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4. Multiply 41 by 67; 161 by 41; 61 by 81; 92 by 8 125 by 93; 2 of 183 by 44.

Find the cost of:

5. 25 cords of wood at $73 a cord. 6. 4 tons of hay at $18.50 a ton. 7. 25 pairs of shoes at $6.371⁄2 a pair. 8. 30 yards of ribbon at $.121⁄2 a yard. 9. 63 pounds of beef at $.124 a pound. 10. How many feet are there in 53 rods?

11. I bought 36 pounds of coffee at 30 a pound, and sold it at a gain of 20%. How much did I receive for it?

12. At $10 a ton, how much will of a ton of straw cost?

13. How many yards are there in 24 rods?

14. If oranges are sold at the rate of 3 for 10%, how much will be paid for 124 dozen?

15. A merchant sold 3 pieces of silk containing 17 yd., 133 yd., 18ğ yd. respectively at $1.92 a yard. How much did he receive for the silk?

=

16. $1 + $1 + $ how many cents?

17. What is 75% of $422? .75 of $422?

LESSON 56

1. By what number must you multiply both terms of the fraction to change it to 18? Is 18 greater than ?

30

30

2. How many rods are there in 3 of 3 of a mile? In of of a mile ?

GRAD. ARITH. V. - -5

3. Change to 36ths.

By what number must you multiply both terms of to change it to 36ths? How do you find the number by which you must multiply?

4. How many 36ths are there in 1? In ? In å? 5. In changing 14 to 8ths, are the fractional parts larger or smaller? Are there more or less parts?

6. What does the denominator of a fraction show?

7. Name three common divisors of 24 and 36, and tell which is greatest.

8. How many seconds are there in of 2 minutes?

9. A man has a garden 12 rd. long and 10 rd. wide. How many square rods are in of it? How many square yards are in1⁄2 of it?

10. What are of 23? of 31? % of 61 ? of 4?

11. A lady bought at one time 23 yards of tape and at another 3 yards. How much did it all cost her at 12 a yard?

12. Minnie bought of a yard of lace and used of it. What part of a yard had she left?

13. A man who owned of 263 acres of land sold ₫ of what he owned. How many acres did he sell?

14. Julia is 15 years old, and her grandfather is 4 times as old. How old is her grandfather?

LESSON 57

1. What part of a yard is 1 foot? What per cent of a quantity is of it? What per cent of a yard is 1 foot? 2. What part of a yard is 2 feet? What per cent of a quantity is of it? What per cent of a yard is 2 feet?

3. 6 is what part of 24? 6 is what per cent of 24 ? 4. What per cent of a day is 6 hr. ? 5. 25 is what part of a dollar? cent of a dollar?

6. What part of $100 is $25 ? of $100?

7. 75 is what part of $1?

75

8. 4 is what per cent of 8? 32?

12 hr. ? 8 hr. ? 25 is what per

$25 is what per cent

is what per cent of $1? 12? 16? 20? 24?

9. If a man bought an article for $12 and sold it for $15, how many dollars did he gain? The gain is what part of the cost? The gain is what per cent of the cost? 10. What per cent of a bushel is 8 qt.? 16 qt. ?

11. A man sold goods that cost $20 for $25. How much did he gain? The gain is what part of the cost? The gain is what per cent of the cost?

12. If $4 is of what John paid for a hat, $4 is what per cent of its cost?

13. If $9 is 50 % of the cost of a coat, find the cost.

14. How many sheets of paper are there in a quire? 12 sheets are what part of quire? 12 sheets are what per cent of a quire?

DIVISION

LESSON 58

1. If 2 pocket knives cost $, what is the price of one? What is of ? 1 × 1 = ?

How do you divide a fraction by an integer (whole number) when the numerator of the fraction is a multiple of the divisor?

2. What is the cost of 1 book if 4 cost $285

?

3. If is divided equally among 3 boys, what part of a dollar does each receive?

4. If 3 mental arithmetics cost $, what is the price of one? What is of ? × ? =

How do you divide a fraction by an integer when the numerator of the fraction is not a multiple of the divisor? 5. Divide by 4.

MODEL. To divide a number by 4 is to find of it. | of } = 3. 6. Divide by 2, 3, 4, 5, 6, 7, 8, 9, 10.

7. Divide ğ by 5, 3, 7, 8, 6, 4, 2, 9, 10.

8. How many times is 3 contained in ? ? ? 11?

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Since dividing a number by 6 is the same as finding of it, we proceed as in multiplication. By canceling the common factor 6, and multiplying, we get, the required quotient.

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12. If it takes 43 yards of cloth to make 5 suits of clothes, how many yards will be needed to make one suit? 12 suits?

13. A boy picked 153 quarts of berries in 2 hours. At the same rate, how many quarts would he pick in 1 hour? 5 hours?

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18 contains 1, 18 times, 18 contains 4, 4 times 18, or 72 times, 18 contains, of 4 times 18, or of 18, or 3 × 18, which, by cancellation

4

1

6

× 18 = 24 Ans.

Therefore, to divide a fraction, we invert the divisor and proceed as in multiplication of fractions.

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