Skillswise Mental Math ~ Add And Subtract

By Princessa
Special Thanks to BBC Skillswise.

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5 Ways To Add And Subtract In Your Head:

Mental methods are about trying to get to the correct answer in the quickest and easiest way!
There are lots of ways to add and subtract numbers in your head.

By the time you have looked through the factsheets in this module you will have used 5 different methods for mental addition and subtraction!

Try to remember them by using the word "Shared".

When you've read about them, practise the methods you like and can remember most easily.
Ask other people about the methods they use - and share your methods too!

Keep practising, and HAVE FUN!
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Reminders To Help You Add And Subtract:

Here are three reminders to help you with mental addition and subtraction.

A reminder about place value...

Have a look at the number 623.

6 is the hundreds digit.

2 is the tens digit.

3 is the units digit.

A reminder about adding..

Have a look at these sums.

Here you can see that the same numbers added together in a different order will give the same answer.

Addition and subtraction are opposites.

You can check the answer to a subtraction sum by turning the numbers around and adding them up. Have a look below.

Here you've done the sum 10 - 25 and got the answer 15.

To check the answer, turn the sum around to 15 + 10 and see if you get 25.
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Splitting Up Numbers:

Splitting up numbers is a good method to use for both addition and subtraction. It is sometimes called partitioning.
Addition

Take a look at this addition sum:
80 + 49

To make it easier, split the 49 into 40 + 9. This makes the sum:
80 + 40 + 9 = 129

First, add the first two numbers:
80 + 40 = 120

Then add the result of that sum to the third number to get the answer:
120 + 9 = 129


Subtraction

Take a look at this subtraction sum:
150 - 34

To make it easier, split the - 34 into 30 - 4. This makes the sum:
150 - 30 - 4

First, subtract the 30 from 150:
150 - 30 = 120

Then, subtract the 4 from the 120 to get the answer:
120 - 4 = 116
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Hundreds, Tens, And Ones:


To make addition sums easier, you can separate the hundreds, tens and units and add them up separately.

Have a look at how separating works for this sum:
31 + 22

Using this method you can work out that 31 + 22 = 53.

Now look at this sum with hundreds as well as tens and units:
125 + 100 + 235 + 132

Using this method you can work out that 125 + 100 + 235 + 132 = 592.
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Rounding ~ Addition:

Rounding is a method for mental addition which is useful in many different situations.

Imagine you are in a shop and you have to quickly work out an amount.
£3.70 + £1.00 = £4.70. Taking away 10p gives £4.60
Have a look at how this addition sum can be solved with rounding:
75 + 19

First, round the 19 up to 20 and work out the sum:
75 + 20 = 95

As 20 is 1 more than 19, you then need to subtract 1 from the total.
95 - 1 = 94

Then you can see that:
75 + 19 = 94

Further reading.
These tables have some more information to help you with addition by rounding.

The first shows methods and examples for adding a number between 11 and 14 to another number.

This table shows methods and examples for adding a number between 15 and 19 to another number.
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Rounding ~ Subtraction:

Rounding is a method for mental subtraction which is useful in many different situations.
Imagine you are shopping and need to work out an amount quickly.

£3.70 - £1.00 = £2.70. Adding 10p gives £2.80.
Have a look at how this subtraction sum can be solved with rounding:
64 - 17

First, round the 17 up to 20 and work out the sum:
64 - 20 = 44

As 20 is 3 more than 17, you have taken 3 too many from the total. So you need to add 3:
44 + 3 = 47

So you can see that:
64 - 17 = 47
Further reading.
These tables have some more information to help you with subtraction by rounding.

The first shows you a methods and examples for subtracting a number between 11 and 14 from another number.

This table shows methods and examples for subtracting a number between 15 and 19 to another number.
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Empty Number Line For Counting On:

Counting on using an empty number line is a good method for subtracting numbers mentally.
Use this method to find the difference between 37 and 50. This is the same as the sum
50 - 37.

When you have pictured that line, count on from 37 to 40, which makes 3. Keep that 3 in your head. Then, count from 40 to 50, which is 10.

Have a look below to see how this works.

Now all you need to do is add the 3 to the 10. This makes 13. So:

The difference between 37 and 50 is 13.

Or..

50 - 37 = 13
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Doubling:

If you are adding together two numbers that are nearly the same, you can double one of them and then adjust the difference. Imagine you are adding together 38 and 35.
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Keywords For Mental Addition:

Here are some of the words which will crop up when doing addition sums.
Have a look below to see how they can be used in the simple sum 3 + 4 = 7.

Add

3 add 4 is 7

Altogether

Altogether, 3 and 4 make 7.

Increase

If you increase 3 by 4 you get 7.

More

7 is 3 more than 4.

Plus

3 plus 4 is 7.

Sum

The sum of 3 and 4 is 7.

Total

The total of 3 and 4 is 7.
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Keywords For Mental Subtraction:

Here are some of the words which will crop up when doing subtraction sums.

Have a look below to see how they can be used in the simple sum 8 - 5 = 3.

Decrease

If you decrease 8 by 5 you get 3.

Difference

The difference between 8 and 5 is 3.

Fewer than

3 is 5 fewer than 8.

Less than

3 is 5 less than 8.

Minus

8 minus 5 is 3.

Reduce

If you reduce 8 by 5 you get 3.

Subtract

8 subtract 5 is 3.

Take away

8 take away 5 is 3.
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