Mental arithmetic is the invaluable maths skill of doing calculations in your head, without the use of any tools, such as a calculator or pen and paper, or fingers! It can come in handy in countless everyday situations, from working out the best multi-buy deal in the supermarket, to calculating how long you will need to wait for the next train.

People who need to use maths in their jobs, whether accountancy, retail or engineering for example, often do quite complex and fast estimations in their heads, so that they have a good idea of what the answer will be before they take the time to do a more complex calculation.

Mental arithmetic also helps to develop a real understanding of the mathematical methods of arithmetic, rather than just doing calculations through a process of memorization.

Practising mental arithmetic might seem like hard work, and to some people who find maths difficult it might even seem like a scary prospect. But as with all things, the more you do it, the easier it gets. This page gives you some helpful hints and tips to make the process quicker, easier and a whole lot less scary.

Everyone can learn mental maths hacks! They are not just for maths wizards.

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Multiplying numbers by 10, 100 and 1000 and their multiples

To do simple multiplications, you need to have a basic understanding of place value. For more on this, see our page on Numbers. Two things to remember here are:

• Zeros are important
• Decimal points always separate the whole numbers from the ‘bits’.

To mentally multiply any number by 10:

Keep the decimal point where it is. In your head, move all the digits one place to the left and add a zero to the end if needed.

24 × 10 = 24.0 × 10 = 240
175 × 10 = 175.0 × 10 = 1750
3.56 × 10 = 35.6

To multiply any number by 100:

Either
Keep the decimal point where it is. Move the digits two places to the left, adding zeros to the end if needed:
845 × 100 = 845.00 ×100 = 84500
37.64 × 100 = 3764

OR
Move the decimal point two places to the right:
56.734 × 100 = 5673.4

To multiply any number by 1000:

Use either of the two methods as before and move three places:
Move the digits to the left:
23.476 × 1000 = 23476
Or move the decimal point to the right:
8.45692 × 1000 = 8456.92

Multiplying by multiples of tens, hundreds and thousands or more:

The basic idea: If you need to multiply a number by 200, multiply by 2 first, then move the digits. You can do this with any quantity. For example, if you need to multiply something by 5000, multiply your number by 5 first, then move three decimal places.

The number of places you move is always the same as the number of zeros.

For example, multiply 25 by 5000. This seems quite hard to do in your head, but the trick is to break it down into easy calculations.

First multiply 25 by 5:
25 × 5 = 125

Then move the digits three places to the left (or the decimal point three places to the right):
125 × 1000 = 125000.

Dividing by 10, 100, 1000 and multiples

This process is exactly the same as with multiplication, but in reverse.

To divide by 10 you either

keep the decimal point where it is and move your digits one place to the right,

or

move your decimal point one place to the left.

For 100, you move two places.
For 1000, you move three places, and so on.

Examples:

785 ÷ 100 = 7.85
56 ÷ 1000 = 0.056

450 ÷ 1000 = 0.450 = 0.45

Diving by multiples of tens, hundreds or thousands (or more):

The basic idea: If you need to divide by 7000, first divide by 7, then move your digits three spaces.

For example, 56 ÷ 7000:
56 ÷ 7 = 8
8 ÷ 1000 = 0.008

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Adding and subtracting in your head

In the same way as you did with mental multiplication and mental division, you can learn some tricks for making mental addition and subtraction easier.

As before, these tricks don’t involve any maths wizardry, it is simply a case of breaking the problem down into smaller parts that are easier to tackle in your head.

The best way to do this is with some examples.

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Adding and multiplying in your head

Sometimes you might have a really tricky calculation to do in your head and it just seems impossible. However, if you look at how it can be split up using the skills you have learned in the examples above, something really tricky can become much simpler.

For example, calculate 97 × 7 in your head.

There are two ways you could tackle this one and you might find one way easier than the other:

Method 1:

97 is the same as (100 − 3), so you can think of the calculation as
7 × (100-3)
This is the same as
(7 × 100) – (7 × 3)

Now you have replaced the difficult multiplication with two simple multiplications and a subtraction:

7 × 100 = 700
7 × 3 = 21
700 – 21 = 700 – 20 – 1 = 679

Therefore 97 × 7 = 679

Method 2:

97 is almost 100, so you can begin by working out 7 × 100 = 700.
The next step is to take account of the difference between 97 and 100, which is 3.
So 7 lots of 3 is 21.

700 – 21 = 679

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Conclusion

Mental arithmetic can seem quite scary, but with practice, you can use these mental maths hacks to break a difficult problem down into smaller chunks that are easier to think about. There is no wizardry involved, it is just a matter of seeing the problem in a different way.

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