Why Fractions?

Do we really need them and why are they so awkward to work with?

Well ‘yes’ is the answer to the first part of the question. And with a bit of understanding, they are not so awkward.

First a few simple divisions.

1. 12÷4     2. 28÷7     3. 48÷6     4. 96÷8

No problems here, the answers are all integers (whole numbers)

But what about?

5. 3÷4     6. 5÷6     7. 3÷7     8. 1÷2     9. 7÷3

You might reach for a calculator and find that the answers all are decimals, but easier than this is:-

And this is where fractions come from. When one number does not divide exactly by another then fractions are needed.

In fact using fractions means that the ÷ sign is not needed at all.

If you want to write you just write

Because fractions are a way of writing division and division is the exact opposite of multiplication, multiplying fractions is easy

eg. Just multiply the tops (the numerators) and multiply the bottoms (the denominators).

And division is almost as easy

eg.

So you never need to divide, just turn the second number upside down ("invert the divisor" if you want to be technical) and multiply.

A few questions to practise on.

Answers               Adding and Subtracting Fractions

Return to Homepage