# Dividing Algebraic Fractions

Algebraic fractions can be divided.

Imagine you wanted to divide ab by cd.

# How to Divide Algebraic Fractions

To divide algebraic fractions, use the rule:

# A Real Example of How to Divide Algebraic Fractions

#### An Example Question

Divide the algebraic fractions below.

Step 1

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

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:

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:

# Another Real Example of How to Divide Algebraic Fractions

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

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# Understanding The Rule

Dividing fractions requires:

• replacing the divisor (the fraction you are dividing by) with its reciprocal...

• ... and replacing the division with a multiplication:

Then the fractions can be multiplied:

• multiplying the numerators together to form the numerator of the product...

• ... and multiplying the denominators together to form the denominator of the product:

This gives the rule:

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: