Dividing Fractions

We now turn to quotients, beginning with dividing a fraction by a whole number. Suppose, for instance, that you want to share of a pizza with a friend, that is, to divide the into two equal parts. What part of the whole pizza will each of you receive?

This diagram shows of a pizza.

If we split the third into two equal parts, each part is of the pizza.

You and your friend will each get of the whole pizza, which you can compute as follows.

Note that dividing a number by 2 is the same as taking of it. This equivalence suggests the procedure for dividing fractions shown on the next page.

This procedure involves inverting, or finding the reciprocal of the divisor. The reciprocal is found by switching the numerator and denominator.

You may want to justify this procedure as follows:

To Divide Fractions

• change the divisor to its reciprocal,
• multiply the resulting fractions, and
• simplify the answer.

EXAMPLE 1

Divide:

Solution

As in any division problem, we can check our answer by multiplying it by the divisor.

Because is the dividend, we have confirmed our answer.

TIP

In a division problem, the fraction to the right of the division sign is ther divisor. Always invert the divisor —the second fraction—not the dividend—the first fraction.

EXAMPLE 2

What is divided by 20?

Solution

EXAMPLE 3

To stop the developing process, photographers use a chemical called stop bath. Suppose that a photographer needs bottle of stop bath for each roll of film. If the photographer has bottle of stop bath left, can he develop 3 rolls of film?

Solution

We want to find out how many ’s there are in that is, to compute .

So the photographer cannot develop 3 rolls of film.