Basic Mathematics for College Students

398 Chapter 4 Decimals

If the sum of the digits in any place-value column

is greater than 9, we must carry.

If the subtraction of the digits in any place-value

column requires that we subtract a larger digit

from a smaller digit, we must borrowor regroup.

Subtract:

Write the problem in vertical formand subtract, column-by-column,

working right to left.

9

To check: The sum of the difference and the subtrahend should

equal the minuend.

Difference

Subtrahend

Minuend

5.3

1

7

1

1

 3.029

8.400

Insert extra zeros.

First, borrow from the tenths column: then

borrow from the hundredths column.

8.4

3

0

10

0

10

 3.029

5.371

8.43.029

To add signed decimals,we use the same rules that

are used for adding integers.

With like signs:Add their absolute values and

attach their common sign to the sum.

With unlike signs:Subtract their absolute values

(the smaller from the larger). If the positive

decimal has the larger absolute value, the final

answer is positive. If the negative decimal has the

larger absolute value, make the final answer

negative.

Add:

Find the absolute values: and

Add the absolute values, 21.35

and 64.52, to get 85.87. Since

both decimals are negative, make

the final result negative.

Add:

Find the absolute values: and

Subtract the smaller absolute value from the

larger: 9.8 7.4 2.4. Since the positive

number, 9.8, has the larger absolute value, the

final answer is positive.

7.49.82.4

0 7.4 0 7.4 0 9.8 0 9.8

7.49.8

21.35(64.52)85.87

0 21.35 0 21.35 0 64.52 0 64.52

21.35(64.52)

To subtract two signed decimals,add the first

decimal to the opposite of the decimal to be

subtracted.

Subtract:

The number to be subtracted is. Subtracting is the same

as adding its opposite, 1.4.

Add...

Use the rule for

adding two decimals

... the opposite with different signs.

8.62(1.4)8.621.47.22

1.4 1.4

8.62(1.4)

Estimation can be used to check the

reasonableness of an answer to a decimal addition

or subtraction.

Estimate the sum by rounding the addends to the nearest ten:

Estimate the difference by using front-end rounding:

Each number is rounded to its largest place value.

Round to the nearest hundred.

Round to the nearest ten.

This is the estimate.

300

 40

260

302.47

 36.9

265.57

302.4736.9

Round to the nearest ten.

Round to the nearest ten.

This is the estimate.

330

 460

790

328.99

 459.02

788.01

328.99459.02

We can use the five-step problem-solving strategy

to solve application problems that involve decimals.

See Examples 10–12 that begin on page 337 to review how to solve

application problems by adding and subtracting decimals.