# Arithmetic » Basic rules/calculation order

## The calculation order in arithmetic is:

1. What is between Brackets
2. Powers and Roots from left to right
3. Multiplications and Divisions from left to right
4. Additions and Subtractions from left to right

Note: In some countries they use parentheses instead of brackets and/or indices or exponents instead of powers.

In operators/signs:     In letters:      Mnemonic:

 ( ) #2 √ × ÷ + –

 B P R M D A S

 Big Puffy Rats Make Dora Always Scared

To reduce the risk of a mistake, you solve these exercises with intermediate steps.

Note: Writing intermediate steps is different from making calculations.
Take a look at the examples below. In the first exercise the calculation '3 × 5 = 15' is not written down! Because you changed 3 × 5 in your intermediate step to 15 you show that that is what you calculated.

Examples

 12 + 3 × 5 = 12 + 15 = 27
 12 ÷ 2 – 2 × 2 = 6 – 4 = 2

 18 ÷ 3 × 2 = 6 × 2 = 12
 (3 + 4) × 9 = 7 × 9 = 63

 24 – (7 + 3 × 2 ) = 24 – (7 + 6 ) = 24 – 13 = 11
 9 + –43 × – = 9 + –64 × –4 = 9 + 256 = 265

## No more possible confusion?

With such clear 'rules of way' there will not be any mistakes with the calculation order anymore, right? ... Wrong. Look at the exercise 8/2(4).
Perhaps you knew already, but you are allowed to leave out the multiplication sign, so this exercise means 8 ÷ 2 × 4 = 4 × 4 = 16. However, there are people who say that because the multiplication is left out, that means the 2 × 4 has to be done first, as those 'clearly' belong to each other.
In that case, we will get 8 ÷ 8 = 1.
Unfortunately the calculator also does not help in giving one clear answer.

It is not for nothing mathematicians like to write divisions as a fraction.
That way we will get 82(4) = 16 and 82(4) = 1. No confusion possible.