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20. From a bin containing 4281⁄2 bushels of wheat, 3171⁄2 bushels were sold: how many bushels remained?

21. A man bought a horse for $231 and sold it for $219 what was the loss?

22. A lady gave a clerk a twenty dollar bill in payment for 2 pairs of gloves at $12 a pair, some ribbon worth $7, and some lace worth $5% how much change did she receive?

23. From a piece of cloth containing 33 yards, a clothier cut 11 yards, 9 yards, and 125. yards: how much remained?

24. From 2483 bushels, take the difference between. 3103 and 198 bushels.

25. A dealer owning 394 tons of coal, sold 94 tons to one customer, 1133 tons to another, and 773 tons to a third how much had he left?

26. Illustrate by an original problem subtraction of fractions.

Review Problems.

ORAL EXERCISES.

1. John having $2, gave of a dollar for a reader and of a dollar for an arithmetic: how much had he left?

2. From a piece of cloth containing 12 yards, 3 yards were cut at one time, and 22 yards at another time: how much remained?

3. A man owning 10 and 2 acres to another he keep?

acres, sold 31 to one neighbor neighbor: how many acres did

4. Mary's mother gave her of a pound of candy and her father gave her of a pound. She presented her sister with of a pound: how much did she retain ?

5. Thomas having of a dollar, spent of a dollar · for a ball and of a dollar for a bat: how much had he left?

6. Sarah bought 23 yards of ribbon and used 14 yards on one of her dolls and 14 yards on another doll: how much remained?

7. If William hands a clerk a five-dollar bill in payment for a hat costing $2 and a pair of gloves costing $2 how much change should he receive?

8. One fourth of the length of a pole is in the mud, in the water, and the rest in the air: what part of the pole is in the air?

9. A man owning a ship sold of it to one person and to another: what part of the ship did he still own?

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10. From a cask containing 17 gallons of cider, 113 gallons were sold: how much remained?

11. A man left of his property to his daughter, to his son, and the remainder to his wife: what part of his property did his wife receive ?

12. A farmer having 2 bushels of flax-seed, sold 11 bushels to one man and 1 bushels to another: how much did he keep?

13. Albert bought of a pound of raisins and gave of a pound to each of his two playmates: how much was left ?

14. Thomas having $3, earned $14, and then spent $21 how much had he left?

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15. From a pile of coal containing 11 tons, a dealer sold 43 tons to one customer and 5 tons to another customer how much remained?

16. From a barrel of flour weighing 196 pounds, a grocer sold 37 pounds to one person and 40 pounds to another: how much was left?

17. Mary having $23, bought a pair of gloves for $14 and some lace for of a dollar: how much had she left ?

18. Richard walked 4 miles, Harry 5 miles, and Samuel 2 miles farther than both: how far did Samuel walk?

19. How much greater is 33 + 43 than 23 + 41 ? 20. What is the difference between ++ and Į + 1 + } ?

WRITTEN EXERCISES.

1. From the sum of 32 and 283, subtract the difference between 481 and 33.

2. From 395 bushels take the difference between 317 bushels and 2295 bushels.

3. A man bought a horse for $175, a sleigh for $111, and sold them both for $300: how much did he gain?

4. A farmer owning 248 acres of land, sold 109

acres to one man and 95 acres to another how much was left ?

5. From a piece of cloth containing 133 yards, a tailor cut 73 yards for one customer, and 49 yards for another customer: how many yards remained?

6. Maria having $20, paid $2 for a pair of gloves, $11 for a bonnet, and 4 for some silk how much had she left?

7. A has $114, B has $114, C has $11, and D has of a dollar more than all of them has D?

how much money

He burned 5 tons

8. Mr. B bought 17 tons of coal. in January, 5 tons in February, and 5 tons in March: how many tons remained?

9. From a cask containing 47 gallons of molasses, a grocer sold to one customer 11 gallons, to another 10% gallons, and to another 83 gallons: how many gallons remained?

10. A father willed of his property to each of his three daughters, to each of his two sons, to his wife, and the remainder to his servant: what part of his property was received by his servant?

11. The sum of two fractions is 3 and one of the fractions is: what is the other?

12. The sum of two mixed numbers is 77 and one of them is 333: what is the other?

13. Mr. A paid $3844 for a painting and $275 for another painting: for what sum must he sell the two so as to gain $1137?

14. Three men joined in buying a load of coal containing 3943 tons. A was entitled to 113 tons, and B to 131 tons: to how many tons was C entitled ?

15. Illustrate by an original problem addition and subtraction of fractions.

Multiplication of Fractions.

ORAL EXERCISES.

GENERAL NOTE ON MULTIPLICATION OF FRACTIONS.-Multiply 2 by . The multiplier is of 1, or of 5. Multiplying by the whole of 5, we get 15. But we were not to multiply by 5, but by of 5. Having multiplied by a multiplier 6 times the true multiplier, the product is six times as large as it ought to be. Hence we divide by 6 to obtain the true product, which is done by multiplying the denominator of the multiplicand by 6. Thus 2×1=14=1.

ART. 153.-1. At of a dollar apiece, how much will 3 books cost?

Solution. Three books will cost 3 times of a dollar, or of a dollar, equal to 1 dollars. The result is obtained by multiplying the numerator of the fraction by the whole number and writing the product over the denominator.

2. At of a dollar a yard, what is the cost of 7 yards of camel's hair cloth ?

3. What is the cost of 5 turkeys at $ apiece?

4. At 6 cts. a yd., what is the cost of 6 yds. of calico?

5. What must I pay for 8 pounds of sugar at 62 cents a pound?

6. How much will 10 readers cost at $4 apiece?

7. Warren walked of a mile an hour: how far did he walk in 7 hours?

8. What is the cost of 11 bushels of turnips at of a dollar a bushel ?

9. What must I pay for 9 bbl. of flour at $81⁄2 a bbl. ?

ART. 154. —11. John is 13 years old, and his sister is as old: what is her age ?

Solution. His sister's age is of 13 years, which is 39 years, or 93 years. The result is obtained by multiplying the whole number by the numerator of the fraction and writing the product over the denominator.

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