Mental Math – Tips and Tricks for Quick Calculations

This course provides a collection of tips and tricks for performing mental math calculations quickly and efficiently. It is designed for anyone looking to improve their ability to perform arithmetic in their head, focusing on practical methods for (common) mathematical tasks.

Multiplying by 5

To multiply a number by 5, first multiply it by 10 and then halve the result.

To calculate 39*5, do 39*10 and then 390/2=195

Dividing by 5

To divide a number by 5, multiply it by 2 and then divide by 10.

To calculate 160/5, multiply the numerator and denumerator by 2, to get 320/10. People find it usually easy to divide a number by 10.

Approximating Square Roots

For a rough estimate of the square root of a number, find the nearest perfect squares and use them as reference points.

To estimate \sqrt{50}, note that \sqrt{49} = 7 and \sqrt{64} = 8. \sqrt{50} is closer to 7 since 50 is closer to 49, so in the range of [7, 8] the answer to \sqrt{50} is way closer to 7.

N^2 – (N-1)^2

To subtract squares of consecutive numbers, use the formula

(1)   \begin{equation*} N^2 - (N-1)^2 = 2N - 1 \end{equation*}

5000^2 - 4999^2 = 2*5000 - 1 = 9999

Sum Numbers from A to B

To sum up all numbers from 1 to N, simply use the formula:

(2)   \begin{equation*} \frac{N*(N+1)}{2} \end{equation*}

To sum up all numbers from 1 to 10, we do 10*11/2 = 55.
In case you need to sum up all number from 101 to 200, we do 200*201/2 - 100*101/2 = 20100 - 5050 = 15050

New Tricks?

Write them in the comments below! Any valuable tips and tricks will be added to this list.