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.
Reciprocal of 7.
- 2.
Reciprocal of −2.
- 3.
Reciprocal of 2/9.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
What is the reciprocal of −3/4? Verify by multiplying.
- 2.
If the reciprocal of x is −2/5, what is x?