Basic Mathematics for College Students

20 Chapter 1 Whole Numbers

EXAMPLE (^6) Use front-end rounding to estimate the sum:
3,714 2,489  781 5,500  303
Strategy We will use front-end rounding to approximate each addend. Then we
will find the sum of the approximations.
WHY Front-end rounding produces addends containing many 0’s. Such numbers
are easier to add.
Solution
Each of the addends is rounded to its largest place valueso that all but its first digit
is zero. Then we add the approximations using vertical form.
The estimate is 13,100.
If we calculate 3,714 2,489  781 5,500 303, the sum is exactly 12,787.
Note that the estimate is close: It’s just 313 more than 12,787. This illustrates the
tradeoff when using estimation: The calculations are easier to perform and they
take less time, but the answers are not exact.
Round to the nearest thousand.
Round to the nearest thousand.
Round to the nearest hundred.
Round to the nearest thousand.
Round to the nearest hundred.

3,714 4,000

2,489 2,000

781 800

5,500 6,000

 303  300

13,100

Self Check 6

Use front-end rounding to

estimate the sum:

Now TryProblem 61

6,780

3,278

566

4,230

 1,923











3 Estimate sums of whole numbers.

Estimation is used to find an approximate answer to a problem. Estimates are helpful

in two ways. First, they serve as an accuracy check that can find errors. If an answer

does not seem reasonable when compared to the estimate, the original problem

should be reworked. Second, some situations call for only an approximate answer

rather than the exact answer.

There are several ways to estimate, but the objective is the same: Simplify the

numbers in the problem so that the calculations can be made easily and quickly. One

popular method of estimation is called front-end rounding.

b.Each step of the addition is explained separately. Your solution should look

like the last step.

The sum is 1,117.

Add the bold numbers in the hundreds column.

Think: (2 8)  1  10  1 11.

2

1

0

1

1

8 6 7

 4 9

1 , 1 1 7

Add the bold numbers in the tens column.

Think: (6 4)  1  10  1  11.

Write the 1 and carry the 1.

2

1

0

1

1

8 6 7

 4 9

1 7

Add the bold numbers in the ones column first.

Think: (9 1)  7  10  7 17.

Write the 7 and carry the 1.

2 0

1

1

8 6 7

 4 9

7