The main principle: simplify the problem
The brain struggles to hold many intermediate numbers — working memory is limited. So all mental math tricks come down to one idea: turn a hard operation into a few easy ones with round numbers and fewer of them.
10 tricks
1. Add left to right
At school we learn column addition from right to left, but mentally it is easier to start with the biggest place values: 47 + 38 = (40 + 30) + (7 + 8) = 70 + 15 = 85. You know the rough answer straight away.
2. Round and adjust
298 + 456 = 300 + 456 − 2 = 754. 83 − 29 = 83 − 30 + 1 = 54. The same trick helps with serial sevens: subtracting 7 is the same as subtracting 10 and adding 3.
3. Subtract with complements
1000 − 387: take each digit except the last away from 9, and the last from 10. 3 → 6, 8 → 1, 7 → 3. Answer: 613. Handy for working out change.
4. Multiplying by 5
Multiply by 10 and halve: 46 × 5 = 460 / 2 = 230.
5. Multiplying by 9 and 11
× 9 = × 10 minus the number: 37 × 9 = 370 − 37 = 333. A two-digit number × 11: add the digits and put the sum in the middle: 53 × 11 = 5 (5 + 3) 3 = 583. If the sum is over 9, carry the one: 78 × 11 = 7 (15) 8 = 858.
6. Multiplying by 25
Divide by 4 and multiply by 100: 36 × 25 = 9 × 100 = 900.
7. Rearrange factors
16 × 35 = 8 × 70 = 560. If you double one factor and halve the other, the product stays the same — look for a pair that gives a round number.
8. Squaring numbers ending in 5
Multiply the tens digit by the next number up and append 25: 35² = (3 × 4) then 25 = 1225; 85² = (8 × 9) then 25 = 7225.
9. Percentages
- 10% — move the decimal point: 10% of 340 = 34.
- 5% — half of 10%: 17.
- 15% = 10% + 5% = 51 — handy for tips.
- x% of y = y% of x: 8% of 50 = 50% of 8 = 4.
Practise in the Percentages and Percent Guess games.
10. Estimate first
Before calculating exactly, estimate the magnitude: 19 × 21 is about 400 (actually 399). Estimation protects you from big mistakes and is a useful skill in itself — Greater or Less and Fermi Estimation train it.
What about the soroban?
Mental arithmetic on the Japanese abacus is a separate path: first you learn to calculate on a real or virtual soroban, then on an imagined one. It takes time but gives very high speed for adding and subtracting large numbers. Try it in the Mental Arithmetic game.
A practice plan
- Week 1. Pick 2–3 tricks from the list and use them in real life: in shops, when working out tips. Every day, 5 minutes of Quick Math on easy difficulty.
- Week 2. Add 2–3 more tricks. In the games, aim for no mistakes rather than speed.
- Week 3. Raise difficulty and speed. Add Flash Count, where the problem is visible for one second.
- Week 4. Mixed practice: percentages, Greater or Less, serial subtraction.
Math anxiety is common, and it actually makes calculating harder by eating up working memory. Short, low-stakes games with clear results help lower the tension: start at the easiest level and celebrate a streak of correct answers rather than speed.