# Reciprocals

Example 1: What is the relationship between three-fourths and four-thirds?

Analysis: Let's try finding three-fourths of four-thirds. The word OF means "times", which indicates that we need to multiply.

Solution:

Answer: The product of three-fourths and four-thirds is 1.

This product is no coincidence. Three-fourths and four-thirds are reciprocals.

Definition:   Two numbers whose product is 1 are called reciprocals of each other.

Reciprocals come in pairs. We can find the reciprocal of a nonzero number in fractional form by inverting it (that is, by switching positions of the numerator and denominator).

### Watch This Fraction in Action!

Let's look at some more examples of reciprocals.

Example 2: The following pairs of numbers are reciprocals.

Note that the last fraction listed above was an improper fraction. To find the reciprocal of a mixed number, you must convert it to an improper fraction first.

Example 3: What is the reciprocal of 3 and 1/2?

Solution Step 1:

Solution Step 2:

Example 4: What is the reciprocal of 5 and 7/8?

Solution Step 1:

Solution Step 2:

Summary: Two numbers whose product is 1 are called reciprocals of each other.

### Exercises

Directions: Find the reciprocal of each number below. Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.

Note: To write the fraction three-fourths, enter 3/4 into the form.