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.

## Table of Contents

## Multiplying by 5

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

To calculate , do and then

## Dividing by 5

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

To calculate , multiply the numerator and denumerator by 2, to get . 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 , note that and . is closer to 7 since 50 is closer to 49, so in the range of [7, 8] the answer to 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 .
- The difference between .
- Next, you divide the difference (9) bij the round square root (18) and you divide this always by 2, so you have .
- Finally, you add this number on top of the round root (18), so your answer would be .
- What’s the real answer? It’s 18.248, which is very close to our approximation.

## N^2 – (N-1)^2

To subtract squares of consecutive numbers, use the formula

(1)

## Sum All Numbers from A to B

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

(2)

To sum up all numbers from 1 to 10, we do

(3)

In case you need to sum up all number from 101 to 200, we do

(4)

## Sum Odd Numbers from A to B

To sum up the odd numbers from 1 to N, where N is the last odd number, use the formula:

(5)

So, what is the sum of all odd numbers from 100 to 200?

Let’s sum up all odd numbers in the range from 0 to 200. The last odd number is 199. To sum up all odd numbers up to 199 is calculated by

(6)

Second, let’s sum up all numbers in the range from 0 to 100. The last odd number is 99. To sum up all odd numbers up to 99 is calculated by

(7)

The sum of all odd numbers from 100 to 200 is then given by 10000 – 2500 = 7500.

## New Tricks?

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