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Dividing Algebraic Fractions
(KS3, Year 8)
The Lesson
Algebraic fractions can be divided. Imagine you wanted to divide ^{a}⁄_{b} by ^{c}⁄_{d}.How to Divide Algebraic Fractions
To divide algebraic fractions, use the rule:A Real Example of How to Divide Algebraic Fractions
Question
Divide the algebraic fractions below.StepbyStep:
1
Compare the fractions you are dividing with the rule shown above.
By comparing, we see that a = x, b = 2, c = y, d = 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:
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 ^{x}⁄_{2} by ^{y}⁄_{3}:Understanding The Rule
Dividing fractions requires: replacing the divisor (the fraction you are dividing by) with its reciprocal...

... and replacing the division with a multiplication:

multiplying the numerators together to form the numerator of the product...

... and multiplying the denominators together to form the denominator of the product:
The letters written next to each other means 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.
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