How to Multiply Algebraic Fractions (Mathematics Lesson)
Multiplying Algebraic Fractions
Algebraic fractions can be multiplied.
Imagine you wanted to multiply ^{a}⁄_{b} and ^{c}⁄_{d}.
How to Multiply Algebraic Fractions
To multiply algebraic fractions, use the rule:
A Real Example of How to Multiply Algebraic Fractions
An Example Question
Multiply the algebraic fractions below.
Compare the fractions you are multiplying with the rule shown above.
By comparing, we see that a = x, b = 2, c = y, d = 3.
Use the rule, with a = x, b = 2, c = y, d = 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
We have multiplied ^{x}⁄_{2} and ^{y}⁄_{3} together:
Another Real Example of How to Multiply Algebraic Fractions
The slider below shows a real example of how to multiply algebraic fractions.
Interactive Test
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Here's a third test on multiplying algebraic fractions.
Note
Understanding the Rule
Multiplying fractions requires:

multiplying the numerators together to form the numerator of the product...
 ... and multiplying the denominators together to form the denominator of the product:
This gives the rule:
The letters written next to each other denotes that they are multiplying each other.
The rule works when the a, b, c and d are numbers, letters, terms or expressions.
Make sure you can:
Top Tip
Cancelling Terms
When the numerator of one fraction equals the denominator of the other fraction, they cancel each other out:
This is how to simplify algebraic fractions.