Basic Mathematics for College Students

46 Chapter 1 Whole Numbers

EXAMPLE (^6) Find the product:
Strategy We will use the associative property to group 50 with 2.
WHY It is helpful to regroup because 50 and 2 are a pair of numbers that are easily
multiplied.
Solution
We will write the solution in horizontal form.
Use the associative property of multiplication to
regroup the factors.
Do the multiplication within the parentheses first.
1,700 Since 100 has two zeros, attach two 0’s after 17.

 17  100

(1750) 2  17 (502)

(1750) 2

Self Check 6

Find the product:

Now TryProblem 45

(2325) 4

5 Estimate products of whole numbers.

Estimation is used to find an approximate answer to a problem.

EXAMPLE (^7) Estimate the product:
Strategy We will use front-end rounding to approximate the factors 59 and 334.
Then we will find the product of the approximations.
WHY Front-end rounding produces whole numbers containing many 0’s. Such
numbers are easier to multiply.
Solution
Both of the factors are rounded to their largest place valueso that all but their first
digit is zero.
Round to the nearest ten.
Round to the nearest hundred.
To find the product of the approximations, 6 0  300 , we simply multiply 6 by 3, to get
18, and attach 3 zeros. Thus, the estimate is 18, 000.
If we calculate , the product is exactly 19,706. Note that the estimate is
close: It’s only 1,706 less than 19,706.

59  334

59  334 60  300

59  334

Self Check 7

Estimate the product:

Now TryProblem 51

74  488

6 Solve application problems by multiplying whole numbers.

Application problems that involve repeated addition are often more easily solved

using multiplication.

EXAMPLE (^8) Daily Pay In 2008, the average U.S. manufacturing worker
made $18 per hour. At that rate, how much money was earned in an 8-hour
workday? (Source: Bureau of Labor Statistics)
Strategy To find the amount earned in an 8-hour workday, we will multiply the
hourly rate of $18 by 8.
WHY For each of the 8 hours, the average manufacturing worker earned $18. The
amount earned for the day is the sum of eight 18’s: 18  18  18  18  18  18 
18 18. This repeated addition can be calculated more simply by multiplication.
Solution
We translate the words of the problem to numbers and symbols.
Self Check 8
DAILY PAYIn 2008, the average
U.S. construction worker made
$22 per hour. At that rate, how
much money was earned in an
8-hour workday? (Source:
Bureau of Labor Statistics)
Now TryProblem 86