2Warm Up in Spiral Estimate by rounding to the nearest integer. – 7.47–Multiply.81618 7663,9926. 1,240 83102,920 712584,552 154,530
3Standards California Extension of NS2.3 Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations.(Also a review of 5th grade NS2.1)CaliforniaStandards
4One of the coolest summers on record in the Midwest was in 1992 One of the coolest summers on record in the Midwest was in The average summertime temperature that year was 66.8°F. Normally, the average temperature is 4°F higher than it was in 1992.To find the normal average summertime temperature in the Midwest, you can add 66.8°F and 4°F.
566.8 + 4.0 70.8 Use zero as a placeholder so that both numbers have the same numberof digits after their decimal points.70.8Add each column just as you wouldadd integers.Line up the decimal points.The normal average summertime temperature in the Midwest is 70.8°F.
6Additional Example 1A: Adding and Subtracting Decimals Add. Estimate to check whether the answer isreasonable.4.55Line up the decimal points.Use zero as a placeholder.15.85Add.Estimate= 1615.85 is a reasonable answer.
7Additional Example 1B: Adding and Subtracting Decimals Subtract. Estimate to check whether the answer is reasonable.28 –28.000Use zeros as placeholders.–15.911Line up the decimal points.12.089Subtract.Estimate28 – 16 = 12is a reasonable answer.
8Check It Out! Example 1AAdd. Estimate to check whether the answer isis reasonable.6.78Line up the decimal points.Use zero as a placeholder.19.98Add.Estimate= 2019.98 is a reasonable answer.
9Subtract. Estimate to check whether the answer is reasonable. Check It Out! Example 1BSubtract. Estimate to check whether the answer is reasonable.34 –34.000Use zeros as placeholders.–12.462Line up the decimal points.21.538Subtract.Estimate34 – 12 = 22is a reasonable answer.
107 8 56 0.7 0.8 0. 56 1 decimal place 1 decimal place To multiply decimals, multiply as you would with integers, and then place the decimal point. The product should have the same number of decimal places as the sum of the decimal places in the factors.7 8560.7 0.81 decimal place1 decimal place+0.562 decimal placesSame digits
11Additional Example 2A: Multiplying Decimals Multiply. Estimate to check whether the answer is reasonable.2.4 22.4 21 decimal place0 decimal places4.81 + 0 = 1 decimal placeEstimate2 2 = 44.8 is a reasonable answer.
12Additional Example 2B: Multiplying Decimals Multiply. Estimate to check whether the answer is reasonable.–3.84 0.9–3.84 0.92 decimal places1 decimal place–3.4562 + 1 = 3 decimal placesEstimate–4 1 = –4–3.456 is a reasonable answer.
13Check It Out! Example 2AMultiply. Estimate to check whether the answer is reasonable.3.2 1.63.2 1.61 decimal place1 decimal place1 92+ 3 205.121 + 1 = 2 decimal placesEstimate3 2 = 65.12 is a reasonable answer.
14Check It Out! Example 2BMultiply. Estimate to check whether the answer is reasonable.–2.96 0.7–2.96 0.72 decimal places1 decimal place–2.0722 + 1 = 3 decimal placesEstimate–3 1 = –3–2.072 is a reasonable answer.
15Additional Example 3: Application To find your weight on another planet, multiply the relative gravitational pull of the planet and your weight. The relative gravitational pull on Mars is What would a person who weighs 85 pounds on Earth weigh on Mars?0.38 852 decimal places0 decimal places1 9032.302 + 0 = 2 decimal placesThe person would weigh 32.3 pounds on Mars.
16Check It Out! Example 3Jet fuel weighs approximately 6.2 poundsper gallon. If a plane was serviced with 1,012 gallons of fuel, how many pounds of fuel were used? 6.21,0120 decimal places1 decimal place202 46274.41 + 0 = 1 decimal placeA plane would use 6,274.4 pounds of fuel.
17Lesson QuizAdd, subtract, or multiply. Estimate to check whether your answer is reasonable.1.21.25; Estimate: = 216.72 – 184.108.40.206; Estimate: 7 – 4 = 3 4.1 (–5.4)5. Dennis runs 7.2 miles per day. How far does he run in 5 days?13.94; Estimate: 3 • 4 = 12–41.148; Estimate: 8 • (–5) = –4036 miles