Basic Mathematics for College Students

1.9 Order of Operations 105

Solution
a.The expression does not contain any parentheses, nor are there any exponents,
nor any multiplication or division. We perform the additions and subtractions
as they occur, from left to right.
Do the subtraction:
Do the addition.

b.By the order of operations rule, we must perform the operation within the
parentheses first.
Do the addition: Read as “12 minus the
quantity of 3 plus 5.”
 4 Do the subtraction.

12 ( 3  5 ) 12  8 3  5 8.

 14

12  3  5  9  5 12  3 9.

The Language of Mathematics When we read the expression

as “12 minus the quantityof 3 plus 5,” the word quantityalerts the reader to

the parentheses that are used as grouping symbols.

12 (35)

EXAMPLE (^6) Evaluate:
StrategyWe will perform the operation within the parentheses first.
WHYThis is the first step of the order of operations rule.
Solution
Read as “The cube of the quantity of
2 plus 6.” Do the addition.
Evaluate the exponential expression:
83  8  8  8 512.

 512

( 2  6 )^3  83

(26)^3

Self Check 6

Evaluate:

Now TryProblem 35

(13)^4

EXAMPLE (^7) Evaluate:
StrategyWe will perform the multiplication within the parentheses first.
WHYWhen there is more than one operation to perform within parentheses, we
follow the order of operations rule. Multiplication is to be performed before
subtraction.
Solution
We apply the order of operations rule within the parentheses to evaluate
Do the multiplication within the
parentheses.
Do the subtraction within the parentheses.
Do the multiplication:
 11 Do the addition.

 5  6 2(3)6.

 5 2(3)

5 2(13 5  2 ) 5 2(13 10 )

13  5 2.

5 2(13 5 2)

Self Check 7

Evaluate:

Now TryProblem 39

50 4(12 5 2)

Some expressions contain two or more sets of grouping symbols. Since it can be
confusing to read an expression such as we use a pair of
bracketsin place of the second pair of parentheses.

16  6 [ 42 3(52)]

16 6(4^2 3(52)),

6

3

4

 8

512