Mental Maths Tricks
Fast mental maths is not about being a genius. It comes from a small set of techniques that turn awkward sums into easy ones. Here are ten worth learning, each with a worked example.
1. Round and adjust when adding
Move one number to a round figure, add, then correct. For 48 + 37, think 50 + 37 = 87, then take away the 2 you added: 85.
2. Count up to subtract
Instead of taking away, count from the smaller number to the bigger one. For 83 − 68, go from 68 to 70 (that is 2), then from 70 to 83 (that is 13). The answer is 15.
3. Multiply by 5 by halving
Multiply by 10 and halve the result. For 5 × 46, take 460 and halve it: 230.
4. Multiply by 9 using 10
Multiply by 10 and take one lot away. For 9 × 14, take 140 − 14 = 126.
5. Multiply by 11
Multiply by 10 and add one more lot. For 11 × 23, take 230 + 23 = 253. With a two-digit number you can also add its digits and put the total in the middle: 2, then 2 + 3 = 5, then 3.
6. Double and halve
Doubling one number and halving the other keeps the answer the same. 16 × 25 becomes 8 × 50, then 4 × 100, which is 400.
7. Multiply by 4 and 8 by doubling
Multiplying by 4 is doubling twice, and by 8 is doubling three times. For 8 × 13, double to 26, then 52, then 104.
8. Square numbers ending in 5
Multiply the tens digit by the next number up, then put 25 on the end. For 35 × 35, take 3 × 4 = 12 and write 25 after it: 1225.
9. Build percentages from 10%
Find 10% by dividing by 10, then combine. For 15% of 180: 10% is 18, 5% is half of that, 9, so the answer is 27.
10. Swap percentages round
x% of y is always the same as y% of x. So 8% of 50 is the same as 50% of 8, which is simply 4.
Make them automatic
Reading a trick is not the same as owning it. Pick one, then use it for a minute of timed practice until you no longer have to think about the steps. The topic pages for addition, subtraction, multiplication and percentages each start a game for that skill, and times tables has a page for every table.