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Succeed with maths: part 1
Succeed with maths: part 1

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3.1 Practising dividing fractions

You now know that to divide by a fraction, you convert the second fraction (the one you are dividing by) into its reciprocal, then multiply by that fraction instead.

Just once more, consider six division two divided by five.

If you swap the numerator and the denominator of two divided by five, you will have five divided by two: this is the reciprocal of two divided by five.

Thus, equation sequence part 1 six division two divided by five equals part 2 six multiplication five divided by two equals part 3 six cubed divided by one multiplication five divided by two sub one equals part 4 three divided by one multiplication five divided by one equals part 5 15 divided by one equals part 6 15

So, dividing a number by two divided by five is the same as multiplying the number by five divided by two.

This process of finding the reciprocal of the fraction that appears after the division sign, and then multiplying by that value, can be used in any division problem.

Take the example below.

Aman wants to know how fast she was driving. She drove three divided by five of a mile in half a minute. To work out speed, you need to divide distance by time. Therefore you can work out how fast she was driving by doing three divided by five divided by one divided by two. Using the rule for dividing fractions, that means three divided by five multiplication two divided by one equals six divided by five. So, Aman was driving at six divided by fiveor one and one divided by fiveper minute.

Now you are going to look at dividing mixed numbers and fractions.