Multiplying Algebraic Fractions
(KS3, Year 8)

The Lesson

Algebraic fractions can be multiplied. Imagine you wanted to multiply ab and cd.

a over b times c over d

How to Multiply Algebraic Fractions

To multiply algebraic fractions, use the rule:

a over b times c over d equals a c over b d

A Real Example of How to Multiply Algebraic Fractions

Question

Multiply the algebraic fractions below.
x over 2 times y over 3

Step-by-Step:

1

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

compare a over b times c over d and x over 2 times 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)(y) = x × y = xy (2)(3) = 2 × 3 = 6

Answer:

We have multiplied x2 and y3 together:

x over 2 times y over 3 equals x y over 6

Lesson Slides

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

Understanding The Rule

a over b times c over d equals a c over b d Multiplying fractions requires:
  • multiplying the numerators together to form the numerator of the product...

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

    b times d equals b d
This gives the rule:

a over b times c times d equals a c over b d The letters written next to each other denotes 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.
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See Also

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