Preview Warm Up California Standards Lesson Presentation

Warm Up in Spiral Estimate by rounding to the nearest integer. 1. 3.62 + 4.1 2. 8.23 – 7.47 3. 8.52 – 3.16 4. 5.826 + 11.729 Multiply. 8 1 6 18 5. 842  76 63,992 6. 1,240  83 102,920 7. 821  712 584,552 8. 302  15 4,530

Standards 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) California Standards

One of the coolest summers on record in the Midwest was in 1992 One of the coolest summers on record in the Midwest was in 1992. 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.

66.8 + 4.0 70.8 Use zero as a placeholder so that both numbers have the same number of digits after their decimal points. 70.8 Add each column just as you would add integers. Line up the decimal points. The normal average summertime temperature in the Midwest is 70.8°F.

Additional Example 1A: Adding and Subtracting Decimals Add. Estimate to check whether the answer is reasonable. 4.55 + 11.3 4.55 + 11.30 Line up the decimal points. Use zero as a placeholder. 15.85 Add. Estimate 5 + 11 = 16 15.85 is a reasonable answer.

Additional Example 1B: Adding and Subtracting Decimals Subtract. Estimate to check whether the answer is reasonable. 28 – 15.911 7 9 9 10 28.000 Use zeros as placeholders. –15.911 Line up the decimal points. 12.089 Subtract. Estimate 28 – 16 = 12 12.089 is a reasonable answer.

Check It Out! Example 1A Add. Estimate to check whether the answer is is reasonable. 6.78 + 13.2 6.78 + 13.20 Line up the decimal points. Use zero as a placeholder. 19.98 Add. Estimate 7 + 13 = 20 19.98 is a reasonable answer.

Subtract. Estimate to check whether the answer is reasonable. Check It Out! Example 1B Subtract. Estimate to check whether the answer is reasonable. 34 – 12.462 3 9 9 10 34.000 Use zeros as placeholders. –12.462 Line up the decimal points. 21.538 Subtract. Estimate 34 – 12 = 22 21.538 is a reasonable answer.

7  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  8 56 0.7  0.8 1 decimal place 1 decimal place + 0. 56 2 decimal places Same digits

Additional Example 2A: Multiplying Decimals Multiply. Estimate to check whether the answer is reasonable. 2.4  2 2.4  2 1 decimal place 0 decimal places 4.8 1 + 0 = 1 decimal place Estimate 2  2 = 4 4.8 is a reasonable answer.

Additional Example 2B: Multiplying Decimals Multiply. Estimate to check whether the answer is reasonable. –3.84  0.9 –3.84  0.9 2 decimal places 1 decimal place –3.456 2 + 1 = 3 decimal places Estimate –4  1 = –4 –3.456 is a reasonable answer.

Check It Out! Example 2A Multiply. Estimate to check whether the answer is reasonable. 3.2  1.6 3.2  1.6 1 decimal place 1 decimal place 1 92 + 3 20 5.12 1 + 1 = 2 decimal places Estimate 3  2 = 6 5.12 is a reasonable answer.

Check It Out! Example 2B Multiply. Estimate to check whether the answer is reasonable. –2.96  0.7 –2.96  0.7 2 decimal places 1 decimal place –2.072 2 + 1 = 3 decimal places Estimate –3  1 = –3 –2.072 is a reasonable answer.

Additional 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 0.38. What would a person who weighs 85 pounds on Earth weigh on Mars? 0.38  85 2 decimal places 0 decimal places 1 90 + 30 40 32.30 2 + 0 = 2 decimal places The person would weigh 32.3 pounds on Mars.

Check It Out! Example 3 Jet fuel weighs approximately 6.2 pounds per gallon. If a plane was serviced with 1,012 gallons of fuel, how many pounds of fuel were used?  6.2 1,012 0 decimal places 1 decimal place 202 4 + 6072 0 6274.4 1 + 0 = 1 decimal place A plane would use 6,274.4 pounds of fuel.

Lesson Quiz Add, subtract, or multiply. Estimate to check whether your answer is reasonable. 1. 6.98 + 14.27 21.25; Estimate: 7 + 14 = 21 6.72 – 4.16 2. 2.56; Estimate: 7 – 4 = 3 3. 3.4  4.1 4. 7.62  (–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) = –40 36 miles