Algebraic fractions can be simplified (or reduced).
Imagine you wanted to simplify
Please tell us using

^{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

Find the top of the fraction (called the numerator). In our example, the numerator is

**4x**.^{2}y## 2

Find the bottom of the fraction (called the denominator). In our example, the numerator is

**2xz**.## 3

Find the greatest common factor of the numerator (4x

^{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**. 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.## You might also like...

algebra curriculumdividing algebraic fractionsfinding the reciprocal of an algebraic fractionhow to find a power of an algebraic fraction

#### Help Us Improve Mathematics Monster

- Do you disagree with something on this page?
- Did you spot a typo?

__this form__.

#### Find Us Quicker!

- When using a search engine (e.g., Google, Bing), you will find Mathematics Monster quicker if you add
**#mm**to your search term.

#### Share This Page

If you like Grammar Monster (or this page in particular), please link to it or share it with others.

If you do, __please tell us__. It helps us a lot!

#### Create a QR Code

Use our handy widget to create a QR code for this page...or any page.