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30 Cool Math Tricks

These cool math tricks help you solve basic math problems in your head, with speed and great accuracy. No calculator needed! Each trick comes with worked examples, a short explanation of why it works, and a problem to try yourself.

1Multiply by 9 using your fingers

Even if you know your multiplication table, this trick comes in handy when you have a sudden brain freeze. It works for 9 × 1 through 9 × 10.

Hold up both hands, palms facing you. Starting with your left little finger, number your fingers from 1 to 10, as shown below.

To find 9 × n, fold down finger n. Fingers to the left of it are the tens, and fingers to the right are the ones.

Example 1: 9 × 5

Fold down your fifth finger.

There are 4 fingers to the left of the folded finger and 5 fingers to the right. So 9 × 5 = 45.

Example 2: 9 × 6

Fold down your sixth finger.

There are 5 fingers to the left of the folded finger and 4 fingers to the right. So 9 × 6 = 54.

Why it works: folding finger n leaves n − 1 fingers on the left and 10 − n on the right. And 9 × n is exactly (n − 1) tens plus (10 − n) ones. For n = 6: 5 tens + 4 ones = 54.

Try it: 9 × 7 (tap for the answer)

Fold down finger 7. There are 6 fingers on the left and 3 on the right, so 9 × 7 = 63.

2Add two-digit numbers from left to right

On paper, most of us add from right to left, and that's fine. But to add two-digit numbers fast in your head, it's easier to work from left to right: add the tens first, then the ones.

Split the second number into tens and ones. Add the tens, then add the ones.

Example 3: 56 + 23

Step 1: Rewrite 23 as 20 + 3.

Step 2: Add the tens: 56 + 20 = 76.

Step 3: Add the ones: 76 + 3 = 79.

Example 4: 64 + 35

Step 1: Rewrite 35 as 30 + 5.

Step 2: 64 + 30 = 94

Step 3: 94 + 5 = 99

Why it works: adding tens only changes the tens digit, which is easy to do in your head. Then you only have one small number left to add.

Try it: 47 + 38 (tap for the answer)

47 + 30 = 77, then 77 + 8 = 85.

3Multiply any number by 10, 100, 1,000…

For a whole number, write one zero at the end for each zero in 10, 100, 1,000 and so on.

× 10: write one zero at the end.
× 100: write two zeros at the end.
× 1,000: write three zeros at the end.

Example 5: 65 × 10 = 650

Example 6: 14,778 × 1,000 = 14,778,000

Decimals: adding zeros doesn't work for decimals (3.5 × 10 is not 3.50). Instead, move the decimal point one place to the right for each zero: 3.5 × 10 = 35, and 3.5 × 100 = 350.

Why it works: multiplying by 10 makes every digit worth 10 times more, so each digit shifts one place to the left. The new zero fills the empty ones place.

Try it: 230 × 100 (tap for the answer)

Write two zeros at the end: 23,000.

4Square a two-digit number fast

This trick squares a two-digit number much faster than the usual multiplication. The goal is to change the two numbers being multiplied so that one of them ends in zero.

$Cool math tricks$

To square 14, subtract 4 from one 14 to get 10, and add 4 to the other to get 18. Multiply 10 × 18 = 180, then add 4² = 16. So 14² = 196.

Why do we add 4²? Multiply out 10 × 18:

10 × 18 = (14 − 4)(14 + 4)
= 14 × 14 + 14 × 4 − 4 × 14 − 4 × 4
= 14² − 4²

So 10 × 18 is 4² less than 14². Adding 4² back gives exactly 14²:

14² = 10 × 18 + 4²

In general: x² = (x − c)(x + c) + c². Choose c so that x − c or x + c ends in zero.

Example 7: 17²

17² = (17 − 7)(17 + 7) + 7²

= 10 × 24 + 49

= 240 + 49 = 289

Try it: 23² (tap for the answer)

Use c = 3: 20 × 26 + 3² = 520 + 9 = 529.

5Multiply 6 by an even number

When you multiply 6 by 2, 4, 6 or 8, the answer follows a pattern:

The ones digit is the even number itself. The tens digit is half of the even number.

Example 8: 6 × 8 → ones digit 8, tens digit 4 → 48

6 × 6 → ones digit 6, tens digit 3 → 36

Why it works: 6 × n = 5 × n + n. For an even n, 5 × n is a whole number of tens (n ÷ 2 tens), and the extra n gives the ones digit.

Try it: 6 × 4 (tap for the answer)

Ones digit 4, tens digit 2: 24.

6Multiply any number by 9

Multiply the number by 10, then subtract the number.

Example 9: 18 × 9

Step 1: 18 × 10 = 180

Step 2: 180 − 18 = 162

Why it works: 9 is one less than 10.

18 × 9 = 18 × (10 − 1) = 18 × 10 − 18 = 180 − 18

We use it because multiplying by 10 is easy.

Try it: 37 × 9 (tap for the answer)

370 − 37 = 333.

7Subtract quickly

Suppose you're subtracting 28 from 65. Vertical subtraction works, but when you need an answer fast, there's no time for borrowing and regrouping.

Round the number you're subtracting up to a ten (or hundred). Subtract that, then add back the extra.

65 − 28: subtract 30 to get 35. You took away 2 too many, so add 2: 37.

Example 10: 461 − 297

461 − 300 = 161

161 + 3 = 164

Done in a snap, with no borrowing at all.

Try it: 83 − 49 (tap for the answer)

83 − 50 = 33, then 33 + 1 = 34.

8Square a two-digit number ending in 1

Subtract 1 to get a number ending in 0. Square it, then add twice that number, then add 1.

41²: subtract 1 to get 40.

40² + 40 + 40 + 1 = 1,600 + 80 + 1 = 1,681

Example 11: 61²

61² = 60² + 60 + 60 + 1 = 3,600 + 120 + 1 = 3,721

Why it works: (a + 1)² = a² + 2a + 1. When a ends in zero, a² and 2a are both easy to find in your head.

Try it: 71² (tap for the answer)

70² + 140 + 1 = 4,900 + 140 + 1 = 5,041.

9Quickly test if a number is divisible by 2 to 10

Need to know whether something can be shared evenly between 2, 3, 4… or 10 people? Skip the long division and use the divisibility rules:

By	A number is divisible if…
2	its last digit is even (0, 2, 4, 6 or 8)
3	the sum of its digits is divisible by 3
4	its last two digits form a number divisible by 4
5	its last digit is 0 or 5
6	it is divisible by both 2 and 3
7	doubling the last digit and subtracting it from the rest of the number gives a multiple of 7
8	its last three digits form a number divisible by 8
9	the sum of its digits is divisible by 9
10	its last digit is 0

Example 12

Can you share $4,557 evenly between you and your two sisters?

That's 3 people, so check divisibility by 3.

4 + 5 + 5 + 7 = 21, and 21 is divisible by 3.

So the answer is yes.

Try it: Is 1,236 divisible by 6? (tap for the answer)

It's even, so it's divisible by 2. Its digits add up to 1 + 2 + 3 + 6 = 12, which is divisible by 3. Divisible by both 2 and 3 means yes (1,236 ÷ 6 = 206).

10Divide without long division

Split the number into parts that are easy to divide, divide each part, then add the results.

Example 13: 4,557 ÷ 3

3 × 1,500 = 4,500, so take 4,500 first.

That leaves 4,557 − 4,500 = 57.

3 × 19 = 57

4,557 ÷ 3 = 1,500 + 19 = 1,519

So each person in Example 12 gets $1,519.

Try it: 2,568 ÷ 4 (tap for the answer)

4 × 600 = 2,400, leaving 168. And 4 × 42 = 168. So 2,568 ÷ 4 = 600 + 42 = 642.

22 more cool math tricks

Each trick below has its own lesson with examples.

How to solve some basic math puzzles

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30 Cool Math Tricks