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5. To abbreviate expressions, and to indicate the relations of numbers to each other, we sometimes ase signs instead of words.

6. This mark, $, is often used as a sign of the word dollar, or dollars; thus, the expression $1, stands for one dollar; $4 stands for four dollars.

7. The sign of equality,=, signifies that the quantities between which it stands are equal to each other; thus, $1: 100 cents; that is, one dollar equals one hundred cents.

=

8. The sign of addition, +, called plus or and, denotes that the quantities between which it stands are to be added together; thus, 3+2=5; that is, three plus two equals five, or three and two are five.

9. The sign of subtraction,—, called minus or less, signifies that the number after it is to be taken from the number before it; thus, 7-43; that is, seven minus four, or seven less four, equals three.

10. The sign of multiplication, X, signifies that the two numbers between which it stands are to be multiplied together; thus, 6 × 5 = 30; that is, six multiplied by five equals thirty, or six times five are thirty.

11. The sign of division,÷, indicates that the number before it is to be divided by the number after it; thus, 8 ÷ 2 4; that is, eight divided by two equals four, or two in eight, four times.

LESSON II.

1. MASSACHUSETTS has 14 counties, Rhode Island has 5, and Connecticut has 8; how many counties have the three States? Ans. 14+5+8 - : 27.

2. How many more counties has Massachusetts than Rhode Island? Ans. 14—5—9.

3. If I pay $9 for a barrel of flour, $8 for a hundred pounds of pork, and $3 for a bushel of beans, how many dollars shall I pay for all?

4. If a ton of coal costs $8, and a cord of wood costs $5, what do they both cost? does the coal cost than the wood?

How much more

=

5. How many are 9+8+3? 9 6. How many are 6+4+7? 8 7. How many are 7+5+9? 9 8. How many are 5+8+7? 7 9. How many are 8+6+7? 8 10. How many are 6+7+4? 9 11. If 1 barrel of flour costs $9, what will 8 barrels cost? Ans. $9 × 8: $72. 12. How many are 12 × 5? 13. How many are 6 × 7? 14. How many are 10 × 5? 15. How many are 5 × 11? 6 × 12? 16. How many are 9 × 7? 5 X 11? 17. How many are 7 × 10? 18. How many are 9 × 10? 6 × 7? 19. How many are 4 × 12? 7×8?

11 × 7?
9-X6?
8 × 7?

6 × 8?

9 cents.

20. If 8 pounds of sugar cost 72 cents, what is the price of 1 pound? Ans. 72 cents÷8: 21. How many are 56 ÷ 7? 63 ÷ 9? 22. How many are 328? 24 ÷ 6? 23. How many are 40÷ 5? 42

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24. How many are 56÷8? 56 ÷ 7?

- 6?

25. How many are 6010? 26. How many are 72 ÷ 12? 27. How many are 49 ÷ 7? 28. How many are 8 6? 9+7? 29. How many are 7 × 8 6? 8×4+8? 30. How many are 48÷4+3? 60÷10—2? 31. How many are 9+6+8 3? 4863? 32. Take 6, add 4, multiply by 2, divide by 5, divide ty 2, add 7, divide by 3, multiply by 4, subtract 2; result?

45 ÷ 9? 66÷6? 64÷8?

33. Take 9, subtract 3, divide by 2, add 5, multiply by 4, subtract 2, divide by 6, add 7; result?

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LESSON III,

1. A MAN bought a tub of butter for 12 dollars, and a cheese for 4 dollars; how many dollars did he pay for both?

2. A farmer has 8 cows in one pasture, and 12 in another; how many has he in both? How many more in one than in the other?

3. George found 6 marbles, Arthur gave him 10, and he bought 8; how many marbles had he then?

4. One morning Mary found in her flower-garden 8 roses, 5 peonies, 7 tulips, and 10 other blossoms; she picked 4 roses, 1 peony, 3 tulips, and 7 other blossoms; how many blossoms did she find? How many did she leave in the garden?

5. A farmer sold 8 bushels of wheat, 9 bushels of corn, 3 bushels of rye, and 7 bushels of barley; how many bushels of grain did he sell?

6. A drover bought 10 sheep of one man, 7 of another, and 8 of another, and he afterwards sold 12 sheep; how many did he buy? How many did he keep?

7. If I earn 12 dollars, and spend 7 dollars, a week, how many dollars shall I save in a week? How many in 4 weeks?

8. Bought 9 yards of cloth, at 4 dollars a yard, and sold the whole of it for 9 dollars more than I paid; what did I receive for the 9 yards? What for each yard?

9. Bought 8 yards of cloth, at 5 dollars a yard, and sold all of it for 32 dollars; did I gain or lose? How much on the whole? How much on a yard?

10. Mr. Flint had 10 sheep in each of 5 pastures, but he has sold 5 from one pasture, 7 from another, and 8 from another; how many sheep has he now ?

11. When flour is worth 8 dollars a barrel, and hay 12 dollars a ton, how many tons of hay will pay for 6 barrels of flour?

12. In a certain orchard there were 7 rows of trees, and 8 trees in each row, but 2 trees have been taken from each row; how many trees still remain in the orchard?

13. Daniel, Joseph, and James went a fishing. James caught 2 fishes, Joseph caught 3 times as many as James, and Daniel caught twice as many as James and Joseph together; how many did Daniel catch?

14. Thomas had twice 15 peaches, which he divided equally between his 3 brothers; how many did he give to each?

15. The distance from Boston to Malden is 5 miles; from Malden to Reading, 7 miles; from Reading to Wilmington, 3 miles; from Wilmington to Andover, 8 miles; from Andover to Lawrence, 3 miles : how far is it from Boston to Lawrence?

16. The distance from Boston to Somerville is 3 miles; from Somerville to Waltham, 7 miles; from Waltham to Concord, 10 miles; from Concord to Littleton, 11 miles; from Littleton to Groton, 4 miles; from Groton to Fitchburg, 15 miles: how far is it from Boston to Fitchburg?

LESSON IV.

THE following exercises are designed to discipline the pupil in changing from one subject to another with rapidity and accuracy.

Let the examples be read across the page; thus, 1 and 1 are 2; 1 from 2 leaves 1; once 1 is 1; 1 in 1, once; etc. etc.

1 and 1? 1 and 2?

1 and 3?

1 and 4?

1 and

5?

1 and 6?

1 from 2?
1 from 3?
1 from 4?

1 from

5?

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