1. Algebraic Fractions
Algebraic fractions are exactly what their name suggests:
fractions with algebra in!
Here is an example of an algebraic fraction:
Note that this cannot be cancelled!
Just as with ordinary fractions, you can multiply, divide, add and
subtract algebraic fractions. In fact, the methods are similar.
Algebraic fractions crop up a lot in C3 and C4 – today you will look at how to multiply and divide them.

2. Algebraic Fractions
Multiplying first. Just as with multiplying ordinary fractions, you
multiply the tops (numerators) together, then multiply the
bottoms (denominators) together.
Example:
The answer is:

3. Algebraic Fractions: Questions
Simplify these, leaving your answers in their lowest forms.

4. Algebraic Fractions: Answers

5. Leave as factorised as possible!
Algebraic Fractions
Sometimes the multiplication can be made easier by cancelling.
Example:
This looks like it will take a while! Can you do any cancelling
before you start multiplying, to make it quicker?
Leave as factorised as possible!
Yes! 3x + 15 is 3 (x + 5), so you can cancel: 3

6. Algebraic Fractions Finally... Example:
Factorise as much as possible to see what to cancel. That gives:
Cancelling gives:

7. Algebraic Fractions: Questions
Simplify these, giving your answers in their lowest terms.

8. Algebraic Fractions: Answers

9. Algebraic Fractions Now look at dividing algebraic fractions. Example:
As with ordinary fractions you use a trick to divide. Turn the
fraction on the right upside down and multiply instead:
Then proceed as before. The answer is:

10. Algebraic Fractions Example:
Again find the reciprocal of the fraction on the right and
multiply. Can you do any cancelling before the multiplying?
Yes!

11. Algebraic Fractions: Questions
Simplify these, leaving your answers in their lowest terms.

12. Algebraic Fractions: Answers

13. Algebraic Fractions: Plenary
From C3 Specimen Paper:
Express
as a single fraction in its simplest form.
Reveal Answer