10 Mental Math Tricks to Calculate Faster
Mental maths is not about being a genius. Most people who calculate quickly in their heads simply know a few shortcuts that turn hard sums into easy ones. Here are ten tricks that work every time, each with a worked example you can check for yourself, plus tips on how to practise them.
Multiplication shortcuts
1. Multiply a two-digit number by 11
Split the two digits apart and put their sum in the middle. For 36 × 11, the digits are 3 and 6, and 3 + 6 = 9, so the answer is 396.
If the middle sum is 10 or more, carry the 1 to the first digit. For 58 × 11, 5 + 8 = 13. Write the 3 in the middle and add 1 to the 5, giving 638.
2. Multiply by 5
Multiplying by 5 is the same as multiplying by 10 and then halving. For 48 × 5, halve 48 to get 24, then multiply by 10: 240. For an odd number such as 37 × 5, it is easier to multiply by 10 first: 370, then halve it to get 185.
3. Multiply by 9
Multiply by 10, then subtract the original number once. For 27 × 9, work out 27 × 10 = 270, then 270 − 27 = 243.
4. Multiply by 25
Because 25 is a quarter of 100, multiply by 100 and divide by 4. For 36 × 25, 36 × 100 = 3,600, and 3,600 ÷ 4 = 900. Alternatively, divide by 4 first: 36 ÷ 4 = 9, then 9 × 100 = 900.
Squares and numbers near 100
5. Square a number ending in 5
Take the digits before the 5, multiply that number by the next whole number up, and then write 25 on the end. For 35², the digit before the 5 is 3, and 3 × 4 = 12, so the answer is 1,225. For 85², 8 × 9 = 72, giving 7,225.
6. Multiply two numbers just below 100
Find how far each number is below 100. For 97 × 96, the gaps are 3 and 4. Subtract one gap from the other number: 96 − 3 = 93 (or 97 − 4, which is also 93). Then multiply the gaps: 3 × 4 = 12. Put them together to get 9,312. If the product of the gaps is a single digit, write it with a leading zero, so 98 × 97 becomes 95 followed by 06, which is 9,506.
Breaking numbers apart
7. Split a number into tens and units
Big multiplications become easy when you break one number into friendly parts. For 7 × 48, think of 48 as 40 + 8. Then 7 × 40 = 280 and 7 × 8 = 56, and 280 + 56 = 336. This works because multiplying a sum is the same as multiplying each part and adding the results.
8. Double and halve
If one number is even, you can halve it and double the other without changing the answer. For 16 × 35, halve 16 to 8 and double 35 to 70: 8 × 70 = 560. You can repeat the trick: 4 × 140, then 2 × 280, all equal 560.
Adding and subtracting quickly
9. Round and adjust
When a number is close to a round number, use the round number and then fix the difference. For 298 + 467, add 300 instead: 300 + 467 = 767. You added 2 too many, so subtract 2 to get 765. The same idea works for subtraction: 534 − 199 is 534 − 200 = 334, then add back 1 to get 335.
Bonus: subtract from 1,000
To take a three-digit number away from 1,000, subtract each of the first two digits from 9 and the last digit from 10. For 1,000 − 374, work out 9 − 3 = 6, 9 − 7 = 2 and 10 − 4 = 6, giving 626. This is handy for working out change. It works whenever the last digit is not zero.
Percentages made simple
10. Use 10 percent and swap when helpful
To find 10 percent of any number, move the decimal point one place to the left: 10 percent of 60 is 6. From there, many percentages are easy. Five percent is half of 10 percent, so 15 percent of 60 is 6 + 3 = 9. Twenty percent is double 10 percent, so 20 percent of 45 is 4.5 × 2 = 9.
There is also a neat swap trick: x percent of y is always the same as y percent of x. So 8 percent of 50 is the same as 50 percent of 8, which is 4. Whenever one version looks hard, try the other.
How to practise
Knowing a trick is not the same as using it quickly. A few habits help the shortcuts stick:
- Learn one or two at a time. Practise a single trick for a few days before adding the next.
- Use real life. Work out shopping totals, discounts and tips in your head, then check them on your phone.
- Check your work. Accuracy matters more than speed. A quick wrong answer is worse than a slower right one.
- Play timed games. Our Quick Math game gives you fast arithmetic questions against the clock, which is excellent practice for recall.
If you enjoy stretching your brain, try logic games such as Sudoku too, and read our balanced look at whether puzzle games are good for your brain.
Key takeaways
- Multiply by 11 by adding the two digits and placing the sum in the middle.
- Multiply by 5, 9 and 25 using 10 and 100 as stepping stones.
- Square numbers ending in 5 by multiplying the leading part by the next number and adding 25.
- Break numbers into parts, or double and halve, to simplify multiplication.
- Round and adjust for addition, and use 10 percent as a base for percentages.
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