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What happens when you multiply reciprocal fractions?

You know that a reciprocal is a fraction whose numerator and denominator have been reversed. For example:

What is the reciprocal of the fraction 1811?

Reverse the order of the numerator and denominator. The reciprocal of 1811 is 1118.

Reciprocals have a special relationship when they are multiplied together. If you multiply a fraction by its reciprocal, the product will always be the number 1. For example:

Show that the fractions 75 and 57 are reciprocals.

You can show that these two fractions are reciprocals by showing that their product is the number 1.

Set up the multiplication problem.

75⋅57

Use cross-cancelation to reduce the fractions before multiplying.

1751⋅1571

Multiply the numerators and then multiply the denominators.

11⋅11=11

Make sure that your answer is in simplest form.

11=1 ÷ 1=1

How well do you understand the concept of a reciprocal fraction? Use the activity below to find out.

1. If two fractions are each other's reciprocal, what is their product?

  1. 12
  2. 0

2. Is the fraction 94 the reciprocal of the fraction 47?

  1. No, because the product of 94 and 47 is not 0.
  2. No, because the product of 94 and 47 is not 12.

3. Which shows that the fractions 53 and 35 are reciprocals?

  1. 53+35=1
  2. 53 ÷ 35=1

Summary

Questions answered correctly:

Questions answered incorrectly:

Question

Does the number 0 have a reciprocal? Why or why not?

Think about how to make a whole number a fraction and how to turn that fraction into a reciprocal.

No, the number 0 does not have a reciprocal. One way to represent the number 0 as a fraction is the fraction 01. This fraction does exist. The reciprocal, if it existed, would be 10. But 10=1 ÷ 0, which is undefined. The number 0 does not have a reciprocal.