How to Divide Algebraic Fractions

Dividing Algebraic Fractions

Algebraic fractions can be divided.

Imagine you wanted to divide ab by cd.

a over b divide by c over d

How to Divide Algebraic Fractions

To divide algebraic fractions, use the rule:

a over b divide by c over d equals a d over b c

A Real Example of How to Divide Algebraic Fractions

Question

Divide the algebraic fractions below.

x over 2 divide by y over 3

Step-by-Step:

1

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

compare a over b divide by c over d and x over 2 divide by 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)(3) = x × 3 = 3x

(2)(y) = 2 × y = 2y

Answer:

We have divided x2 by y3:

x over 2 divide by y over 3 equals 3 x over 2 y

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See Also

What is algebra? What is an algebraic fraction? What is a numerator? What is a denominator? Finding the reciprocal of a fraction Multiplying letters Multiplying terms Multiplying expressions Simplifying algebraic fractions