How to Add Algebraic Fractions

Adding Algebraic Fractions

Algebraic fractions can be added.

Imagine you wanted to add ab and cd.

a over b plus c over d

How to Add Algebraic Fractions

To add algebraic fractions, use the rule:

a over b plus c over d equals a d plus b c over c d

A Real Example of How to Add Algebraic Fractions

Question

Add the algebraic fractions below.

x over 2 plus y over 3

Step-by-Step:

1

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

compare a over b plus c over d and x over 2 plus 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 d plus bc over bd, 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)(3) = x × 3 = 3x

(2)(y) = 2 × y = 2y

(2)(3) = 2 × 3 = 6

Answer:

We have added x2 and y3:

x over 2 plus y over 3 equals 3 x plus 2 y over 6

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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