How to Divide Algebraic Fractions (Mathematics Lesson)
Dividing Algebraic Fractions
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
An Example Question
Divide the algebraic fractions below.
Compare the fractions you are dividing 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)(3) = x × 3 = 3x
(2)(y) = 2 × y = 2y
We have divided ^{x}⁄_{2} by ^{y}⁄_{3}:
Another Real Example of How to Divide Algebraic Fractions
The slider below shows a real example of how to divide algebraic fractions.
Interactive Test
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Note
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:
Then the fractions can be multiplied:

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 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: