Follow Us on Twitter

How to Divide Algebraic Fractions (Mathematics Lesson)

Dividing Algebraic Fractions

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

An Example Question

Divide the algebraic fractions below.

x over 2 divide by y over 3
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.

Step 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
Step 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

We have divided x2 by y3:

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

Another Real Example of How to Divide Algebraic Fractions

The slider below shows a real example of how to divide algebraic fractions.

Interactive Test
  show
 

Here's a second test on dividing algebraic fractions.
Here's a third test on dividing algebraic fractions.

Note

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: