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3-3 Adding and Subtracting Decimals Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

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3-3 Adding and Subtracting Decimals Warm Up Estimate by rounding to the indicated place value. 1. 70.27 + 15.36; ones 2. 84.37 – 21.82; tenths Estimate each product or quotient. 3. 27.25 8.7 4. 44.52 ÷ 3.27 85 62.6 270 15

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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.

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3-3 Adding and Subtracting Decimals Learn to add and subtract decimals.

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3-3 Adding and Subtracting Decimals Estimating before you add or subtract will help you check whether your answer is reasonable. Helpful Hint

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3-3 Adding and Subtracting Decimals Carly Patterson’s Preliminary Scores EventPoints Floor exercise9.7 Balance beam9.7 Vault9.3 Uneven bars9.45 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.

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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 Find the sum of 9.7, 9.3, and 9.45.

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3-3 Adding and Subtracting Decimals Additional Example 1A Continued Add. 9.70 9.30 +9.45 28.45 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.

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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 -9.3 0.7 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.

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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 Find the sum of 9.7, 9.7, and 9.45.

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3-3 Adding and Subtracting Decimals Check It Out: Example 1A Continued Add 9.700 +9.450 28.850 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.

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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 -9.45 0.55 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.

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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 Think: What number added to 0.7 is 1? 4 – 0.7 = 3.3 0.7 + 0.3 = 1 So 1 – 0.7 = 0.3

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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 Think: What number added to 0.3 is 1? 6 – 0.3 = 5.7 0.3 + 0.7 = 1 So 1 – 0.3 = 0.7

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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.

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3-3 Adding and Subtracting Decimals You can place any number of zeros at the end of a decimal number without changing its value. Helpful Hint

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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.

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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.

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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.

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3-3 Adding and Subtracting Decimals Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

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3-3 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

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3-3 Adding and Subtracting Decimals 1. Identify the sum. 9.4 + 3.6 A. 12.8 B. 13 C. 14 D. 15.5 Lesson Quiz for Student Response Systems

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3-3 Adding and Subtracting Decimals 2. Identify the difference. 12.6 – 6 A. 5 B. 5.6 C. 6 D. 6.6 Lesson Quiz for Student Response Systems

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3-3 Adding and Subtracting Decimals 3. Identify the sum. 19.91 + 9.09 A. 27 B. 28 C. 29 D. 30 Lesson Quiz for Student Response Systems

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3-3 Adding and Subtracting Decimals 4. During an gymnastics competition, Jack scored the following points: 9.2, 7.8, and 6.5. What was Jack’s total score? A. 21.5 points B. 22.5 points C. 23.5 points D. 24.5 points Lesson Quiz for Student Response Systems

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