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20. From a bin containing 428.; bushels of wheat, 317 bushels were sold : how many bushels remained ?

21. A man bought a horse for $2314 and sold it for $2193 : what was the loss ?

22. A lady gave a clerk a twenty dollar bill in payment for 2 pairs of gloves at $1} a pair, some ribbon worth $7), and some lace worth $510 : how much change did she receive?

23. From a piece of cloth containing 334 yards, i clothier cut 11į yards, 9f yards, and 125. yards : how much remained ?

24. From 2487 bushels, take the difference between 3103 and 198, bushels.

25. A dealer owning 3947 tons of coal, sold 944 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, 34 yards were cut at one time, and 24 yards at another time : how much remained ?

3. A man owning 10% acres, sold 37 to one neighbor and 2} acres to another neighbor : how many acres did he keep ?

4. Mary's mother gave her i 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 i% of a dollar, spent # of a dollar for a ball and 3 of a dollar for a bat : how much had he left ?

6. Sarah bought 23 yards of ribbon and used 1} 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 $27 and a pair of gloves costing $210, 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 put to another : what part of the ship did he still own ?

10. From a cask containing 177 gallons of cider, 11} gallons were sold : how much remained ?

11. A man left 4 of his property to his daughter, s to his son, and the remainder to his wife : what part of his property did his wife receive ?

12. A farmer having 24 bushels of flax-seed, sold 1} bushels to one man and 17 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 $24 : how much had he left ?

15. From a pile of coal containing 11 tons, a dealer sold 43 tons to one customer and 54 tons to another customer : how much remained ?

16. From a barrel of flour weighing 196 pounds, a grocer sold 374 pounds to one person and 404 pounds to another: how much was left ?

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

18. Richard walked 44 miles, Harry 58 miles, and Samuel 24 miles farther than both : how far did Samuel walk ?

19. How much greater is 3} + 43 than 2+ 4} ?

20. What is the difference between + + and } + + + ?

WRITTEN EXERCISES. 1. From the sum of 324 and 283, subtract the difference between 481 and 333.

2. From 395 bushels take the difference between 3177 bushels and 2293 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 2484 acres of land, sold 1094

acres to one man and 954 acres to another: how much was left ?

5. From a piece of cloth containing 1334 yards, a tailor cut 738 yards for one customer, and 49% yards for another customer : how many yards remained ?

6. Maria having $20, paid $24 for a pair of gloves, $11} for a bonnet, and 41% for some silk : how much had she left ?

7. A has $114, B has $114, C has $117), and D has 1% of a dollar more than all of them : how much money has D?

8. Mr. B bought 174 tons of coal. He burned 54 tons in January, 54 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 117 gallons, to another 10% gallons, and to another 87 gallons : how many gallons remained ?

10. A father willed ☆ of his property to each of his three daughters, } to each of his two sons, t 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 53 and one of the fractions is £ : what is the other ?

12. The sum of two mixed numbers is 771 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 $11317 ?

14. Three men joined in buying a load of coal containing 3943 tons. A was entitled to 113; tons, and B to 1314 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 { by The multiplier is of 1, or ở of 5. Multiplying å by the whole of 5, we get leo. 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•

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 14 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 $ ty apiece ? 4. At 64 cts. a yd., what is the cost of 6 yds. of calico ?

5. What must I pay for 8 pounds of sugar at 6x cents a pound ?

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

7. Warren walked ã 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 $8 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 å of 13 years, which is 32 years, or 9 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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