When you multiply numbers together, you’re looking at how many groups of, or lots of, something you have.

You can use this same thinking, when you are multiplying fractions. For example:

\( \frac{2}{3} \) × 3 = ?

You can think about this as 3 lots of \( \frac{2}{3} \), or 3 group of \( \frac{2}{3} \), which is 2.

Therefore:

\( \frac{2}{3} \) × 3 = 2

You can multiply fractions by whole integers, or multiply fractions together.

Now, look at this calculation:

6 × \( \frac{1}{2} \) = ?

You are looking for a half group of 6, which is 3.

Sometimes you need to multiply a fraction by another fraction.

\( \frac{1}{4} \) × \( \frac{1}{3} \) = ?

You need to find \( \frac{1}{3} \) of a group of \( \frac{1}{4} \), which is \( \frac{1}{12} \).

You can also find the answer to a calculation using only the fraction symbols.

In this calculation, you are looking for \( \frac{2}{3} \) of a group of \( \frac{5}{6} \):

When you multiply two fractions, you multiply the denominators.

6 multiplied by 3 gives you the new denominator of 18, or eighteenths.

Then multiply the numerators together, to find out how many of these parts there are.

5 multiplied by 2 gives you the new numerator of 10.

So the answer is \( \frac{10}{18} \).