses twenty- five dollars and ten cents. 8. What then do the figures in the two places at the right of the point express? Cents. 9. What does $31.63 express? $9.81 express? 10. What does a figure written in the third place at the right of the point express? Mills. 11. What then does $8,656 express? It expresses eight dollars sixty-five cents six mills. 12. What does $19,425 express? $73,187 express? Write and read : — 13. S69. 16. $100.50. 14. $81. 17. $63,579. 15. $42. 18. $8,606. 19. $12,375. 20. $93.06. 21. $78,055. ARITUMETIC. 73 JEKSICK \^^"^.J?*ss LESSON LXXXI. 1. What is avoirdupois weight ? Avoirdupois Weight is that used in weighing common articles, as tea, sugar, butter, etc. 2. Recite the table : — 16 ounces are 1 pound. 100 pounds, 1 hundred weight. 20 hundred weight, 1 ton. Also, 25 pounds are 1 quarter ; 2000 pounds 1 ton. 3. How many ounces are there in 1 pound? In 1 half of a pound ? 4. How many pounds are there in a quarter? 5. How many quarters in 1 hundred weight ? In 2 liundred weight? In 3 hundred weight? 6. How many hundred weight in 1 ton? In G tons? At 4 dollars a hundred weight, what will 1 ton of hay eost? 1 half of a ton? V 74 PRIMARY LESSOIT LXXXII. 1. What is Troy Tveight ? Troy Weight is that used in weighing gold, silver, and jewels. 2. Recite the table : — 24 grains are 1 pennyweight. 20 pennyweights, 1 ounce. 12 ounces, 1 pound. 3. How many grains make 1 pennyweight ? 4. How many pennyweights are there in 1 ounce ? 5. How many pennyweights are there in 1 half of an ounce ? In 1 fourth of an ounce ? 6. How many ounces in 1 pound ? In 1 half of a pound ? In 1 fourth of a pound ? LESSO]^ LXXXIII. 1. What is linear or long measure ? Linear Measure is that used for measurino; distances and lengths. 2. Recit-e the table : — 12 inches are 1 foot. 3 feet, 1 yard. 5^ yards, or 16^ feet, 1 rod. 320 rods, 1 mile. Also, 40 rods 1 furlong ; 8 furlongs 1 mile. 3. How many inches are there in , 1 , I'll! 1 foot ? In 1 half of a foot ? i lycu. 4. How many feet in 1 yard? In 2 yards? In 3 yitrds? In 5 yards? 5. How many yards arc there in 1 rod ? ARITHMETIC. 75 6. How many rods are there in 1 furlong ? 7. How many furlongs in 1 mile ? In 1 half of a miile ? In 2 miles ? 8. How many yards in a piece of tape 27 feet long? 9 If your arithmetic is 6 inches long and your slate 9 inches, how much longer is the slate ? 10 In 3 feet how many yards? In 6 feet? In 18 feet ? 11. In 3 miles how many furlongs? In 6 miles? In 7 miles? LESSON LXXXIV. 1. What is liquid measure? Liquid Measure is that used hi measuring liquids, as molasses, milk, etc. 2. Recite the table ; — 4 gills are 1 pint. 2 pints, 1 quart. 4 quarts, 1 gallon. ^[^Ist^Ss^&on 3. How many gills are there in 1 pint? In 2 pints? In 3 pints? 4. How many pints are there in 1 quart? In 2 quarts? In 8 quarts? 5. How many quarts in 1 gallon? In 2 gallons? In 6 gallons? 6. In 12 gills how many pints? In 16 gills? 7. In 4 quarts how many gallons? In 8 quarts? In 16 quarts? 8. In 5 pints how many gills? In 6 pints? In 8 pints? 76 PRIMARY 9. Ho^Y many gills are there in 1 half of a pint? 10. How many quarts are there in 16 pints? 11. How many gallons in 20 quarts? In 36 quarts? 12. At 6 cents a quart, what costs 1 gallon of milk? 13. At 12 cents a quart, what costs 1 pint of mo- lasses ? 14. AVhen oil costs 10 cents a pint, what is the cost of a quart? 15. How many gills in 1 quart? In 2 quarts? In 3 quarts? LESSOIT LXXXV. 1 What is dry measure? Dry Measure is that used in measuring dry articles, as grain, apples, corn, etc. 2. Hecite the table : — 2 pints are 1 quart. 8 quarts, 1 peck. 1 pecks, 1 bushel. 3 How many pints are there in 1 quart? In 3 quarts? In 5 quarts? 4. How many quarts in 1 peck? In 2 pecks? In 3 pecks? 5. How many pecks in 1 bushel? In 2 bushels? In 3 bushels? 6. In 4 pints how many quarts? In 8 pints? 7. In 16 quarts how many pecks? In 24 quarts? ARITHMETIC. 77 8. What costs 1 quart of cherries, at 6 cents a pint? 9. At 5 cents a quart, what costs 1 peck of beans? 10. In 28 pecks how many bushels? In 32 pecks? 11. At 2 dolkirs a peck, what costs 1 bushel of ber- ries? 2 bushels? 12. How many pecks in three bushels and 3 pecks? 13. At 1 dollar a peck, what cost 3 bushels and 3 pecks of walnuts? * LESSON LXXXYI. 1. What is time? Time is a measured portion of duration. 2. Recite the table : — 60 seconds are 1 minute. 60 minutes, 1 hour. 24 hours, 1 day. 305 days, 1 common year. 366 days, 1 leap year. 3. Recite the table of MONTHS. 1. January has 31 days. 7. July has 31 days. 2. February, 28 or 29. 8. August, ' 31 3. March, 31 days. 9. September, 30 4. April, 30 " 10. October, 31 5. :May, 31 " 11. November, 30 6. June, 30 '• 12. December, 31 78 PRIMARY February hag in leap years 29 days, and in common years 28 days. 4. How many seconds are there in 1 minute? 5. How many minutes make 1 hour? 6. How many hours make 1 day? 7. How many days are there in a common year? In tsb leap year ? 8. How many days has January ? February? March? April? 9. What month has in leap year 29 days ? 10. How many days has May? June? July? Au- gust? 11. How many days has September? October? No- vember ? December ? LESSOIT LXXXYII. 1. How many units or ones are 1 ten? 2 tens? 3 tens? 4 tens? 5 tens? 6 tens? 7 tens? 8 tens? 9 tens ? 10 tens ? 2. How many tens in 20 units? In 30 units? In 40 units? In 50 units? In 60 units? In 80 units? In 90 units? In 100 units? 3. What are 100 units or ones called? One Hundred. 4. How can you express one hundred by figures ? By writing the figure 1 with 00 on the right; thus, 100. 5. What are 10 hundreds called? One Thousand. 6. How can you express one thousand by figures? By writing the figure 1 with 000 on the right; thus, 1000, ARITHMETIC. 79 7. \Miat is that which you have now been attending to called? Arithmetic. 8. Of what does arithmetic treat? Numbers. 9. What does arithmetic teach? Arithmetic teaches how to reckon by numbers. 10. Write on the slate or blackboard, in figures, the fii'st nine numbers. 11. Write and read the numbers expressed by the figures, 2, 5, 6, 4, 8, 10, 9, 11, 12. 12. Begin at the right and recite the names of the places or orders of figures in the following Table. r^ 30 .§ i g "3 H 5 h t3 9. Nine. 1 6. Sixteen. 4 2 3. Four hundred twenty-three. 5 7 6 8. Five thousand seven hundi^ed sixty-eight. 13. What number is expressed by 9 ? By 16 ? 14. What number is expressed by 423? 4 hundj-eds 2 tens 3 units, or four hundi'ed twenty-three. 15. What number is expressed by 5768? 5 thou- sands 7 hundreds 6 tens 8 units, or five thousand seven hundred sixty-eight. 16. What is expressed by a figure standing alone ? Units, 17. What; is expressed by a figure in the second or- der, or in the place next to the left of units? Tens. 18. What is expressed by a figure in the third order? Hundreds. 19. What is expressed by a figure "in the fourtli order? ^ Thousands. / ) 80 PRIMARY LESSON LXXXYIII. 1. TVhat is notation? Notation is the method of writing numbers. 2. What is numeration? Numeration is the method of readino; numbers. 3. Recite the table : — 10 units are 1 ten. 10 tens. 1 hundred, 10 hundreds, 1 thousand. 4. How many units are 1 ten? How many tens are 1 hundred? 2 hundreds? 5. How many hundreds are 1 thousand? 2 thou- sands? 3 thousands? 8 thousand ? ARITHMETIC. 81 LESSON LXXXIX. Write and read : — (1-) (2.) (3.) (4.) (5.) 26 71 99 82 88 39 80 28 13 96 40 4 ■ 31 49 70 (6.) (V.) (8.) (9.) (10.) 83 110 118 501 899 95 89 105 66 998 100 109 150 606 989 (11.) (12.) (13.) (14.) 144 303 6708 1234 1144 300 4576 5636 6110 1330 3421 7396 (15.) (16.) (17.) (18.) 2161 745 450 3215 4502 600 632 6215 1234 1302 1725 6215 3107 7805 2141 3145 Write in fig ures : — 19. Eleven. 24. One hundred six. 20. Thirty-two. 25. Two hundred ten. 21. Seventy -nine. 26. Three hundred nine. 22. Eighty- one. 2T. Four hundred sixty. 23. Ninety- seven. 28. Six hundred forty-five, 29. One thousand two hundi-ed fifty-six. 30. Three thousand five hundred sixty-three. 31. Five thousand two hundred fifty-one. 6 82 F 1 PRIMARY LESSON XO. Write and read : — (10 (20 (30 (40 10 111 400 123 15 125 500 456 23 362 440 789 61 410 444 321 70 397 555 654 (5.) (60 (70 (80 1234 3456 3000 2640 2000 5463 3003 1346 2200 5602 4500 2132 5550 6052 4005 3671 6789 2005 7077 2005 (90 (10.) (11.) (12.) 1422 3405 2231 9834 6171 6725 3225 8352 3140 4IO6 4252 6761 1233 4455 734 365 Write in figures : — 13. Seventeen. 14. Seventy-one. ' 15. Ninety-nine. 16. One hundred. 17. Ninety-three. 19. One hundred eleven. 20. Two hundred three. 21. Three hundred three. 22. Four hundred forty-four. 23. Seven hundred eighty. 24. Eight hundred nineteen. 18. Three hundred. 25. One thousand one hundred twelve. 26. Two thousand five hundred fifty. 27. Eight thousand sixty-seven. 28. Nine thousand nine hundred ninety-nine. ARITHMETIC. LESSOIT XOI. 1. Ho-^ may numbers be expressed? By words. 2. What is the method of expressing numbers by fig- uies called? The Arabic Method. 3. Why is it so called? Because it was obtained from the Ai'abs. 4. What character besides figures are sometimes used in expressing numbers? Letters. 5. How many different letters are used? Seven. 6. Name the letters. I, V, X, L, C, D, M. 7. For what number does the letter I stand? One. 8. For what number does the letter Y stand? Five. 9. For what number does the letter X stand? Ten. 10. For what number does the letter L stand? Fifty. 11. For what number does the letter C stand? One Hundred. 12. For what number does the letter M stand? One Thousand. 13. What is the method of expressing numbers by letters called ? The Roman Method. 14. Why is it so called ? Because it was obtained from the Romans.. Write the letter standing: — 15. For one. 19. For one hundred. 16. For five. 20. For five hundred. IT. For ten. 21. For one thousand. 18. For lirty. 84 PRIMARY LESSOIT XOII. 1. What is the effect of repeating a letter? Repeat- ing a letter repeats the number it denotes. 2 If then I stands for one, for how many do III stand ? Three. 3. What is expressed by writing a letter denoting a, less number before a letter denoting a greater number? The Difference of those numbers. 4. If then X stands for ten, for how many does IX stand ? For the difference between one and ten, or nine. 5. What is expressed by writing a letter denoting a less number after a letter denoting a greater number? The Sum of those numbers. 6. If then L stands for fifty, for how many do LI stand? Fifty and one, or fifty-one. 7. Write the letters of the following table, and tell the numbers expressed. Numbers. Letters. Numbers. Letters. One, I. Thirty, XXX. Two, II. Forty, XL. Three, III. Fifty, L. Four, IV. Sixty, LX. Five, Y. Seventy, LXX. Six, YL Eighty, LXXX. 'Seven, YII. Ninety, XC. Eight, YIII. One hundred. c. Nine, IX. Two hundred, cc. Ten, X. Five hundred. D. Eleven, XL Six hundred. DC. Twenty, XX. One thousand, M. ARITHMETIC. 85 LESSOIT XOIII. 1. How many are 7 and 3 ? 6 and 5 and 1 ? 2. What is addition ? Addition is tlie finding a number equal to two or more numbers of the same kind. 3. What number is equal to 9 and 4 ? 4. What IS the sum of two or more numbers? The Sum of two or more numbers is that number which is equal to those numbers. 5. What is the sum of 8 and 5? Of 6 and 7? How many are (6.) (T.) (8.) 9. 2 and 2? 17. 1 and 5? 25. 4 and 4? 10 3 ana 2? 18. 6 and 2? 26. 5 and 5? 11. 4 and 6? 19. 5 and 7? 27. 6 and 6? 12. 2 and 4? 20. 8 and 1? 28. 4 and 5? 13. 5 and 3? 21. 1 and 3? 29. 5 and 2? 14. 3 and 6? 22. 6 and 5? 30. 10 and 3 ? 15. 1 and 9? 23. 9 and 0? 31. 5 and 10? 16. 7 and 4? 24. 5 and 8? 32. 11 and 5? WBITTBX EXERCISES. Write and add: (33.) (34.) (35.) (36.) (37.) (38.) 16 17 60 13 14 16 31 11 70 33 30 16 41 42 55 40 12 ' 34 v39.) (40.) (41.) (42.) (43.) (44.) 167 564 271 924 • 516 810 710 432 808 442 731 201 311 500 520 412 102 401 86 PRIMARY LESSON XOIV. How many are 1. 2 and 2 and 1? 9. 4 and 3 and 7? 2. 3 and 2 and 2? • 10. 8 and 1 and 0? 3. 5 and 3 and 3? 11. 9 and 2 and 5? 4. 7 and 1 and 4? 12. . 2 and 6 and 1? 5. 6 and 4 and 5? 13. 10 and 5 and 4? 6. 1 and 9 and 6? 14. 6 and 1 and 3? 7. 10 and 2 and 8? 15. 11 and 4 and 7? 8. 11 and 5 and 4? 16. 12 and 3 and 7? WRITTEN EXERCISES, Write and add : - — (17.) (18.) (19.) (20.) (21.) (22.) 610 612 171 143 816 771 132 390 301 261 191 117 70 10 112 412 101 231 (23.) (24.) (25.) (26.) (27.) (28.) 781 257 126 391 182 910 631 861 275 710 921 297 (29.) (30.) (31.) (32.) (33.) (34.) 416 413 103 129 812 700 112 142 451 310 104 511 301 603 261 230 222 132 (35.) (36.) (37.) (38.) (39.1 4131 5410 7102 8201 9102 4121 3444 1703 2143 1034 (40.) (41.) (42.) (43.) (44.) 4831 9102 1111 1345 9810 7201 6132 9109 19 1518 ARITHMETIC. 87 LESSON XOV. 1. What is the sign of addition? The Sign of Addition is an erect cross, -j-, and is called p/i