1. Estimating before you add or subtract will help you check whether your answer is reasonable.
Helpful Hint

2. Carly Patterson’s Preliminary Scores
At the 2004 U.S. Gymnastics Championships, Carly Patterson and Courtney Kupets tied for the All-Around title.
Carly Patterson’s Preliminary Scores
Event
Points
Floor exercise
9.7
Balance beam
Vault
9.3
Uneven bars
9.45
To find the total number of points, you add all of the scores.

3. Additional Example 1A: Sports Application
What was Carly Patterson’s total for the events other than the floor exercise?
Find the sum of 9.7, 9.3, and 9.45.
Estimate by rounding to the nearest whole number.
The total is about 28 points.
= 28

4. Additional Example 1A Continued
Align the decimal points.
9.70
Use zeros as placeholders.
9.30
+9.45
Add. Then place the decimal point.
28.45
Since is close to the estimate of 28, the answer is reasonable. Carly Patterson’s total for the events other than the floor exercise was

5. Additional Example 1B: Sports Application
How many more points did Carly need on the vault to have a perfect score of 10?
Find the difference between 10 and 9.3.
Align the decimal points.
10.0
Use zeros as placeholders.
-9.3
0.7
Subtract. Then place the decimal point.
Carly needed another 0.7 of a point to have a perfect score.

6. Check It Out: Example 1A
What was Carly Patterson’s total for the events other than the vault exercise?
Find the sum of 9.7, 9.7, and 9.45.
Estimate by rounding to the nearest whole number.
The total is about 29 points.
= 29

7. Check It Out: Example 1A Continued
Add
Align the decimal points.
9.700
Use zeros as placeholders.
9.700
+9.450
Add. Then place the decimal point.
28.850
Since is close to the estimate of 29, the answer is reasonable. Carly Patterson’s total for the events other than the vault exercise was

8. Check It Out: Example 1B
How many more points did Carly need on the uneven bars to have a perfect score of 10?
Find the difference between 10 and 9.45.
Align the decimal points.
10.00
Use zeros as placeholders.
-9.45
0.55
Subtract. Then place the decimal point.
Carly needed another 0.55 of a point to have a perfect score.

9. Additional Example 2: Using Mental Math to Add and Subtract Decimals
Find each sum or difference. A
B. 4 – 0.7
Think: = 1.
= 2.0
Think: What number added to 0.7 is 1?
= 1 So 1 – 0.7 = 0.3
4 – 0.7 = 3.3

10. Check It Out: Example 2
Find each sum or difference. A
B. 6 – 0.3
= 2.0
Think: = 1.
Think: What number added to 0.3 is 1?
= 1 So 1 – 0.3 = 0.7
6 – 0.3 = 5.7

11. Additional Example 3A: Evaluating Decimal Expressions
Evaluate 6.73 – x for each value of x.
x = 3.8
6.73 – x
Substitute 3.8 for x.
6.73 – 3.8
6.73
Align the decimal points.
Use a zero as a placeholder.
– 3.80
Subtract. Place the decimal point.
2.93

12. You can place any number of zeros at the
end of a decimal number without changing
its value.
Helpful Hint

13. Additional Example 3B: Evaluating Decimal Expressions
Evaluate 6.73 – x for each value of x.
x =
6.73 – x
Substitute for x.
6.73 –
6.7300
Align the decimal points.
Use zeros as placeholders.
–2.9765
Subtract. Place the decimal point.
3.7535

14. Check It Out: Example 3A
Evaluate 7.58 – x for each value of x.
x = 3.8
7.58 – x
Substitute 3.8 for x.
7.58 – 3.8
7.58
Align the decimal points.
Use a zero as a placeholder.
–3.80
Subtract. Place the decimal point.
3.78