## 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.## Step-by-Step:

# 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.# 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:

**a**,

**b**,

**c**and

**d**are numbers, letters, terms or expressions. Make sure you can: