School teaches arithmetic right to left, on paper, one column at a time. Mental arithmetic works the other way round: left to right, biggest part first, with an estimate before the answer. Relearning that direction is most of the improvement. The rest is a handful of shortcuts and a few minutes of practice a day.
1. Work left to right
To add 47 and 38, do not start with 7 + 8. Start with 40 + 30 = 70, then 7 + 8 = 15, then 85. You hold one running total instead of carrying digits. For 63 − 27: 63 − 20 = 43, then 43 − 7 = 36. The method scales to three digits without change: 348 + 275 is 500, then 610, then 623.
2. Round, then adjust
Awkward numbers are near friendly ones. 49 + 36 is 50 + 36 minus 1: 85. 8 × 29 is 8 × 30 minus 8: 232. 198 + 467 is 200 + 467 minus 2: 665. Train yourself to see the friendly number first and the correction second.
3. Break multiplication apart
Multiply the tens and the units separately, then add. 7 × 46 is 7 × 40 = 280 plus 7 × 6 = 42, so 322. For two two-digit numbers, use the same idea twice: 23 × 14 is 23 × 10 = 230 plus 23 × 4 = 92, so 322. You will notice both examples give 322; checking that kind of coincidence is a useful habit in itself.
4. Learn four shortcuts and no more
- Multiply by 11. Spread the digits and put their sum in the middle: 11 × 53 = 5 (5+3) 3 = 583. Carry if the sum is 10 or more: 11 × 78 = 7 (15) 8 = 858.
- Square a number ending in 5. Multiply the tens digit by one more than itself and append 25: 65² = 6 × 7 = 42, so 4225.
- Difference of squares. 48 × 52 is (50 − 2)(50 + 2) = 2500 − 4 = 2496. Works whenever two numbers straddle a round one.
- Halve and double. 16 × 35 is 8 × 70 = 560. Move factors of 2 to whichever number becomes friendlier.
5. Estimate before every answer
A one-second estimate catches most errors. “About 400” before working out 47 × 8 means you will not accept 276. In tests and interviews, an estimate is often all that is being asked for; the exact answer is a bonus.
6. Practise for minutes, daily
The randomised trials that found cognitive benefits from simple arithmetic used short daily sessions over months, not long occasional ones, and the learning literature agrees that spaced practice is retained better. A plan that works:
- Weeks 1–2: one sixty-second round a day at level 1 of the trainer, addition and subtraction only, aiming for accuracy over speed.
- Weeks 3–4: level 2, mixed operations, two rounds a day. Review the wrong answers and name the method you should have used.
- Month 2 onward: level 3 once a day, plus the two daily maths puzzles in Brisk’s challenge for variety.
For what the trials actually measured and how much weight they can bear, see is mental maths good for your brain?
Common questions
I was never good at maths. Is it too late?
Mental arithmetic is a small, learnable skill, separate from mathematical ability. Adults who practise five minutes a day for a month reliably get faster and more accurate. The randomised trials of simple daily calculation were run with people in their seventies and eighties.
Should I learn tricks like Vedic maths?
A few shortcuts pay off: squaring numbers ending in 5, multiplying by 11, and the difference of squares. Most elaborate systems cost more to remember than they save. Fluency with the basics beats a bag of tricks.
How do I stop making careless errors?
Estimate first, then calculate. If 47 × 8 comes out as 276 and you had already thought “about 400”, you catch it. Most careless errors are order-of-magnitude slips that a two-second estimate prevents.