Numbers: Integers
Order of operations
Operation
An operation is an action involving two numbers, such as an addition.
How an operation should be executed, has been agreed upon. For example, in primary school we learned how to add two numbers.
Examples
\begin{array}{rcl}\text{Addition:}& & 3+5\\\text{Subtraction:}&& 9-4\\\text{Multiplication:}&& 2 \times 9\\\text{Division:}&& 9:3\end{array}
When there are multiple operations in a calculation, we have to choose which operation to do first. For this, we have a couple of important rules.
When a calculation only includes additions and subtractions, we work from left to right. |
Example |
When a calculation only includes multiplications and divisions, we also work from left to right. |
Example |
Multiplications and divisions are always done before additions and subtractions. |
Example |
Always first calculate what is in between brackets. The calculation between brackets is always done before any other operation. |
Example |
#\begin{array}{rcl}
10000-59-41&=&9941-41\\&&\phantom{xxx}\blue{\text{first subtraction}} \\
&=&9900 \\&&\phantom{xxx}\blue{\text{subtracted}} \\
\end{array}#
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