3-3 adding and subtracting decimals warm up warm up lesson presentation lesson presentation problem...
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3-3 Adding and Subtracting Decimals
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
3-3 Adding and Subtracting Decimals
Warm UpEstimate by rounding to the indicated place value.
1. 70.27 + 15.36; ones2. 84.37 – 21.82; tenths
Estimate each product or quotient.3. 27.25 8.74. 44.52 ÷ 3.27
8562.6
27015
3-3 Adding and Subtracting Decimals
Problem of the Day
Find a three-digit number that rounds to 440 and includes a digit that is the quotient of 24 and 3. Is there more than one possible answer? Explain your thinking.438; no; the numbers that round to 440 are 435-444, 24 divided by 3 is 8, and 438 is the only number with 8 as a digit.
3-3 Adding and Subtracting Decimals
MA.6.A.5.3 Estimate the results of computations with…decimals…and judge the reasonableness of the results.
Also Review of MA.5.A.2.2
Sunshine State Standards
3-3 Adding and Subtracting Decimals
Estimating before you add or subtract will help you check whether your answer is reasonable.
Helpful Hint
3-3 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.
3-3 Adding and Subtracting Decimals
Additional Example 1A: Sports Application
What was Carly Patterson’s total for the events other than the floor exercise?
Estimate by rounding to the nearest whole number.
9.7 + 9.3 + 9.45
The total is about 28 points.10 + 9 + 9 = 28
First estimate the sum of 9.7, 9.3, and 9.45.
3-3 Adding and Subtracting Decimals
Additional Example 1A Continued
Then add.
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.
3-3 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.
3-3 Adding and Subtracting Decimals
Check It Out: Example 1A
What was Carly Patterson’s total for the events other than the vault exercise?
Estimate by rounding to the nearest whole number.9.7 + 9.7 + 9.45
The total is about 29 points.10 + 10 + 9 = 29
First estimate the sum of 9.7, 9.7, and 9.45.
3-3 Adding and Subtracting Decimals
Check It Out: Example 1A Continued
Then add.
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.
3-3 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.
3-3 Adding and Subtracting Decimals
Additional Example 2: Using Mental Math to Add and Subtract Decimals
Find each sum or difference.
A. 1.8 + 0.2
B. 4 – 0.7
Think: 0.8 + 0.2 = 1.1.8 + 0.2 = 2.0
4 – 0.7 = 3.3 Think: 0.7 + 0.3 = 1, so 1 – 0.7 = 0.3.
3-3 Adding and Subtracting Decimals
Check It Out: Example 2
Find each sum or difference.
A. 1.6 + 0.4
B. 6 – 0.3
Think: 0.6 + 0.4 = 1.1.6 + 0.4 = 2.0
6 – 0.3 = 5.7 Think: 0.3 + 0.7 = 1, so 1 – 0.3 = 0.7.
3-3 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.
3-3 Adding and Subtracting Decimals
You can place any number of zeros at theend of a decimal number without changing its value.
Helpful Hint
3-3 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.
3-3 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.
3-3 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.