Division

2-8The Reciprocal of a Real Number

Overview

The reciprocal of a (a ≠ 0) is 1/a. A number times its reciprocal equals 1.

Key ideas

  • Reciprocal of a/b is b/a.
  • 0 has no reciprocal.
  • Reciprocal of a negative number is also negative.

Worked examples

Example 1

Problem. Reciprocal of 5.

Solution. 1/5

Example 2

Problem. Reciprocal of −3/4.

Solution. −4/3

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Reciprocal of 7.

  2. 2.

    Reciprocal of −2.

  3. 3.

    Reciprocal of 2/9.

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    What is the reciprocal of −3/4? Verify by multiplying.

  2. 2.

    If the reciprocal of x is −2/5, what is x?