Divide, Then Multiply!

Imagine eighty-four golden tickets stacked in front of you. Someone asks for three quarters of them. Count them one by one? Far too slow. But watch this... two tiny steps will reveal the answer.

To find a fraction of a quantity, look at the bottom number first. That is the denominator. It tells you how many EQUAL groups to make. So, for one quarter of twelve counters, divide twelve into four equal groups. Each group contains three counters. Equal really matters. If one group has two counters and another has four, those are not quarters. The whole must be shared fairly - every group the same size. Four equal groups of three show four quarters of the twelve. Now look at the top number, the numerator. It tells you how many groups you need. For three quarters, take three of the four equal groups. Divide by the denominator first... then multiply by the numerator. Bottom, then top.

Try this eleven-plus question. A theatre has eighty-four seats. Three quarters are filled. How many seats are filled? Start with the denominator, four. Split all eighty-four seats into four equal groups. So calculate eighty-four divided by four. Eighty-four divided by four is twenty-one. That means ONE quarter is twenty-one seats. Check the groups: four groups of twenty-one rebuild the full eighty-four. Equal groups, with nothing left over. Good. We need three quarters, so take three groups. Twenty-one multiplied by three is sixty-three. Therefore, sixty-three seats are filled. Notice the order: we divided by four, then multiplied by three. We did not divide by three - the numerator tells us how many groups to TAKE.

So remember: denominator means divide into equal groups; numerator means multiply to take the groups you need. Divide by the bottom, multiply by the top... and fractions of quantities are yours!