1
Order Of Operations
ORDER OF OPERATIONS
The order of operations is the procedure you must follow to correctly perform any
mathematical sentence. The order of operations is especially important when
expressions involve brackets and exponents.
The order of operations dictates that expressions be simplified in the following order:
1. Brackets (work inside brackets first)
2. Exponents
3. Division and multiplication from left to right
4. Addition and subtraction from left to right
Students can remember this easily by the name BEDMAS, which
stands for brackets, exponents, division and multiplication,
addition and subtraction.
B: Brackets (
)
E: Exponents²
D: Divisions ÷
M: Multiplications x
A: Additions +
S: Subtractions Note that the two steps Division and Multiplication can be done together as one step,
and the same applies for Addition and Subtraction.
Definition: Exponents- a symbol indicating to what power a quantity is to be raised. For
example, in 3², ² is the exponent, indicating that 3 is to be squared.
2
Example 1: 14 ÷ 2 – (6-5)
Step 1 – Calculate subtraction in the brackets (6-5)
= 14 ÷ 2 – 1
Step 2 – Calculate division 14 ÷ 2
=7–1
Step 3 – Calculate subtraction 7-1
=6
Example 2: 4 + 8 – 9 ÷ 3
Step 1 – Divide
9÷3
Step 2 – Add
4+8-3
Step 3 – Subtract
12-3
=9
Example 3:
(8 + 5) x 3
= 13 x 3
= 39
Example 4:
8 + (5 x 3)
= 8 + 15
= 23
In examples 3 and 4, notice
that the two expressions have
the same numbers and the
same operations, but the
results are different because
of the grouping symbols.
Example 5: [(36 ÷ 36) + (2 x 3)] - 7
Step 1 – Calculate inside brackets, division first (36 ÷ 36)
=[1 + (2 x 3)] - 7
Step 2 – Calculate multiplication inside brackets (2 x 3)
=[1 + 6] - 7
Step 3 – Calculate addition inside brackets
=7–7
Step 4 – Calculate subtraction
=0