Basic Mathematics for College Students

184 Chapter 2 The Integers

EXAMPLE (^2) Evaluate:
StrategyWe will perform the multiplication first.
WHYThere are no operations to perform within parentheses, nor are there any
exponents.
Solution
Working from left to right,
do the multiplications.
 6 Do the addition.

12(3)(5)(3)(2) 36 ( 30 )

12(3)(5)(3)(2)

Self Check 2

Evaluate:

Now TryProblem 17

4(9)(4)(3)(2)

EXAMPLE (^3) Evaluate:
StrategyThis expression contains the operations of division and multiplication.
We will perform the divisions and multiplications as they occur from left to right.
WHYThere are no operations to perform within parentheses, nor are there any
exponents.
Solution
Do the division first: 40 (4) 10.
 50 Do the multiplication.

40 (4) 5  10  5

40 (4)5

Self Check 3

Evaluate:

Now TryProblem 21

45 (5)3

Caution! In Example 3, a common mistake is to forget to work from left to

right and incorrectly perform the multiplication first. This produces the wrong

answer,.

 2

40 (4)5 40 (20)

 2

EXAMPLE (^4) Evaluate:
StrategyThere are two exponential expressions to evaluate and a subtraction to
perform. We will begin with the exponential expressions.
WHYSince there are no operations to perform within parentheses, we begin with
step 2 of the order of operations rule: Evaluate all exponential expressions.
SolutionRecall from Section 2.4 that the values of and are not the
same.
Evaluate the exponential expressions:
 22 (2 2) 4 and (2)^2 2(2) 4.
If it is helpful, use the subtraction rule: Add the
opposite of 4, which is 4.
 8 Do the addition.

 4 (4)

 22 (2)^2  4  4

 22 (2)^2

 22 (2)^2

Self Check 4

Evaluate:

Now TryProblem 25

 32 (3)^2

2 Evaluate expressions containing grouping symbols.

Recall that parentheses(),brackets[],absolute value symbols@@, and the

fraction bar— are called grouping symbols.When evaluating expressions, we must

perform all calculations within parentheses and other grouping symbols first.