2. 2
Adding and Subtracting Decimals
Activity
You can use base-ten pieces to model decimal
addition and subtraction.
0.76
1
Model the sum of 0.76
and 0.58 using base-ten
pieces.
2
Combine and group the
pieces.
3
Trade 10 tenths for 1 one and
10 hundredths for 1 tenth.
0.58
= 1.34
Adding and Subtracting Decimals
2. 2
Use a vertical format to add or subtract decimals. Begin by lining up the
decimal points. Then add or subtract as you would with whole numbers.
Be sure to write the decimal point in the answer.
EXAMPLE
1
Adding and Subtracting Decimals
6.047 + 13.46
SOLUTION
6.047
+ 13.460
–––––––
19.507
Write zero as
a placeholder.
Adding and Subtracting Decimals
2. 2
Use a vertical format to add or subtract decimals. Begin by lining up the
decimal points. Then add or subtract as you would with whole numbers.
Be sure to write the decimal point in the answer.
EXAMPLE
1
Adding and Subtracting Decimals
9 – 5.28
6.047 + 13.46
SOLUTION
6.047
+ 13.460
–––––––
19.507
SOLUTION
Write zero as
a placeholder.
9 .00
– 5.28
––––––
3.72
Write zeros as
placeholders.
Adding and Subtracting Decimals
2. 2
EXAMPLE
2
Evaluating a Variable Expression
Evaluate 6.7 + r – t when r = 2.14 and t = 5.2.
SOLUTION
6.7 + r – t = 6.7 + 2.14
r – 5.2
t
Substitute 2.14 for r and 5.2 for t.
= 6.78.84
+ 2.14 – 5.2
Add.
= 3.64
Subtract.
2. 2
Adding and Subtracting Decimals
Estimation When you do not need to find an exact sum, you can estimate. One
type of estimation is front-end estimation. To use front-end estimation to
estimate a sum, add the front-end digits, estimate the sum of the remaining
digits, and then add the results.
Adding and Subtracting Decimals
2. 2
EXAMPLE
3
Estimating a Sum
Video Games For your birthday you receive a
$25 gift certificate. You want to buy 3 used video
games whose prices are shown. Can you buy all
3 games using the gift certificate?
SOLUTION
1
Add the front-end
digits: the dollars.
$8.79
$7.29
+ $7.89
–––––––
$22
ANSWER
2
Estimate the sum
of the remaining
digits: the cents.
$8.79
$7.29
+ $7.89
–––––––
$1
$1
__
$2
3
Add the results.
$22
+ $2
––––
$24
The estimated sum is less than $25, so you can buy all three
games using the gift certificate.