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QUESTIONS ON THE FOREGOING. 2. What does Number show? 1. How is it represented ? 1 What letters and what figures stand for one, four, five and nine ? What for ten? Ans. The figure 1 and 0 called naught or cipher.

3. What letters and what figures stand for eleven? For twelve! Fifteen? Twenty? Forty? Fifty? Ninety? What different numbers may be represented by the figures 1 and 5 written together? Ans Fifeen and fifty-one; as, 15:51. ; 4. What different numbers may be expressed by the figures 1 and 9? 2 and 5? What number is expressed by c? by D? by m? What by 7, D, and M, with a dash over each.

5. What figures stand for one hundred? For two hundred? One thousand? Ten thousand? One hundred thousand? One million ?

ADDITION.

QUESTIONS. II. 1. Thomas has 3 dollars and Rufus 5 dollars. How mas y dollars have they both? Say 3 and 5 are 8.

A. 8 dollars, 2. A farmer has 5 cows in his yard, and 6 in the pasture. How many cows has he in both places ?

3. A man bought a hat for 5 dollars, and a pair of boots for 7 dollars. How many dollars did he pay for both?

4. A man lost 7 dollars, and then had 8 dollars left? How many dollars had he at first?

5. A man gave 8 dollars for a saddle, 5 dollars for a bridle, and 2 dollars for a whip. What did the whole cost him?

6. pose there are 8 oranges in a basket, 5 on a table, and 4 in my pockets. How many will they all make?

7. A grocer sold to one man 6 barrels of flour, to another 9 barrels, and still had 5 barrels left. How many barrels had he at first?

8. In a certain class are 6 large boys, 7 small ones, and 10 girls. How many scholars are there in the class?

9. A boy has 10 dollars, his father gave him 10 more, and he has 5 owing to him. How many will they all make ?

10. Thomas read 19 pages of history in one day, 12 in another, and 9 in another. How many pages did he read in all ?

11. Suppose you are 10 years old, and that your brother was 10 years old when you were born. What is his age now?

12. A man gave 10 dollars more for his horse than for his wagon, and the wagon cost him 30 dollars. What did they both cost him.?

13. How many are 10 and 30 and 40 ? 60 and 10 and 20 ? 100 and 200 and 400 ? 600 and 300 and 100?

| Addition, [L. additio.] Any thing added; adding; joining; upiting two ci more numbers in one sum.

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14. When it is 1 o'clock, a regular clock strikes once; when it is 3 o'clock, twice; when it is 3 o'clock, thrice. How many strokes will these make? A. 6 strokes: because 1 and 2 are 3, and 3 are 6.

15. Add together all the strokes that a clock strikes in 12 hours, as in the above picture of a clock. [Thus 1 and 2 are 3, and 3 are 6, and 4 are 10, and so on up to 12.]

In the following table the single figures are combined' by pairs in every possible manner; so that, if it be committed to memory, the learner can add with facility” any two numbers whatever.

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1 and 1 are 2 2 and 9 or 3 and 8 or 4 and 7 5

11 1 and 2 are 3 3 and 9 or 4 and 8 or 5 and 7 or 6 and 6 are 12 1 and 3 or 2 and 2 are 4

4 and 9
5 and 8

7 1 and 4 or 2 and 3 are 5 5 and 9 or 6 and 8 or 9 and 7 are 14

2 and 4 or 3 and 3 are 6 6 and 9 or 7 and 8 are 15 1 and 6 or 2 and 5 or 3 and 4 are ng 7 and 9 or 8 and 8 are 16 7 6 3 5 or 4 4

8 9 1 and 8 or 2 and 7 or 3 and 6 or 4 and 5 are 9 9 and 9 are 18 1 and 9 or 2 and 8 or 3 and 7 or 4 and 6 or 5 and 5 are

10

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16. Repeat the above table beginning at the top on the left. What are all the different pairs of single figures that together make 7 ? make 9? 10 ? 12? 13? 142 15? 16 ? 17 ? 18?

17. How many are 8 and 4 ? 18 and 4 ? 28 and 4 ? 48 and 4? 7 and 6 ? 17 and 6 ? 26 and 7! 57 and 6 ? 86 and 7 ? 96 and 7 ?

18. How many are 9 and 5 ? 19 and 5 ? 55 and 9? 8 and 8? 38 and 8 ? 98 and 8? 5 and 7 ? 65 and 7? 9 and 8 ? 49 and 8 ? 99 and 8 ?

19. Add.together audibly: 10 twos: 10 threes: 10 fours : 10 fives 10 sixes : 10 sevens :: 10 eights : 10 nines: 10 tens.

20. How many are 78 and 10 and 3 ? 78 and 13? 91 and 14 [10 and 4]? 105 and 15 [10 and 5]? 120 and 16 ? 136 and 17 ? 153 an 18? 171 and 19?

21. Add together audibly: all the different numbers under 20, beginning with the lowest.

1 COMBINED, United closely; associated; leagued; confederated. 2 Facility, (L. facilitas.] Easiness to be performed; readiness ; affability. 3 AUDIBLY, In a manner so as to be heard; in an audible manner

SUBTRACTION.

QUESTIONS.

III. 1. A boy having 15 cents lost 10; how many had he left! Say 10 from 15 leaves 5; because 10 and 5 are 15. A. 5 cents.

2. A man owing 12 dollars paid 7 dollars. How many dollars did he still owe? 7 from 12 leaves how many and why?

3. A grocer bought a barrel of molasses for 15 dollars, and sold it for 18 dollars. How much did he make on it?

4. Suppose your age to be 12 years, and your brother's 20 years What is the difference between your age and his?

5. A farmer bought a cow for 20 dollars and sold her for 1-5 dol. lars. What was his loss?

6. Thomas and William counted their nuts; the former had 30 and the latter 50. How many had one more than the other?

7. A certain cistern has one pipe by which 25 gallons run in every hour, and another pipe by which 19 gallons run out every hour. How many gallons will stay in every hour ?

8. How many are left in taking 3 from 11? 3 from 21 ? 3 from 51? 4 from 13? 4 from 23 ? 4 from 53? 4 from 83 ?

9. How many does 5 from 12 leave? 5 from 32? 6 from 16 2 6 from 36 ? 7 from 15? 9 from 17 ? 9 from 37 ? 9 from 107?

10. How many cents added to 100 cents will make 200 cents ? 11. What is the difference between 300 cents and 700 cents ? 12. How much smaller is 70 than 270? 500 than 1000? 13. How much larger is 590 than 90 ? 1275 than 275 ?

14. A gentleman paid 250 dollars for his carriage, and 50 dollars less for his horse. What was the price of his horse ?

MULTIPLICATION

QUESTIONS. IV. 1. A farmer gave 10 dollars for a calf, 10 dollars for a plough and 10 dollars for a load of hay. What did he pay for the whole ?

Say 10 and 10 and 10 are 30; or as 10 is taken 3 times, rather say at once, 3 times 10 are 30, as in the Table. A. 30 dollars.

2. What will 5 hats cost at 4 dollars a-piece ? A. 20 dollars. 3. A man bought 10 sheep for 3 dollars a-piece.

What did he pay fur the whole ? How many are 3 times 10?

4. If a shoemaker can manufacture 4 pair of shoes in one day, now many can he make at that rate in 8 days ? In 10 days?

I SUBTRACTION, (L subtractio.] The act of taking a part from the rest. 2 MULTIPLICATION. (multiplicatio.] The act of inereasing in number.

6. If 5 yards of cloth will make a suit of clothes, how many yards will it require to make 2 suits ? 8 suits ? 11 suits ? Repeat the following multiplication table :

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9 10 times times times times times times times times times 1 are 2 1 are 3 1 are 4 l are 5 1 are 6

1 are 7 I are 8 1 are 9 I are 10 2. 4 2. 6 2. 8 2.10 2.12 2.14 2.16 18 20 3. 6 3. 9 3.12 3.15 3.18 3.21 3.24 3 27 3 30 4. 8 4.12 4.16 4.20 4.24 4.28 4.32 4. 36 4. 40 5.10 5.15 5. 20 5.25 5.30 5.35 5.40 5. 45 5 6.12 6.

18
6.24

6.30 6.36 6. 42 6.48 6. 54 6 60 7.14 7.21 7.287.35 7.42 7.49 7.56 7. 63 7 8.16 8.24 8.32 8.40 8.48 8.56 8.64 8 72 8. 80 9.18 9 9.36 9 45 9.54 9 63 9.72) 9 81 9. 90 10. 2010.30 10.40 10.50 10. 60 10 70 10.80/10 90 10.100 11 .22 11 .33 11 .44 11.55 11.66 11 .77 11 .88 11 99 11.110 12 , 24 12 .36 12 48/12 .60|12 . 72|12 .84)12 . 96) 12 . 108) 12 , 120 11

12 times times times times times

times times times 1 are 114 are 44 7 are 7710 are 110 1 are 12 | 4 are 48 7 are 84 10 are 120 2 22 / 5 558 88 11 121 2 245 608. 96 11. 132 3. 33/6, 66 9. 99 | 12 . 132 3. 366. 729. 108 12 . 144

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6. It takes 4 pecks to make 1 bushel. How many pecks then are there in 3 bushels ? In 5 bushels ? In 7 bushels ?

7. At 6 cents a quart, what will 6 quarts of cherries cost? What will 8 quarts cost? 9 quarts ? 10 quarts? 11 quarts ? 12 quarts ?

8. When the board of a small family costs 7 dollars a week, what will the board for 7 weeks cost? For 8 weeks?

9. When flour is 8 dollars a barrel, how much must you pay for 8 varrels? For 9 barrels ? For 11 barrels ? For 12 barrels ?

10. A man traveled by stage, at the rate of 7 miles an hour. How far did he go in 7 hours ? In 9 hours ? In 12 hours ?

11. When hay is 9 dollars a ton, what will be the cost of 7 tons ? O tons ? 8 tons? 6 tons ?

12. If 10 men can do a job of work in 10 days, how long will it take one man alone to do it, working at the same rate?

13. How many are 6 times 3? 9 times 5? 8 times 7? 7 times 6 ? 8 times 6 ? 12 times 5? 9 times 12?

14. If a cannon ball fly at the rate of 11 miles a minute, how far would it go in 7 minutes ? In 9 minutes ? In 12 minutes ?

15. How many are 10 times 5? 10 times 10? 10 times 20 ? 10 times 30 ? 10 times 40 ? 10 times 90 ? 10 times 100 ?

16. If a regiment consists of 1000 men, of how many men would 2 regiments consist ? 3 regiments ? 5 regiments ?

DIVISION.

QUESTIONS.

V. 1. How many yards of cloth at 2 dollars a yard can you buy for 8 dollars, and why? A. 4 yards; because 4 times 2 are 8.

2. How many yards of cloth at 3 dollars a yard can you buy for 12 dollars ? For 18 dollars ? For 24 dollars ? For 30 dollars ?

3. At 5 dollars a hat, how many hats will 40 dollars buy? As many hats as 5 is contained times in 40.

A. 8 hats. 4. A father having 24 books, gave 3 to each of his children. How many children must he have had ?

5. A merchant bought a quantity of flour for 144 dollars, paying 12 dollars a barrel. How many barrels did he buy?

6. If one man alone can perform a piece of work in 100 days, how long would it take 10 such men to do the same?

7. If a man can travel 6 miles in an hour by stage, how long will it take him to perform a journey of 72 miles? Of 60 miles ?

8. Suppose an orchard to have 132 trees in rows, with 12 trees in a row, of how many rows does the orchard consist?

9. How many times 8 in 96 ? 9 in 63 ? 8 in 56 ? 9 in 108? 11 in 132? 12 in 108? 12 in 1322

10. A man having 300 dollars, gave to his sons 100 dollars a-piece. How many sons had he? How many times 100 300 ?

11. How many times 100 in 500? 5 in 500 ? 200 in 1000? 4 in 800 ? 6 in 1200 ? 10 in 1000? 1000 in 10000 ?

12. If i barrel holds 5 bushels of rye; how many barrels will 21 bushels fill?

A. 4 barrels and I bushel over. 13. How many times 5 in 42, and how many over? 6 in 39, and how many over? 7 in 46 ? 8 in 74 ? 9 in 98 ? 9 in 99 ?

14. Why not say 9 in 99 only 10 times and 9 over ? A. Because His contained in 99 all of 11 times.

15. How many times 6 in 41 ? 8 in 102? 9 in 112? 12 in 155?

FRACTIONS

QUESTIONS. VI. 1. To divide 13 dollars equally among 2 persons; how would ou proceed to find each man's exact part? Say 2 in 13, 6 times and 1 dollar over; the 1 over is considered as divided into 2 equal parts by writing the 2 under the 1, with a line between, making which is read 1-half.

A. 6 dollars. 2. How is any number divided into 2, 3, 4, 5, &c. equal parts ? A. By writing under it as above the dividing numbers, 2,3,5, &c 1 DIVISION, (L. divisio.] The act of dividing any thing into parts; the state of being divided; that which divides or separates; partition ; a part of an arıny or militia; dis anion ; variance.

2 Fraction. (L. fractio.] The act of breaking ; the broken part of a number

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