Succeed with maths – Part 1
Succeed with maths – Part 1

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Succeed with maths – Part 1

3 Introduction to dividing fractions

Dividing fractions is a little more difficult, so you’ll start by considering simple examples. You’ll then attempt to translate that to a more complex question by applying a similar strategy.

Suppose that you have three pizzas, and you divide each of them in half (see Figure 5).

Figure _unit5.3.1 Figure 5 Three circles, each divided into half

How many halves do you have? You can see that there are six halves in three pizzas. Thus this shows how many halves there are in three. This is the same as dividing 3 by a one divided by two. When you calculate three division one divided by two, you can think of this as ‘How many halves are there in three?’ Here are few similar examples to work out how to divide by fractions. There are three pizzas again, but this time the question is 'How many thirds can they be cut up into?' (Figure 6). This is the same as asking what is three division one divided by three.

Figure _unit5.3.2 Figure 6 Three circles, divided into thirds

From this, you can see that there are 9 thirds in 3. So three division one divided by three times multiline equation line 1 line 2 equals nine.

Now divide these three pizzas into quarters, which gives the answer to three division one divided by four. Each pizza will be cut into four parts to give quarters and there are three pizzas, so the total number of slices will be three multiplication four equals 12.

You also know that three division one divided by two times multiline equation line 1 line 2 equals six. Looking at these three calculations, can you see a way of arriving at the answers without drawing out a picture to help? Look at the whole numbers and the denominators.

You may have noticed that if you multiply these together, then you arrive at the answer.

So it seems that equation left hand side three division one divided by two equals right hand side three multiplication two, equation left hand side three division one divided by three equals right hand side three multiplication three and equation left hand side three division one divided by four equals right hand side three multiplication four.

So put into words, you can say that to divide by a fraction, you have to swap the numerator and the denominator, and then multiply.

Or, in mathematical language (so that you can communicate this clearly and concisely to others): when the numerator and denominator change places, the result is called the reciprocal of the original fraction. Thus, dividing by a fraction is the same as multiplying by its reciprocal.

In the next section you’ll look at this in practice.

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