Keep, change, flip! Dividing fractions is no problem when you have this mnemonic to guide you through the process.

Using ‘Keep, change, flip' is simple.
*
Keep
*
the first fraction as is,
*
change
*
the sign from division to multiplication, and
*
flip
*
the second fraction, putting the numerator on the bottom and the denominator on the top. Then multiply the two fractions to solve.

Solve

^{ 3 }⁄

_{ 5 }÷

^{ 2 }⁄

_{ 3 }using ‘Keep, change, flip.'

Step 1: Change the division sign to multiplication.

^{ 3 }⁄

_{ 5 }×

^{ 2 }⁄

_{ 3 }

Step 2: Flip the second fraction.

^{ 3 }⁄

_{ 5 }×

^{ 3 }⁄

_{ 2 }

Step 3: Multiply.

^{ 3 }⁄

_{ 5 }×

^{ 3 }⁄

_{ 2 }= (3 × 3) / (5 × 2) =

^{ 9 }⁄

_{ 10 }

Dividing by 2 and multiplying by

^{ 1 }⁄

_{ 2 }are actually the same thing.

10 ÷ 2 = 5

^{ 10 }⁄

_{ 1 }×

^{ 1 }⁄

_{ 2 }=

^{ 10 }⁄

_{ 2 }= 5

The reciprocal of a fraction is its ‘flipped' counterpart--the denominator of one is the numerator of the other, and vice versa. The reciprocal of

^{ 2 }⁄

_{ 3 }is

^{ 3 }⁄

_{2}, and the reciprocal of

^{ 5 }⁄

_{ 6 }is

^{ 6 }⁄

_{5}.

Dividing by a fraction and multiplying by that fraction's reciprocal will always give you the same thing.