Mental math tricks are shortcuts that turn one hard calculation into two or three easy ones you can hold in your head. The handful below cover everyday adding, subtracting, multiplying, percentages and squares. None of them needs talent. Each one takes a few minutes to learn and becomes automatic with short, regular use.
What are the best mental math tricks?
The best mental math tricks are the ones you will use every day. Add and subtract from left to right, multiply by rounding to a friendly number and fixing the difference, build percentages from 10% and 1%, and keep a few special shortcuts for ×5, ×9, ×11 and ×25. Together they cover most everyday calculations.
Every trick below comes with an example you can try straight away. Start with one or two, use them for a week, then add the next. Learning them one at a time gives each trick the chance to stick.
How do you add numbers in your head quickly?
To add numbers in your head quickly, work from left to right. Add the tens first, then the ones, then combine the two results. Starting with the biggest part gives you a rough answer almost at once, and the rest only refines it. This is the opposite of the written method, which starts on the right.
For 47 + 38, add the tens first, 40 + 30 = 70. Then add the ones, 7 + 8 = 15. Combine them and you get 70 + 15 = 85. Three-digit numbers work the same way. For 256 + 137, add 200 + 100 = 300, then 50 + 30 = 80, then 6 + 7 = 13, which gives 393.
A second option is to make one number round. Move 2 from 47 to 38 and the sum becomes 45 + 40, which is still 85. Left to right is the fastest way through the quick sums in the addition game, where every correct answer lands a punch. A common slip is losing the extra ten from the ones, so say the running total in your head as you go.
How do you subtract in your head without borrowing?
To subtract in your head without borrowing, count up from the smaller number to the bigger one. Jump to the next round number first, then on to the target, and add up the jumps. The total distance is the answer. This skips the borrowing step of the written method, which is the part most people lose track of.
For 83 − 67, go from 67 to 70, which is 3. Then go from 70 to 83, which is 13. Add the jumps and you get 3 + 13 = 16, so 83 − 67 = 16. The same idea works for change from 100. For 100 − 37, go from 37 to 40, which is 3, then from 40 to 100, which is 60, so the answer is 63.
Another way is to subtract a round number and then give some back. For 83 − 67, take away 70 to get 13, then add back the extra 3 you took, which gives 16. Counting up works well in the subtraction game because the round number in the middle is easy to spot. Pick whichever of the two methods feels more natural and stick with it.
How do you multiply big numbers in your head?
To multiply big numbers in your head, round one number to a friendly number such as 10, 20, 50 or 100, multiply, and then fix the difference. A calculation like 19 × 6 becomes 20 × 6 minus one 6. Friendly numbers are easy to multiply, and the fix is usually one small subtraction or addition.
For 19 × 6, work out 20 × 6 = 120, then take away one 6, which gives 114. For 48 × 5, work out 50 × 5 = 250, then take away 2 × 5 = 10, which gives 240. For 98 × 7, work out 100 × 7 = 700, then take away 2 × 7 = 14, which gives 686.
You can also split a number into parts. For 23 × 4, work out 20 × 4 = 80 and 3 × 4 = 12, then add them to get 92. Getting quick at rounding to the nearest friendly number makes every trick in this section faster. A common mistake is fixing by the wrong amount. In 19 × 6 you added one extra 6, so you take away 6, not 1.
Which fast multiplication tricks are worth learning?
The fast multiplication tricks worth learning first are ×5 (multiply by 10, then halve), ×9 (multiply by 10, then subtract the number once), ×11 for two-digit numbers (add the digits and put the sum in the middle) and ×25 (multiply by 100, then divide by 4). Each one swaps a hard step for an easy one.
Multiply by 5
Five is half of ten, so multiply by 10 and halve the result. For 86 × 5, work out 86 × 10 = 860, and half of 860 is 430. This trick also makes multiplication with numbers like 50 and 500 much quicker, because the same halving step applies. For 86 × 50, work out 86 × 100 = 8,600 and halve it to get 4,300.
Multiply by 9
Nine is one less than ten, so multiply by 10 and subtract the number once. For 46 × 9, work out 46 × 10 = 460, then take away 46, which gives 414.
Multiply by 11
For a two-digit number, split the digits and put their sum in the middle. For 43 × 11, the digits are 4 and 3, and 4 + 3 = 7, so the answer is 473. When the middle sum is 10 or more, carry the 1 to the left. For 87 × 11, 8 + 7 = 15, so you write 5 in the middle and add 1 to the 8, which gives 957.
Multiply by 25
Twenty-five is a quarter of 100, so multiply by 100 and divide by 4. Dividing by 4 is easiest as halving twice. For 48 × 25, work out 48 × 100 = 4,800, then halve twice to get 2,400 and then 1,200.
Double one number and halve the other
When one number is even, you can halve it and double the other without changing the answer. For 16 × 25, halve and double to get 8 × 50, then again to get 4 × 100, which is 400. The ×5, ×11 and ×25 tricks have their own levels in the mental math shortcuts part of Math Max, together with squares ending in 5 and pairs around a round number. Each level only sets problems where the shortcut works, so you get used to spotting it.
How do you work out percentages in your head?
To work out percentages in your head, start from 10% and 1%. For 10%, move the decimal point one place to the left. For 1%, move it two places. Most other percentages are built from those two, so 5% is half of 10%, 15% is 10% plus 5%, and 20% is 10% doubled.
Say an item costs 46 and has 15% off. Ten percent of 46 is 4.6, and half of that is 2.3, so 15% is 4.6 + 2.3 = 6.9. The discount is 6.9, and you pay 46 − 6.9 = 39.1.
There is one more trick that few people know. A percentage can be flipped, because x% of y is the same as y% of x. Working out 8% of 25 looks awkward, but 25% of 8 is a quarter of 8, which is 2. In the same way, 4% of 75 is 75% of 4, which is 3. Discounts and price changes are exactly what the percentages topic in Math Max is built around, so it is a good place to use both tricks. You can also try them on the next price tag you see.
How do you square a number in your head?
To square a number in your head, look for a nearby round number. Use the rule a² = (a − b) × (a + b) + b², where b is the distance to the round number. For numbers ending in 5, multiply the tens digit by the next number up and write 25 after the result.
For 19², the round number is 20 and the distance is 1. Work out 20 × 18 = 360, then add 1² = 1, which gives 361. For 52², the distance to 50 is 2. Work out 50 × 54 = 2,700, then add 2² = 4, which gives 2,704.
Numbers ending in 5 are even quicker. For 35², multiply 3 by the next number up, 3 × 4 = 12, then write 25 after it to get 1,225. For 65², 6 × 7 = 42, so the answer is 4,225.
The same rule handles pairs that sit either side of a round number. For 48 × 52, the middle is 50 and the distance is 2, so the answer is 50² − 2² = 2,500 − 4 = 2,496. None of this is magic. It is algebra that you can do in your head once the pattern is familiar.
How do you check a mental math answer?
To check a mental math answer, estimate first and compare. Round both numbers, work out the rough result and see whether your exact answer is close to it. You can also check the last digit, because the last digit of a product depends only on the last digits of the two numbers you multiplied.
For 48 × 19, the estimate is 50 × 20 = 1,000. The exact answer, using rounding and fixing, is 48 × 20 − 48 = 960 − 48 = 912. That is close to 1,000, so the size is right. The last digits are 8 and 9, and 8 × 9 = 72 ends in 2, which matches 912.
Estimating catches the biggest mistakes, like a missing zero or a digit in the wrong place. It is also useful in tests without a calculator, where a quick estimate can show that an answer worked out the long way is wrong before you move on.
How do you get faster at mental math?
You get faster at mental math by using the tricks often, in short sessions, with a little time pressure. Knowing a trick and reaching for it without thinking are different skills, and repetition is what connects them. A few minutes on most days works better than one long session now and then.
The same idea is behind the advice to practise times tables with short daily recall instead of rereading a chart. You answer from memory, often, until the answer arrives before you start calculating.
A game helps because it makes that repetition feel like play. In Math Max your rival gets the same problem, and the race to answer first pushes you to use the shortcut instead of reaching for a calculator. After enough rounds, the habit of estimating first and then refining shows up on its own, in the shop, at work or wherever numbers come up. Grown-ups who want to keep their head for numbers can find more ideas in our guide to math games for adults, which covers how to keep the practice going. It also suggests a simple routine that fits into a busy week.
A few tricks used every day beat a long list you never use
Pick the two tricks that match the math you do most, such as left-to-right adding and percentages from 10%. Use them on purpose for a week until they come without effort, then add the next one. Children who know their times tables can learn most of these tricks in a few minutes, and so can adults. The speed comes from practice, not talent.
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