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How to Find the Reciprocal of a Fraction (Mathematics Lesson)

Finding the Reciprocal of a Fraction

To find the reciprocal of a fraction, turn the fraction upside down.

The reciprocal of 2 over 3 is 3 over 2

Make the numerator the denominator, and the denominator the numerator.

How to Find the Reciprocal of a Fraction

An Example Question

What is the reciprocal of the fraction below?

three fifths
Step 1

Make the numerator of the fraction the denominator of the reciprocal. In our example, the numerator of the fraction is 3.

The numerator of the fraction (3) becomes the denominator of the reciprocal
Step 2

Make the denominator of the fraction the numerator of the reciprocal. In our example, the denominator of the fraction is 5.

The denominator of the fraction (5) becomes the numerator of the reciprocal

We have found the reciprocal of the fraction:

five thirds

Finding the Reciprocal of a Mixed Fraction

The method above can be used to find the reciprocal of proper and improper fractions, but cannot immediately be applied to mixed fractions.

Mixed fractions must first be converted to improper fractions before the method can be applied.

An Example Question

What is the reciprocal of the mixed fraction below?

three and two thirds

Add a preliminary step.

Step 0

Convert the mixed fraction to an improper fraction.

Three and two thirds equals eleven thirds

The method then continues as before.

Step 1

Make the numerator of the fraction the denominator of the reciprocal. In our example, the numerator of the fraction is 11.

The numerator of the fraction (11) becomes the denominator of the fraction
Step 2

Make the denominator of the fraction the numerator of the reciprocal. In our example, the denominator of the fraction is 3.

The denominator of the fraction (3) becomes the denominator of the fraction

We have found the reciprocal of the fraction:

three elevenths

More Real Examples of How to Find the Reciprocal of a Fraction

The slider below shows another real example of how to find the reciprocal of a fraction.

Interactive Test
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Here's a second test on finding the reciprocal of a fraction.
Here's a third test on finding the reciprocal of a fraction.

Note

What Is a Reciprocal?

The reciprocal of a quantity is the result of dividing 1 by that quantity.

Reciprocal of 5 is 1 over 5

Why Is Finding the Reciprocal of a Fraction Useful?

The reciprocal of a fraction is useful for:

Reciprocal When the Numerator Is 1

Consider a fraction where the numerator is 1:

1 over 2

By finding the reciprocal, the denominator becomes 1:

2 divided by 1

But a number divided by 1 is itself:

2 divided by 1 equals 2

The reciprocal of a fraction with a numerator of 1 is simply the denominator.