How to Simplify Algebraic Fractions

Simplifying Algebraic Fractions

Algebraic fractions can be simplified (or reduced).

Imagine you wanted to simplify abbc.

a b over b c

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:

a b over c c

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

a b over b c equals a over c

abbc is simplified to ac.

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.

x over 2 plus y over 3

Step-by-Step:

1

Find the top of the fraction (called the numerator). In our example, the numerator is 4x2y.

The numerator is 4 x squared y

2

Find the bottom of the fraction (called the denominator). In our example, the numerator is 2xz.

The denominator is 2 x z

3

Find the greatest common factor of the numerator (4x2y) 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 is 2 x

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 (4x2y) by the greatest common factor (2x).

4x2y ÷ 2x = 2xy

The numerator of the answer is 2xy.

5

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

4x2y ÷ 2x = 2xy

The denominator of the answer is z.

Answer:

We have simplified the algebraic fraction:

4 x squared y over 2 x z equals 2 x y over z

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.

The greatest common factor is 2 x

If we ignore the common factors in the blue box, we are left with the simplified algebraic fraction:

The remaining factors are 2 x y and z

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See Also

What is algebra? What is an algebraic fraction? What is a numerator? What is a denominator? What is the greatest common factor? Finding the greatest common factor in algebra What is a factor?