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Mental Arithmetic 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.

There is a way to approximate the answer on the comma, even for larger numbers.

Let’s say you want to find the square root of 333.
We know that the closest round number is 18, because $18^2 = 324$ .
The difference between $333-324=9$ .
Next, you divide the difference (9) by the round square root (18) and you divide this always by 2, so you have $\frac{9}{18} / 2 = \frac{9}{36}$ .
Finally, you add this number on top of the round root (18), so your answer would be $18 + \frac{9}{36} = 18.25$ .
What’s the real answer? It’s 18.248, which is very close to our approximation.