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

Like this (press play button):

Fractions

A Fraction (such as ^{3}/_{4}) has two numbers:

Numerator

Denominator

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

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

^{3}/_{8}

^{8}/_{3}

^{5}/_{6}

^{6}/_{5}

^{1}/_{3}

^{3}/_{1} = 3

^{19}/_{7}

^{7}/_{19}

Reciprocal of a Mixed Fraction

To find the reciprocal of a Mixed Fraction, you must first convert it to an Improper Fraction, then switch the numerator and denominator of the improper fraction.

Example: What is the reciprocal of 2 ^{1}/_{3} ?

1. Convert it to an improper fraction: 2 ^{1}/_{3} = ^{7}/_{3}
2. Swap the numerator and denominator: ^{3}/_{7}

The Answer is: ^{3}/_{7}

Multiplying a Fraction by its Reciprocal

If you multiply a fraction by its reciprocal you get 1:

^{5}/_{6} × ^{6}/_{5} = 1

^{1}/_{3} × 3 = 1

That's all. It is just too easy to talk any more about it.