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Numbers, units and arithmetic

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# Try some yourself

## Activity 46

Evaluate each of the following.

• (a)

• (b)

• (c) of 2

• (d) of

• (a) (Cancel by 3 and 11)

• (b) (Cancel by 5 and 3)

• (c) of 2 means

• (d) of means

## Activity 47

A school contains 720 pupils. are girls. How many girls are there in the school?

You want of 720 or . So there are 270 girls in the school.

Alternatively of 720 is 90. So of 720 = 3 × 90 = 270.

## Activity 48

If you divide a cake into 12 equal pieces and then eat 3 pieces, what fraction of the cake is left?

You have eaten (or ) of the cake. So there is (or ) of the cake left.

## Activity 49

A recipe specifies a cooking time of hour and suggests checking and basting of the way through the cooking time. After how long should you check it?

Half an hour. There are several ways to do this calculation.

For example, one third of three quarters is one quarter (in symbols, ). Hence, two thirds (of three quarters) is two quarters, or a half: .

Alternatively gives , i.e. .

Another method is to cancel to give: .

You might also have converted hours to minutes:

now is 45 minutes, and of 45 minutes is 30 minutes.

So check it after half an hour.