5 steps to mastering mental maths

Sometimes, mental maths can be quicker and more convenient than getting your phone out or using a calculator. In a lot of situations, it is definitely more impressive. Arthur Benjamin once said:

“Calculate left-to-right in your head, not right-to-left as you might on paper,”

Taking this into account, we can derive 5 steps to improve and hopefully master mental maths:

1. Break up the problem into small pieces.

Even for the most daunting of problems, small steps can make them easy to solve mentally. For example, calculating a 10% tip mentally seems east but  a 17.5% tip appears a near impossible task. However, calculating 10%, halving it to get 5% , and again to get 2.5%, the total of those three numbers gives you 17.5% with small reasonable steps that are not too hard for the average mind.

2. Simplify multiplication including zeros

First of all when multiplying 6 by 10, we would simply remove the zero multiply the remaining digits and add a zero. ( 6 x 1=6 add a zero =60) This same premise can be applied to any sum with a zero on the end such as 60 x 120.

– Remove the zeros– 6×12

– Multiply the remaining digits–72

– Add on the remaining zeros–7200

3. Pay attention to complements

A complement is the distance between a number and the nearest convenient round number – normally ending in zeroes. For example 1435 – 781 is usually messy. Using complements:

–The first step is to over-subtract : 1435-800=635

–Work out how much you’ve oversubtracted by: 800-781=19

— Add that back onto the over subtraciton: 635+19=654

Therefore 1435-781=654

You’ve just turned a complicated subtraction sum into a easy mental addition problem.

4. Multiplying by 11

When multiplying 2 digit numbers by 11, add the sum of its digits and then insert it between your original numbers. For example, 53×11 is 583.

For 3 digit numbers, work out the sum of the first two digits and the last two and insert them between your the first and last digit of the original number.

e.g. 634 x 11

— 6+3=9 4+3=7

–634×11= 6974

This pattern can be utilised by 4 or more digit numbers but needs to be tweaked a bit and gets a tiny bit complicated. Anyway, it is unlikely that you’ll need to multiply a 4 digit number by 11. If  you are interested though, try 6435 by 11 in a calculator and work out the pattern or ask in the comments and we will explain it to you.

5.Multiplying by 5

Most people memorise their 5 times tables but it does become a bit complex with larger numbers. However, there is a neat trick that will help you out.Take any number, then  halve the number. If the result is whole, add a 0 at the end. If it is not, ignore the remainder and add a 5 at the end.

It works everytime:

2682 x 5 = (2682 / 2) & 5 or 0

2682 / 2 = 1341 (whole number so add 0)

13410

Let’s try another:

5887 x 5

2943.5 (fractional number (ignore remainder, add 5)

29435

Hope these short tips will help you on your path to mastery of mental maths whether you need to use in your everyday life, as part of your job or just to annoy your maths teacher at school.

If you want to try some of these tips yourself, try these:

–5647  x 5

–514 x 11

— 17.5 % of 400

— 2400- 787

— 1400 x 70

Did these tips help you, tell us and share with your friends so that they can learn aswell!