20 Interesting Math Tricks for Quick Solutions

Explore these fun math tricks to simplify calculations, check divisibility, and improve mental math skills! Each trick is designed to make math faster and more enjoyable.

1. Divisibility by 2

If a number ends in an even digit (0, 2, 4, 6, or 8), it is divisible by 2.

• Example: 28 ends in 8, so it’s divisible by 2.
• Example: 46 ends in 6, so it’s divisible by 2.

2. Divisibility by 3

If the sum of all the digits of a number is divisible by 3, then the number itself is divisible by 3.

• Example: 123, sum of digits is 1 + 2 + 3 = 6, which is divisible by 3.
• Example: 453, sum of digits is 4 + 5 + 3 = 12, divisible by 3.

3. Divisibility by 4

If the last two digits of a number form a number divisible by 4, then the entire number is divisible by 4.

• Example: 132, last two digits are 32, which is divisible by 4.

4. Divisibility by 5

If a number ends in 0 or 5, it is divisible by 5.

• Example: 35 and 120 both end in 5 or 0, so they’re divisible by 5.

5. Divisibility by 6

A number is divisible by 6 if it is divisible by both 2 and 3.

• Example: 54 is even (divisible by 2) and 5 + 4 = 9 (divisible by 3). So, 54 is divisible by 6.

6. Divisibility by 9

If the sum of all the digits of a number is divisible by 9, then the number itself is divisible by 9.

• Example: 729, sum of digits is 7 + 2 + 9 = 18, divisible by 9.

7. Multiplying by 5

To multiply by 5 quickly, divide the number by 2 and then multiply by 10.

• Example: 36 × 5, divide by 2 to get 18, then multiply by 10 to get 180.

8. Multiplying by 11

To multiply a two-digit number by 11, add the digits and place the sum in between.

• Example: 23 × 11, add 2 + 3 = 5 and place it between 2 and 3 to get 253.

9. Multiplying by 9

To multiply by 9, multiply by 10 and subtract the original number.

• Example: 8 × 9, calculate 8 × 10 = 80, then 80 - 8 = 72.

10. Squaring Numbers Ending in 5

Square any two-digit number ending in 5 by multiplying the first digit by itself +1, and add 25.

• Example: 45², 4 × 5 = 20, add 25 to get 2025.

11. Divisibility by 8

If the last three digits of a number are divisible by 8, the whole number is divisible by 8.

• Example: 1000, last three digits are 000, divisible by 8.

12. Multiplying by 25

To multiply by 25, divide by 4 and then multiply by 100.

• Example: 16 × 25, divide by 4 to get 4, then multiply by 100 to get 400.

13. Finding 10% of a Number

To find 10% of a number, simply move the decimal point one place to the left.

• Example: 250, 10% is 25.

14. Divisibility by 7

Double the last digit, subtract it from the rest of the number, and if the result is divisible by 7, then the original number is too.

• Example: 203, double the last digit (3 × 2 = 6), 20 - 6 = 14, divisible by 7.

15. Divisibility by 10

If a number ends in 0, it is divisible by 10.

• Example: 130 ends in 0, so it’s divisible by 10.

16. Adding 9 Quickly

To add 9, add 10 and subtract 1.

• Example: 56 + 9, add 10 to get 66, then subtract 1 to get 65.

17. Divisibility by 11

If the difference between the sum of the digits in odd and even positions is 0 or divisible by 11, the number is divisible by 11.

• Example: 121, difference is |1 - 2 + 1| = 0, so it’s divisible by 11.

18. Multiplying by 15

To multiply by 15, multiply the number by 10 and add half of the result.

• Example: 40 × 15, calculate 40 × 10 = 400, then add half (200) to get 600.

19. Subtracting from 1000

To subtract a number from 1000, subtract each digit from 9, except the last digit from 10.

• Example: 1000 - 356, subtract each digit from 9 except the last: 644.

20. Finding 20% of a Number

To find 20%, find 10% and then double it.

• Example: 150, 10% is 15, double it to get 30.