Reciprocal of a Fraction

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

Like this:

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 8 3
56 6 5
197 7 19
12 21 = 2

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

Likewise the reciprocal of 13 is 3 and so on.

Multiplying a Fraction by its Reciprocal

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

Examples:

56 × 65 = 1

13 × 3 = 1

Reciprocal of a Mixed Fraction

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

Example: What is the reciprocal of 2 13 (two and one-third)?

1. Convert it to an improper fraction: 2 13 = 6 3 + 1 3 = 7 3
2. Turn it upside down: 37

The Answer is: 37