Dividing Algebraic Fractions
(KS3, Year 8)

The Lesson

Algebraic fractions can be divided. Imagine you wanted to divide ab by cd.

a over b divide by c over d

How to Divide Algebraic Fractions

To divide algebraic fractions, use the rule:

a over b divide by c over d equals a d over b c

A Real Example of How to Divide Algebraic Fractions

Question

Divide the algebraic fractions below.
x over 2 divide by y over 3

Step-by-Step:

1

Compare the fractions you are dividing with the rule shown above.

compare a over b divide by c over d and x over 2 divide by y over 3 By comparing, we see that a = x, b = 2, c = y, d = 3.

2

Use the rule, with a = x, b = 2, c = y, d = 3:

a c over b d, replacing a with x, b with 2, c with y and d with 3

3

Calculate the terms in the rule. Where we have written two numbers or letters in brackets together, multiply them together:
(x)(3) = x × 3 = 3x (2)(y) = 2 × y = 2y

Answer:

We have divided x2 by y3:

x over 2 divide by y over 3 equals 3 x over 2 y

Lesson Slides

The slider below shows a real example of how to divide algebraic fractions. Open the slider in a new tab

Understanding The Rule

a over b divide by c over d equals a d over b c Dividing fractions requires:
  • replacing the divisor (the fraction you are dividing by) with its reciprocal...
  • ... and replacing the division with a multiplication:

    flip c over d upside down to make d over c and multiply it with a over b
Then the fractions can be multiplied:
  • multiplying the numerators together to form the numerator of the product...

    a times d equals a d
  • ... and multiplying the denominators together to form the denominator of the product:

    b times c equals b c
This gives the rule:

a over b over c over d equals a d over b c The letters written next to each other means that they are multiplying each other. The rule works when the a, b, c and d are numbers, letters, terms or expressions. Make sure you can:

Top Tip

Cancelling Terms

When the numerator of one fraction equals the denominator of the other fraction, they cancel each other out:

Cancel out the b that is on the top and bottom of the fraction This is how to simplify algebraic fractions.
Help Us To Improve Mathematics Monster

  • Do you disagree with something on this page?
  • Did you spot a typo?
Please tell us using this form

See Also

What is algebra? What is an algebraic fraction? What is a numerator? What is a denominator? Finding the reciprocal of a fraction Multiplying letters Multiplying terms Multiplying expressions Simplifying algebraic fractions