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Fractions: Understanding Tips & Tricks

Eleven-Plus Preparation Specialists

In this guide we’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 ⅕ + ⅖ , or adding 1/10 + ⅕ ) you will need to be able to add mixed numbers. This means adding a number followed by a fraction to a fraction. Let’s consider an example:
You might need to add 1 & ⅕ to ⅖

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 & ⅗.

Alternatively, you might need to add two mixed numbers. Perhaps you need to add 1 & ⅖ to 2 & ⅗.

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 ⅖ + ⅗ = 5/5. Remember that 5/5 is 1 (as all the ‘fractions’ 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 ¼ * ½ 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, ¼ divided by 2 is ⅛, as 4 * 2 is 8. Alternatively, you can multiply ¼ * ½ , 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! You’ll find that practising these is simple if you use money as the tool to practise with. Imagine that you buy something that costs £5.40, and pay with a ten pound note. How much change would you get? It would be £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+. Let’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 £20. After, he sells the top for 3/4 of the price that he bought it.

This means that Bob buys the top for £16, as 20% of 20 is 4. If he sells it for ¾ of the price that he bought it for, he must have sold it for £12, as ¼ of 16 is 4 and he sells it for ¾ 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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