Basic Mathematics for College Students

it lines up with the decimal points in the minuendand subtrahend.For example, to find
we proceed as follows:
Ones column
Tenths column
Hundredths column
Vertical form

Difference of the hundredths digits: Think 9  7  2

Difference of the tenths digits: Think 5  2  3

Difference of the ones digits: Think 8  1  7

The difference is 7.32.

Write the decimal point in the difference directly under

the decimal points in the minuend and subtrahend.

8. 5 9 8 .59 is the minuend and 1.27 is the subtrahend.

 1. 2 7

7. 3 2

8.591.27,

4.2 Adding and Subtracting Decimals 333

Subtracting Decimals

To subtract decimal numbers:

1. Write the numbers in vertical form with the decimal points lined up.


2. Subtract the numbers as you would subtract whole numbers from right to left.


3. Write the decimal point in the result from Step 2 directly below the
   decimal points in the minued and the subtrahend.
   As with whole numbers, 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.

EXAMPLE (^2) Subtract:
StrategyAs we prepare to subtract in each column, we will compare the digit in
the subtrahend (bottom number) to the digit directly above it in the minuend (top
number).
WHYIf a digit in the subtrahend is greater than the digit directly above it in the
minuend, we must borrow (regroup) to subtract in that column.
SolutionSince 7 in the tenths column of 138. 7 is greater than 6 in the tenths
column of 279. 6 , we cannot immediately subtract in that column because is
nota whole number. To subtract in the tenths column, we must regroup by
borrowing as shown below.
Recall from Section 1.3 that subtraction can be checked by addition. If a
subtraction is done correctly, the sum of the difference and the subtrahend will
equal the minuend:Difference subtrahend minuend.
Check:
Since the sum of the difference and the subtrahend is the minuend, the subtraction
is correct.
Difference
Subtrahend
Minuend

140

1

.9

 138.7

279.6

To subtract in the tenths column, borrow 1 one in the form of 10 tenths

from the ones column. Add 10 to the 6 in the tenths column to get 16

(shown in blue).

279

8

.6

16

 138.7

140.9

6  7

279.6138.7

Self Check 2

Subtract:

Now TryProblem 27

382.5227.1

Some subtractions require borrowing from two (or more) place-value columns.