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Mental Math Tricks: 15 Shortcuts to Calculate Faster

Published November 2, 2026 · By Sumzo team (AI-assisted)

Mental math tricks for faster calculation: multiplying by 5, 9 and 11, squaring numbers ending in 5, quick percentages, and more — with examples.

Mental math tricks are shortcuts that turn hard-looking calculations into a few easy steps — multiplying by 11 by adding digits, finding 15% from 10% plus half, or squaring numbers that end in 5. Each one works because of a simple piece of algebra, so once you see why, you can rebuild it any time.

1. Multiply by 5: halve, then times 10

$48 \times 5$: half of 48 is 24, times 10 is 240. This works because $5 = \frac{10}{2}$.

2. Multiply by 9: times 10, then subtract

$47 \times 9 = 470 - 47 = 423$. Because $9 = 10 - 1$.

3. Multiply a two-digit number by 11

Put the sum of the digits between them: $43 \times 11$ → 4, then $4 + 3 = 7$, then 3, so 473. If the sum is 10 or more, carry the 1: $78 \times 11$ → 7, $7 + 8 = 15$, 8 → 858.

4. Square a number ending in 5

Multiply the first digit(s) by the next number up, then write 25: $65^2$ → $6 \times 7 = 42$, so 4,225. $35^2 = 1{,}225$ (because $3 \times 4 = 12$). It works because $(10a + 5)^2 = 100a(a + 1) + 25$.

5. Numbers near 100

$98 \times 7 = 700 - 14 = 686$, because $98 = 100 - 2$. Round to an easy number, then fix the difference.

6. Double and halve

$16 \times 25$: halve 16 twice and double 25 twice → $4 \times 100 = 400$. The product doesn’t change when you double one factor and halve the other.

7. The difference of two squares

$21 \times 19 = 20^2 - 1^2 = 399$, because $(a + b)(a - b) = a^2 - b^2$. Works whenever two numbers are the same distance either side of an easy number: $52 \times 48 = 2500 - 4 = 2496$.

8. Percentages from 10% and 1%

10% is the number divided by 10; 1% is divided by 100. Build the rest:

• 15% of 60 = 10% + 5% = 6 + 3 = 9.
• 35% of 80 = 3 × 10% + 5% = 24 + 4 = 28.
• 1% of 250 is 2.5, so 3% is 7.5.

9. Swap a percentage

$x\%$ of $y$ equals $y\%$ of $x$: 8% of 50 is the same as 50% of 8, which is 4.

10. Subtract from 1,000

Take each digit from 9, and the last from 10: $1000 - 386$ → $9 - 3 = 6$, $9 - 8 = 1$, $10 - 6 = 4$ → 614. Handy for working out change.

11. Add by rounding

$198 + 467$: add 200 to get 667, then take back 2 → 665.

12. Divisibility checks

• By 3: the digit sum is divisible by 3 (123 → 6, so 123 is divisible by 3).
• By 9: the digit sum is divisible by 9 (729 → 18).
• By 4: the last two digits are divisible by 4 (316 → 16).
• By 5: it ends in 0 or 5.

These make simplifying fractions much quicker: $\frac{123}{246}$ has 123 in both, so it is $\frac{1}{2}$.

How to practise mental maths

• Learn one trick at a time and use it every day for a week — at the shop, on a receipt, on a scoreboard.
• Check with a calculator afterwards so you trust the method.
• Estimate before every calculation: $4.8 \times 21 \approx 100$. Estimation is the most useful mental skill of all.

Mental tricks are fast, but exam answers need working too. For anything longer, write it down, and check it — the basic calculator shows each step in the right order, and the percentage calculator handles the awkward percentages.

13. Multiply two numbers just under 100

For $97 \times 96$: each is short of 100 by 3 and 4. Take one shortfall from the other number: $97 - 4 = 93$. Multiply the shortfalls: $3 \times 4 = 12$. Put them together: 9,312. It works because $(100 - a)(100 - b) = 100(100 - a - b) + ab$.

14. Divide by 5: double, then divide by 10

$135 \div 5$: double to 270, divide by 10 to get 27. Because dividing by 5 is the same as multiplying by 2 and dividing by 10.

15. Fractions you should know as percentages

• $\frac{1}{2} = 50\%$, $\frac{1}{4} = 25\%$, $\frac{3}{4} = 75\%$
• $\frac{1}{5} = 20\%$, $\frac{1}{10} = 10\%$
• $\frac{1}{8} = 12.5\%$, $\frac{3}{8} = 37.5\%$
• $\frac{1}{3} \approx 33.3\%$, $\frac{2}{3} \approx 66.7\%$

Knowing these turns many percentage questions into fraction questions: 37.5% of 64 is $\frac{3}{8}$ of 64, which is 24.

A practice set with answers

Try these in your head, then check:

• $36 \times 5$ (answer: 180)
• $58 \times 11$ (answer: 638)
• $85^2$ (answer: 7,225)
• $99 \times 8$ (answer: 792)
• 15% of 120 (answer: 18)
• $1000 - 472$ (answer: 528)

If one went wrong, work out which step slipped — that is the trick to practise.

Frequently asked questions

What is the fastest mental math trick? Rounding and adjusting — turning 98 into 100 or 198 into 200, then correcting — works in more situations than any other trick.

How can I get faster at mental maths? Practise a little every day with real numbers you meet, learn the times tables to 12 × 12 well, and estimate before you calculate.

Do mental math tricks help in exams? Yes, especially on non-calculator papers, for checking answers and for estimating. Show your working where the question asks for it.

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