1.3 Order of Operations
Order of Operations for Evaluating Expressions
To evaluate expressions with multiple operations there is an order for evaluation. You may remember it
as PEMDAS: parentheses, exponents, multiplication and division, addition and subtraction.
Example
Evaluate 2 + 3(1 + 4).
2 + 3(1 + 4)
= 2 + 3(5)
= 2 + 15
= 17
Example
Evaluate 8 − [(4 − 7) + (8 − 1)].
8 − [(4 − 7) + (8 − 1)]
= 8 − (−3 + 7)
=8−4
=4
Consider (−2)2 vs −22 .
(−2)2 = (−2)(−2) = 4 whereas −22 = −(2 · 2) = −4. In the second one, without parentheses, the
exponent is only applied to the 2. The negative is considered multiplication by −1 and so exponents
first.
Consider
5+2
. The fraction bar presents the grouping and so parentheses are not necessary.
1+4·5
5+2
1+4·5
=
7
1 + 20
=
7
21
=
1
3
If I were to enter this into my calculator as one expression, I would enter the following:
(5 + 2) ÷ (1 + 4 · 5)