Basic Mathematics for College Students

2.6 Order of Operations and Estimation 187

The Language of Mathematics Multiplication is indicated when a number is

outside and next to an absolute value symbol. For example,

8  40  6  20 means 8 4  0  6  20

EXAMPLE (^10) Evaluate:
StrategyThe absolute value bars are grouping symbols. We will perform the
subtraction within them first.
WHYBy the order of operations rule, we must perform all calculations within
parentheses and other grouping symbols (such as absolute value bars) first.
Solution
If it is helpful, use the subtraction rule
within the absolute value symbol: Add the
opposite of 2, which is 2.
Do the addition within the absolute value symbol:
 6 (2) 8.
Find the absolute value: @ 8 @8.
Do the multiplication: 4(8) 32.
If it is helpful, use the subtraction rule:
Add the opposite of 32, which is 32.
 24 Do the addition.

 8 (32)

 8  32

 8 4(8)

 8  40  80

8  40  6  20  8  40  6 (2) 0

8  40  6  20

4 Estimate the value of an expression.

Recall that the idea behind estimation is to simplify calculations by using rounded
numbers that are close to the actual values in the problem. When an exact answer is
not necessary and a quick approximation will do, we can use estimation.

EXAMPLE (^11) The Stock Market
The change in the Dow Jones Industrial
Average is announced at the end of
each trading day to give a general
picture of how the stock market is
performing. A positive change means a
good performance, while a negative
change indicates a poor performance.
The week of October 13–17, 2008, had
some record changes, as shown below.
Round each number to the nearest ten
and estimate the net gain or loss of
points in the Dow that week.
StrategyTo estimate the net gain or loss, we will round each number to the
nearest ten and addthe approximations.
Self Check 11
THE STOCK MARKETFor the week
of December 15–19, 2008, the
Dow Jones Industrial Average
performance was as follows,
Monday: , Tuesday: ,
Wednesday: , Thursday: ,
Friday:. Round each number
to the nearest ten and estimate
the net gain or loss of points in
the Dow for that week. (Source:
finance.yahoo.com)
Now TryProblems 53 and 97

 27

 98  219

 63  358

EIGHTFISH/Getty Images

Self Check 10

Evaluate:

Now TryProblem 49

7  50  1  60



Monday

Oct. 13, 2008

(largest 1-day

increase)

Tuesday

Oct. 14, 2008

Wednesday

Oct. 15, 2008

(second-largest

1-day decline)

Thursday

Oct. 16, 2008

(tenth-largest

1-day increase)

Friday

Oct. 17, 2008

Source: finance.yahoo.com

3

2

2

12

 8

24