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# Multiplying Algebraic Fractions

(KS3, Year 8)

## The Lesson

Algebraic fractions can be multiplied. Imagine you wanted to multiply^{a}⁄

_{b}and

^{c}⁄

_{d}.

## How to Multiply Algebraic Fractions

To multiply algebraic fractions, use the rule:## A Real Example of How to Multiply Algebraic Fractions

## Question

Multiply the algebraic fractions below.## Step-by-Step:

# 1

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

By comparing, we see that

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:# 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^{x}⁄

_{2}and

^{y}⁄

_{3}together:

## Understanding The Rule

Multiplying fractions requires:-
multiplying the numerators together to form the numerator of the product...

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

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:This is how to simplify algebraic fractions.

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