10 Math Tricks for Quick Calculations in Your Head

Mathematics is often seen as a daunting subject, but there are numerous tricks and shortcuts that can make mental calculations faster and simpler. Whether you’re dealing with basic arithmetic or complex computations, mastering these techniques can significantly enhance your mental math skills. Here are ten math tricks that will help you crunch numbers swiftly and accurately in your head.

1. Multiplying by 11

  • To multiply a two-digit number by 11, add the two digits together and place the sum between the original digits. For instance, 11 x 23 = 253 (2+3 = 5, place 5 between 2 and 3).

2. Squaring Numbers Ending in 5

  • When squaring numbers ending in 5, simply multiply the first digit by itself plus 1, then append 25 to the result. For example, 25² = (2x(2+1))  25 = 625.

3. Doubling and Halving

  • To mentally multiply any number by 25, first halve the number and then multiply by 100. For example, 56 x 25 = (56 ÷ 2) x 100 = 1400.

4. Finding Percentages

  • To calculate percentages quickly, find 10% of the number and adjust accordingly. For instance, to find 20% of 80, know that 10% is 8, so 20% will be 16.

5. Mental Division

  • Simplify division by rounding numbers. For example, to divide 168 by 7, round 168 to 170 and divide by 10, resulting in 17. Then adjust for the rounding: 17 – 2 = 24. This quick approximation can be handy.

6. Fast Squaring of Numbers Near 50

  • For numbers near 50, subtract or add the difference from 50 and square it. For instance, 53² = (50 + 3)  3² = 2809.

7. Calculating Multiples of 9

  • To find the multiple of 9 for a given number, sum its digits. If the sum is a two-digit number, add those digits together until you get a single digit. The result is the multiple of 9. For example, for 234, 2+3+4 = 9, which is a multiple of 9.

8. Quickly Checking for Divisibility

  • To check if a number is divisible by 3, add its digits. If that sum is divisible by 3, then the original number is divisible by 3. Similarly, to check for divisibility by 9, use the rule mentioned in point 7.

9. Square Root Approximations

  • Estimating square roots can be done by finding perfect squares close to the number and then adjusting. For instance, the square root of 85 is close to 81 (9²), so it’s slightly more than 9.

10. Breaking Down Complex Problems

  • Break down complex calculations into smaller, more manageable parts. Simplify each part before integrating the results to find the final answer. This method aids in reducing errors and speeding up mental math.

Mastering these mental math tricks can significantly boost your number crunching abilities, making daily calculations faster, easier, and more accurate. With practice, these techniques can become second nature, allowing you to perform complex math operations swiftly and confidently in your head.