Reciprocal Of A Fraction - Math Is Fun

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Reciprocal of a Fraction

To get the reciprocal of a fraction, turn it upside down.

Like this:

numbers/images/reciprocal.js?numer=3&denom=4

Fractions

A Fraction (such as 34) has two numbers:

NumeratorDenominator

We call the top number the Numerator, it is the number of parts we have. We call the bottom number the Denominator, it is the number of parts the whole is divided into.

dog upside down

Reciprocal of a Fraction

To get the reciprocal of a fraction, just turn it upside down. In other words swap over the Numerator and Denominator.

Examples:

Fraction Reciprocal
38 83
56 65
197 719
12 21 = 2

That last example was interesting. The reciprocal of 12 is 2

This works for unit fractions (fractions that have 1 on top). For example:

  • The reciprocal of 14 is 4
  • The reciprocal of 19 is 9

Multiplying a Fraction by its Reciprocal

When we multiply a fraction by its reciprocal we get 1:

Example:

56 × 65 = 1

Because when we multiply fractions we multiply the top numbers together and the bottom numbers together like this:

56 × 65 = 5 × 66 × 5 = 3030 = 1

Example:

13 × 3 = 1

Because:

13 × 3 = 13 × 31 = 33 = 1

Reciprocal of a Mixed Fraction

To find the reciprocal of a Mixed Fraction, we first convert it to an Improper Fraction, then turn that upside down.

Example: What is the reciprocal of 213 (two and one-third)?

1. Convert it to an improper fraction: 213 = 63 + 13 = 73 2. Turn it upside down: 37

The Answer is: 37

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