# Fractions: Understanding Tips & Tricks

Eleven-Plus Preparation Specialists

In this guide weâ€™ll look at some common question types and how you can go about approaching them.

## Adding whole numbers and fractions

As well as calculating using fractions that share a denominator or whose denominators are multiples (e.g. adding â…• + â…– , or adding 1/10 + â…• ) you will need to be able to add mixed numbers. This means adding a number followed by a fraction to a fraction. Letâ€™s consider an example:
You might need to add 1 & â…• to â…–

Here, you need to understand that 1 represents 5/5. Therefore, you are actually adding 6/5 + 2/5 . This gives 8/5, which can also be represented as 1 & â…—.

Alternatively, you might need to add two mixed numbers. Perhaps you need to add 1 & â…– to 2 & â…—.

Here, the simplest thing to do is to add the whole numbers first. So here, we get 1+2 = 3. Then add the fractions. This gives â…– + â…— = 5/5. Remember that 5/5 is 1 (as all the â€˜fractionsâ€™ of one are full) so we are adding 3+1 = 4.

Alternatively, you could take the numbers and make them into fractions, then add the fractions. This would give you 7/5 + 13/5 = 20/5 = 4.

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## Multiplying and Dividing Fractions

When multiplying and dividing with fractions, you can think of the process as dividing a shape into areas. So Â¼ * Â½ would be like finding the shared area of half a shape and a quarter of a shape – which would be an eighth of that shape. Try drawing this out to see how this makes sense. You must also be able to divide a fraction by a whole number. This is relatively straightforward, as you must just multiply the denominator by the whole number. As an example, Â¼ divided by 2 is â…›, as 4 * 2 is 8. Alternatively, you can multiply Â¼ * Â½ , which gives the same result.

## Using decimals

You must be able to convert between fractions and decimals – that means understanding decimals. Remember that each decimal point means that the number is getting ten times smaller – so the first decimal point is tenths, then the next decimal point is hundredths, then thousandths, etc. This means that 0.8 is 8/10, as it is eight tenths of 1, or 8 lots of a tenth. Think about it in whichever way makes the most sense to you! Youâ€™ll find that practising these is simple if you use money as the tool to practise with. Imagine that you buy something that costs Â£5.40, and pay with a ten pound note. How much change would you get? It would be Â£4.60 – which you will understand using decimals.

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## Using Percentages

Next, you need to be able to link fractions and decimals to percentages too. A percentage means a one hundredth part. Therefore 1% is one hundredth, which is 0.01. Thus 10% is 0.1. This process of conversion will become simple as soon as you practise it a few times, and should be second nature when sitting the 11+. Letâ€™s look at an example of a possible question that mixes percentages, decimals and fractions.

Bob buys a top for a 20% discount. The top normally costs Â£20. After, he sells the top for 3/4 of the price that he bought it.

This means that Bob buys the top for Â£16, as 20% of 20 is 4. If he sells it for Â¾ of the price that he bought it for, he must have sold it for Â£12, as Â¼ of 16 is 4 and he sells it for Â¾ of the price.

We can think of the above in decimal terms too – he buys the top at 0.8 * its normal value, or 0.8 * 20 = 16. He then sells the top for 0.75 * the price he bought it for, or 0.75 * 16 = 12.

## Conclusions

Mixing fractions, decimals and percentages can be confusing at first but soon becomes second nature. Remember that probabilities can be included in this realm too – you might have a 20% chance of something occuring, which is equivalent to a probability of 0.2. Again, this is just converting between percentages and decimals.
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