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

In a lot of countries they use the term parentheses instead of brackets.

In operators/signs:     In letters:      Mnemonic:

( )
#2√  
×:  
+–  

B
PR
MD
AS

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 × square root of 16 =
9 + –64 × –4 =
9 + 256 = 265