How to Divide two Fractions?

The trick to dividing fractions is to invert the right hand fraction, and then to change the fraction division to multiplication, which allows the steps for multiplication of two fractions to be used to find the quotient.

The Steps to Dividing two Fractions:

  • convert both fractions to improper fractions (if necessary)
  • the division of fractions then can be turned into a multiplication of the left fraction's numerator by right fraction's denominator, and the left fraction's denominator by the right fraction's numerator
  • reduce the resultant fraction to its lowest terms.

For example, to divide the following fractions :

 2  2
3
÷
 1  3
4

(Two and Two-Thirds divided by One and Three Quarters)

Step 1: Convert both fractions to improper (vulgar) Fractions, by multiplication of the whole number of each fraction by its denominator and adding to the numerator: 

=
  (2 x 3) + 2
3
÷
  (1 x 4) + 3
4
=
  8
3
÷
  7
4

Step 2: Multiply the left fraction's numerator by the right fraction's denominator, and the left fraction's denominator by the right fraction's numerator :

=
  8 x 4
3 x 7
=
  32
21

Step 3: Check whether the fractions can be reduced to simpler forms and improper fractions 

=
  21 + 11
21
=
 1  11
21

Try this for yourself on our Fraction Arithmetic Calculator

 

Alternative method

As an alternative to Step 2, you can invert the right hand side fraction and change the fraction division into a multiplication:

=
  8
3
÷
  7
4

Is the same as

=
  8
3
x
  4
7

Which results in the quotient:

=
  32
21
=
  21 + 11
21
=
 1  11
21

And this is how to divide fractions!