How to Multiply Algebraic Fractions

Multiplying Algebraic Fractions

Algebraic fractions can be multiplied.

Imagine you wanted to multiply ab and cd.

a over b times c over d

How to Multiply Algebraic Fractions

To multiply algebraic fractions, use the rule:

a over b times c over d equals a c over b d

A Real Example of How to Multiply Algebraic Fractions

Question

Multiply the algebraic fractions below.

x over 2 times y over 3

Step-by-Step:

1

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

compare a over b times c over d and x over 2 times 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 c over b d, 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)(y) = x × y = xy

(2)(3) = 2 × 3 = 6

Answer:

We have multiplied x2 and y3 together:

x over 2 times y over 3 equals x 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 Simplifying algebraic fractions