Basic Mathematics for College Students

1.9 Order of Operations 103

Evaluate the exponential expression:

Do the multiplication:

 24 Do the subtraction.

 32  8 2  16 32.

2  42  8  2  16  8 42 16.

EXAMPLE (^2) Evaluate:
StrategyWe will perform the multiplication first.
WHYThe expression does not contain any parentheses, nor are there any
exponents.
Solution
We will write the steps of the solution in horizontal form.
Do the multiplication:
Working from left to right, do the
subtraction:
 90 Do the addition.
80  6 74.

 74  16

80  3  2  16  80  6  16 3  2 6.

80  3  2  16

Self Check 2

Evaluate:

Now TryProblem 23

60  2  3  22

Caution! In Example 2, a common mistake is to forget to work from left to

right and incorrectlyperform the addition before the subtraction. This error

produces the wrong answer, 58.

Remember to perform additions and subtractions in the order in which they

occur.The same is true for multiplications and divisions.

 58

 80  22

80  3  2  16  80  6  16

EXAMPLE (^3) Evaluate:
StrategyWe will perform the division first.
WHYAlthough the expression contains parentheses, there are no calculations to
perform withinthem. Since there are no exponents, we perform multiplications
and divisions as they are occur from left to right.
Solution
We will write the steps of the solution in horizontal form.
Working from left to right, do the
division:
Working from left to right, do the
multiplication:
Complete the multiplication:
 2 Do the subtraction.

 32  30 15(2)30.

5(3)15.

 32 15(2)

192  6 32.

192  6 5(3)2 32 5(3)2

192  6 5(3)2

Self Check 3

Evaluate:

Now TryProblem 27

144  9 4(2)3

We will use the five-step problem solving strategy introduced in Section 1.6 and
the order of opertions rule to solve the following application problem.

3

2

2

12

 8

24

1

1

6

 2

32

7

1

4

 16

90

Success Tip Calculations

that you cannot perform in

your head should be shown

outside the steps of your

solution.

32

6  192

 18

12

 12

0