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Numbers, units and arithmetic

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# Try some yourself

## Activity 44

Is the following statement true or false?

Adding the same number to the top and bottom of a fraction gives you an equivalent fraction.

False. For example adding 2 to the top and bottom of gives . But is not equivalent to .

## Activity 45

Explain in your own words how to add two fractions, as if to someone who does not know how to do it.

There are obviously many different ways of explaining this. For example one student said:

‘First look at the bottom number of each fraction. If these are the same, then this is also the bottom number of the answer. To get the top number in the answer, add the two top numbers in the given fractions.

‘If the bottom numbers are different, multiply the top and bottom of the first fraction by the bottom number of the second. Then multiply the top and bottom of the second fraction by the bottom number of the first. Now the two fractions have the same bottom number so they can be added as above.’

Your wording may have been very different but it should have given instructions for the case when the denominators are the same and when they are not. Note that the method described here will always work, when bottom numbers are different, although in some cases a quicker method is possible.