Order of operations: BIDMAS
In a nutshell
The order of operations is a rule that states which operation must be performed first. It is very helpful when having to solve multi-step equations.
Order of operations: BIDMAS
BIDMAS is the acronym for the order of equations. It stands for:
- Brackets
- Indices
- Division/Multiplication
- Addition/Subtraction
Note: Division/Multiplication and Addition/Subtraction are written on the same line because it depends what comes first when reading the equation from left to right.
Example 1
What is 30−3×(8−1)?
First, using BIDMAS, simplify any Brackets:
8−1=7
The equation is now:
30−3×7
There are no Indices, so move on to Division/Multiplication:
3×7=21
The equation is now:
30−21
Finally, go through any Addition/Subtraction:
30−21=9
30−3×(8−1)=9
Example 2
Two variables y and x are connected through the formula y=3x2−x+5. What is y when x=4?
Substituting in x=4 into the equation gives:
y=3(4)2−4+5
Going through BIDMAS, there are no Brackets to simplify. So, move onto Indices:
42=16
The equation then becomes:
y=3×16−4+5
Now, move onto Division/Multiplication:
3×16=48
The equation then becomes:
y=48−4+5
Finally, move onto Addition/Subtraction:
Note that even though the addition comes first in BIDMAS, you perform the subtraction first as it comes first when reading the equation from left to right.
48−4=44
44+5=49
y=49
