Mental Maths

Mental maths
1. Breaking down numbers

Here are two different examples where breaking down numbers can help you add or subtract in your head.

40 + 67
40 + 67 is the same as 40 + 60 + 7, which is 100 + 7, which is 107.
Find the difference between 38 and 63
Count on from 38 to 40 and keep that 2 in your head. Now count on from 40 to 60, which is 20, and from 60 to 63, which is 3. Add the 2, 20 and 3 to make 25.

The difference between 38 and 63 is 2 + 20 + 3 = 25

2. Rounding numbers

Rounding numbers to the nearest 1, 10 or 100 can help with lots of mental maths problems. Here are some examples:

To add 9 to another number, add 10 and then subtract 1
36 + 9 = 36 + 10 - 1 = 45
To add 18 to another number, add 20 and then subtract 2
48 + 18 = 48 + 20 - 2 = 66
To add 97 to another number, add 100 and then subtract 3
439 + 97 = 439 + 100 - 3 = 536
To add 0.9 to another number, add 1 and then subtract 0.1
3.7 + 0.9 = 3.7 + 1 - 0.1 = 4.6
To subtract 8 from another number, subtract 10 and then add 2
46 - 8 = 46 - 10 + 2 = 38
To subtract 19 from another number, subtract 20 and then add 1
63 - 19 = 63 - 20 + 1 = 44
To subtract 0.9 from another number, subtract 1 and then add 0.1
8.2 - 0.9 = 8.2 - 1 + 0.1 = 7.3

3. Doubling

If you are adding together two numbers that are nearly the same, doubling one of them will help.

35 + 35 = 70
35 + 36 = 35 + 35 + 1 = double 35 add 1 = 71

4. Using inverses

Addition and subtraction are inverses (opposites). So subtraction can always be checked by adding:
To check 82 - 37 = 45, you could add 45 and 37 and see if you get 82.
Multiplication and division are also inverses. So division can always be checked by multiplication:
To check 81 ÷ 3 = 27, you could multiply 27 by 3 and see if you get 81.

5. Multiplying and dividing by 10 and 100

To multiply a number by 10, move the digits one place to the left, adding a zero if necessary.
58 x 10 = 580

To multiply a number by 100, move the digits two places to the left, adding zeros if necessary.
58 x 100 = 5800

To divide a number by 10, move the digits one place to the right, adding a zero if necessary.
4.3 ÷ 10 = 0.43

To divide a number by 100, move the digits two places to the right, adding zeros if necessary.
4.3 ÷ 100 = 0.043

To multiply or divide by numbers such as 20 or 300, multiply or divide by the 2 or 3 first and then by the 10 or 100.
To do 24 ÷ 20, you could divide 24 by 2 and then divide that answer by 10.
24 ÷ 2 = 12
12 ÷ 10 = 1.2

To do 22 x 300, you could multiply 22 by 3 and then multiply that answer by 100.
22 x 3 = 66
66 x 100 = 6600