Fractions and Decimals

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Fractions and Decimals

You need to be able to:

1. Cancel fractions down.

2. Change improper (top-heavy, e.g. 3/2) fractions into mixed numbers (e.g. 1 ½) and vice-versa.

3. Multiply and divide fractions.

4. Add and subtract fractions.

5. Find fractions of quantities.

6. Use ratio.

Your calculator should have a fraction button which does all of the above easily - learn how to use it properly!

However, now there is a non-calculator exam paper you also need to be able to do all of the above by hand.

We will assume you can do 1 and 2. For the rest just follow these simple tips:

Important: Always change any mixed numbers into improper fractions before you start then cancel the answer down to it's simplest terms and change back to a mixed number if you need to!


Multiply the tops (numerators) together and multiply the bottoms (denominators) together.


Turn the second fraction upside-down and multiply as above.

Adding and subtracting

Find the lowest common denominator. This is the lowest number that the denominators will both go into. Then multiply the top and bottom of each fraction by the same number (the number used for each fraction may be different!).

Now simply add (or subtract) the tops keeping the denominator the same!

Here's an example:

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Looking at the above example, the lowest common denominator of 6 and 8 is 24.

You need to multiply 6 by 4 to get 24. That's why you have to multiply the topand bottom of the first fraction by 4.

You need to multiply 8 by 3 to get 24. That's why you have to multiply the top and bottom of the second fraction by 3.

Finding fractions of quantities

Multiply the quantity by the top of the fraction and divide it by the bottom of the fraction.


Fractions and Decimals

Note: You can divide by 8 first then multiply by 3 if you want!


Ratios behave like fractions. You can cancel them down if you like.

If you want to divide a quantity in a ratio it's the same as finding a fraction of something as we've shown above except the bottom of the fraction (what you want to divide the quantity by) is the total of all the numbers in the ratio.

See what we mean with this one!

Divide 35kg in the ratio 2:5.

This means for every 2kg you put on the left put 5 on the right!

2 + 5 = 7 so we divide 35 by 7 giving 5.

Now put 2 x 5 on the left and 5 x 5 on the right giving 10 : 25

Again your calculator will do this easily but you also need to be able to do it by hand!

To add and subtract numbers with decimal points in them, put them in columns with the decimal points above each other and add or subtract as you would with whole numbers.

To multiply, ignore the decimal points and multiply as you would with whole numbers. When you have the answer count the number of digits after the decimal points in the question and put the point in your answer so you have the same amount of digits after the point.

To divide, move the point the same number of places in both numbers so the second one is no longer a decimal then divide as normal!

Percentages are just fractions out of 100.

Decimals are just tenths, hundredths, thousandths etc.

The simple diagram below shows how to change between them!

Fractions and Decimals

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