How to Learn Mental Math


Despite the ease of using a calculator to solve minor math problems, it will always be faster to pull the correct answer out of thin air. Mental math is the name for the ability to perform seemingly impossible calculations without using calculators or paper. People have mastered its use for party tricks and to make their lives easier on a day to day basis. Mental math only requires the ability to flex the brain slightly beyond its usual use.

  • Learn basic rules of math. Mental math builds upon a knowledge of math, so make sure to know basic addition, subtraction, multiplication and division rules.

  • Understand the pattern of nines. Multiplying by 9 is similar to multiplying by (10-1), meaning the original number is subtracted from 10 times the original number.

  • Use addition to multiply by 11. No matter how big the number multiplied by 11, use this formula: (first number)(first + second numbers)(second + third numbers)...(last number), where each number corresponds to its placement in the original number. For example, 243 x 11 is: (2), (2+4 = 6), (4+3 = 7), (3), which is 2673 when the numbers are placed together.

  • Cut in half to multiply by 5. Because 5 is half of 10, a number can be multiplied by 10 (add a zero to the end) and halved to quickly multiply by 5.

  • Use square numbers to find products. If two numbers differ by 2 (12 and 14, for example), find the square of the number between them and subtract by one to find the product. To find 17 x 19, use [(18 x 18) - 1] to get 323.

  • Square two digit numbers in one step. If a number ends in 5, its square will end in 25. The first place(s) is the tens place times (tens place + 1), so 35x35 = (3x4)25 = 1225.

Tips & Warnings

  • When using this guide, "(first number)" means the number of the largest place in a number. For example, the first number of 3849 is 3. The second is 8, and so on.

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