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# Simplifying Algebraic Fractions

(KS3, Year 8)

## The Lesson

Algebraic fractions can be simplified (or reduced). Imagine you wanted to simplify^{ab}⁄

_{bc}.

## How to Simplify Algebraic Fractions

To simplify algebraic fractions, find any numbers, letters or brackets that appear on both the top*and*bottom of the fraction. In our example,

**b**appears on the top and bottom:

Cancel out the letter (b) that appears on the top and bottom of the algebraic fraction:

^{ab}⁄

_{bc}is simplified to

^{a}⁄

_{c}.

## A Real Example of How to Simplify Algebraic Fractions

In the example above,**b**was the greatest common factor of the top and bottom of the fraction, so it could be cancelled. To simplify algebraic fractions, cancel out the greatest common factor of the numerator and denominator.

## Question

Simplify the algebraic fraction below.## Step-by-Step:

# 1

# 2

# 3

Find the greatest common factor of the numerator (4x

The greatest common factor of the numerator and denominator is

^{2}y) and denominator (2xz). List the factors of the numerator and denominator and look at the letters and numbers that are common to both lists.The greatest common factor of the numerator and denominator is

**2x**. Read more about how to find the greatest common factor in algebra# 4

Divide the numerator (4x

^{2}y) by the greatest common factor (2x).
4x

The numerator of the answer is 2xy.
^{2}y ÷ 2x = 2xy# 5

Divide the denominator (2xz) by the greatest common factor (2x).

4x

The denominator of the answer is z.
^{2}y ÷ 2x = 2xy## Answer:

We have simplified the algebraic fraction:## A Quick Example of How to Simplify Algebraic Fractions

In the example above, we listed the factors of the numerator and denominator to find the greatest common factor.If we ignore the common factors in the blue box, we are left with the simplified algebraic fraction:

## What Is an Algebraic Fraction?

An algebraic fraction is a fraction which contains letters.## What Is a Factor in Algebra?

A factor is a quantity that divides exactly into a term. A factor is one of the numbers, letters and brackets (or a product of them) that are multiplied together to make a term.## What Is the Greatest Common Factor in Algebra?

The greatest common factor in algebra is the largest factor that is common to two or more terms.**Help Us To Improve Mathematics Monster**

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