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22. If of a square is divided into 2 equal parts, what fraction of the square is each part? Then ÷ 2 = 1.

23. If of a square is divided into 2 equal parts, what fraction of the square is each part? Then ÷ 2 = 1. ÷2=1.

24. If of a square is divided into 8 equal parts, what fraction of the square is each part? Then +8=1.

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25. Since ÷ 2 = 1, 1 ÷ 2 = }, and 1÷8=1, how may we divide a fraction by a whole number without dividing the numerator by the whole number?

A fraction may be divided by a whole number by multiplying the denominator by the whole number.

26. In g 3 is it easier to divide the numerator or to multiply the denominator? in § ÷ 5?

27. State the easier method of dividing: by 3; ₫ by 2; 1 by 2; 7 by 7; 8 by 4; 8 by 5.

28. Under what conditions is it easier to divide the numerator? when is it easier to multiply the denominator?

Observing the two methods, divide the following fractions, using the method best adapted to the problem:

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5

=

6

5

=

5

6×4 24

Since multiplying the denominator of a fraction divides the fraction, to divide by 4, multiply the denominator by 4.

3. If 8 yards of ribbon cost $1, find the cost of 1 yard. 4. I bought 6 gallons of oil for $1%. What was the price per gallon?

5. A boy earns $ in a day by working 9 hours. How much does he earn in an hour?

6. If 5 dozen bananas cost $4, how much does 1 dozen cost?

7. Eight men in a day complete 13 of a piece of work. How much of the work could one man complete in a day? 8. It takes of a thousand feet of lumber to make 12 boxes. How many feet are there in each box?

9. If 12 panes of glass cost $3, how much does one pane cost?

10. If 17 handkerchiefs cost $17, how many cents does each cost?

11. In of a day a man earns $9. How long does it take him to earn $1?

12. In of an hour an oil well produces 33 barrels of oil. How long does it take it to produce one barrel?

Dividing any number by a fraction by inverting the terms

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Observe that in each of the examples given above the quotient equals 1 x the denominator, or 1 × 2, 1 × 1, 1 × 51, 1 × 1, 1 × 1, 1 × §.

3. Divide 12 successively by 2, 3, 4, 6. The quotients, 6, 4, 3, 2 respectively, become smaller as the divisors become larger. Then if 1÷= will the quotient of 1÷ be larger or smaller than? Since is 3 times as large as 1, the quotient of 1 ÷

=

=

will be

4. 1÷, and 1 ÷

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of the quotient of 1÷; } of 1 = 1. = 1 of §. 1+1=4, and 1+ § ᄒ

= 1 of {

=

} of. Find the quotients of 1; 1+7; 1÷&;

1. Notice that in every case the quotient equals the divisor with its terms inverted.

The number of times a fraction is contained in 1 equals the denominator of the fraction divided by the numerator, or the fraction inverted.

Find quotients by inverting the divisor and multiplying: Thus: 33 × 1 = 45 = 31.

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1. Divide 128 by 18.

8

16

128÷ =

25

16

128 × 25

Written Work

Since is contained in 1, § times,

= 200 is contained in 128, 128 × 4 or 200 times.

Any number may be divided by a fraction by inverting the terms of the divisor and multiplying.

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2. If a unit is first divided into halves and then each half into halves, into how many parts is the unit divided? Is of a unit larger or smaller than 1⁄2 of a unit?

3. Divide a unit into halves, fourths, eighths, and sixteenths, and show how many sixteenths of a unit it takes to make of the unit; of the unit; of the unit;

unit.

4. Draw equal squares to show that

= or

8

5. Compare and † ; ‡ and 12; § and . 6. How does

with of 16?

of the

of 20 compare with of 20? of 16 of 50 with 1 of 20?

7. A has 40 acres of land, and B 60 acres.

farm compare in size with B's?

8. 8 is what part of 12, 16, 24, 32, 48, 72?

How does A's

SUGGESTION.Make 8 the numerator in each case and the other numbers the denominators and reduce the fractions to their lowest terms. Thus ; ft = 1; 24 = }, etc.

9. If 5 quarts of milk cost 45 cents, how much will 12 quarts cost? 18 quarts? 24 quarts?

10. Elizabeth buys 31 yards of ribbon for 35 cents. At the same rate, how much would she pay for 10 yards?

SUGGESTION. How many times 3 is 101?

11. A woodsman cuts 15 cords of wood in 6 days. How many cords, at the same rate, could he cut in 48 days? 12. Compare 8 and 2; 6 and 4; 2 and 8; 5 and 10.

13. Compare and 1; 1 and 1; 1 and 12.

14. Compare 24 with 4, 6, 8, 48, 72, 16, 20.

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