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Adding and Subtracting Decimals
MAX Strategy Paired Reading• Both students will read the problem and
answer.• When both partners are done reading one
partner will use the whiteboard and marker to explain how to solve the problem.
• The partner must show the steps and tell the other partner the steps as they work it out.
• Then we will switch.
Adding and Subtracting Decimals
I can fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
Adding and Subtracting Decimals
Carly Patterson’s Preliminary Scores
Event Points
Floor exercise 9.7
Balance beam 9.7
Vault 9.3
Uneven bars 9.45
At the 2004 U.S. Gymnastics Championships, Carly Patterson and Courtney Kupets tied for the All-Around title.
To find the total number of points, you add all of the scores.
Adding and Subtracting Decimals
What was Carly Patterson’s total for the events other than the floor exercise?
9.70
9.30
+9.4528.45
Align the decimal points.
Use zeros as placeholders.
Add. Then place the decimal point.
Since 28.45 is close to the estimate of 28, the answer is reasonable. Carly Patterson’s total for the events other than the floor exercise was 28.45.
Find the sum of 9.7, 9.3, and 9.45.
Adding and Subtracting Decimals
Additional Example 1B: Sports Application
How many more points did Carly need on the vault to have a perfect score of 10?
10.0
-9.30.7
Align the decimal points.
Use zeros as placeholders.
Subtract. Then place the decimal point.
Carly needed another 0.7 of a point to have a perfect score.
Find the difference between 10 and 9.3.
Adding and Subtracting Decimals
What was Carly Patterson’s total for the events other than the vault exercise?
9.700
9.700
+9.45028.850
Align the decimal points.
Use zeros as placeholders.
Add. Then place the decimal point.
Since 28.850 is close to the estimate of 29, the answer is reasonable. Carly Patterson’s total for the events other than the vault exercise was 28.85.
Find the sum of 9.7, 9.7, and 9.45.
Adding and Subtracting Decimals
Check It Out: Example 1B
How many more points did Carly need on the uneven bars to have a perfect score of 10?
10.00
-9.450.55
Align the decimal points.
Use zeros as placeholders.
Subtract. Then place the decimal point.
Carly needed another 0.55 of a point to have a perfect score.
Find the difference between 10 and 9.45.
Adding and Subtracting Decimals
Additional Example 3A: Evaluating Decimal Expressions
Evaluate 6.73 – x for each value of x.
x = 3.8
Substitute 3.8 for x.
6.73 – x
6.73 – 3.8 6.73 Align the decimal points.
– 3.80 Use a zero as a placeholder.
2.93 Subtract. Place the decimal point.
Adding and Subtracting Decimals
You can place any number of zeros at theend of a decimal number without changing its value.
Helpful Hint
Adding and Subtracting Decimals
Additional Example 3B: Evaluating Decimal Expressions
Evaluate 6.73 – x for each value of x.
x = 2.9765
Substitute 2.9765 for x.
6.73 – x
6.73 – 2.9765 6.7300 Align the decimal points.
–2.9765 Use zeros as placeholders.
3.7535 Subtract. Place the decimal point.
Adding and Subtracting Decimals
Check It Out: Example 3A
Evaluate 7.58 – x for each value of x.
x = 3.8
Substitute 3.8 for x.
7.58 – x
7.58 – 3.8 7.58 Align the decimal points.
–3.80 Use a zero as a placeholder. 3.78 Subtract. Place the decimal point.
Adding and Subtracting Decimals
Check It Out: Example 3B
Evaluate 8.17 – x for each value of x.
x = 2.9765
Substitute 2.9765 for x.
8.17 – x
8.17 – 2.9765 8.1700 Align the decimal points.
– 2.9765 Use zeros as placeholders.
5.1935 Subtract. Place the decimal point.
Adding and Subtracting Decimals
Lesson Quiz
Find each sum or difference.
1. 8.3 + 2.7
2. 9.7 – 4
3. 22.6 + 8.4
4. Evaluate 12.76 – x for x = 8.41.
5. During an ice-skating competition, Dawn
received the following scores: 4.8, 5.2, 5.4.
What was Dawn’s total score?
5.7
11
31
4.35
15.4
