Extension of NS2.3

1. California Standards 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.

2. 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.

3. 66.8 + 4.0 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.

4. 4.55 + 11.30 Teacher Example 1A: Adding and Subtracting Decimals Add. Estimate to check whether the answer is reasonable. 4.55 + 11.3 Line up the decimal points. Use zero as a placeholder. Add. 15.85 Estimate 5 + 11 = 16 15.85 is a reasonable answer.

5. Teacher 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.

6. 6.78 + 13.20 Student Practice 1A: Add. Estimate to check whether the answer is is reasonable. 6.78 + 13.2 Line up the decimal points. Use zero as a placeholder. Add. 19.98 Estimate 7 + 13 = 20 19.98 is a reasonable answer.

7. Student Practice 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.

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

9. 2.4 2 Teacher Example 2A: Multiplying Decimals Multiply. Estimate to check whether the answer is reasonable. 2.4  2 1 decimal place 0 decimal places 4.8 1 + 0 = 1 decimal place Estimate 4.8 is a reasonable answer. 2  2 = 4

10. –3.84  0.9 Teacher Example 2B: Multiplying Decimals Multiply. Estimate to check whether the answer is reasonable. –3.84  0.9 2 decimal places 1 decimal place –3.456 2 + 1 = 3 decimal places Estimate –3.456 is a reasonable answer. –4  1 = –4

11. 3.2  1.6 Student Practice 2A: Multiply. Estimate to check whether the answer is reasonable. 3.2  1.6 1 decimal place 1 decimal place 1 92 + 3 20 5.12 1 + 1 = 2 decimal places Estimate 5.12 is a reasonable answer. 3  2 = 6

12. –2.96  0.7 Student Practice 2B: Multiply. Estimate to check whether the answer is reasonable. –2.96  0.7 2 decimal places 1 decimal place –2.072 2 + 1 = 3 decimal places Estimate –2.072 is a reasonable answer. –3  1 = –3

13. 0.38  85 Teacher 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? 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.

14. 1,012  6.2 Student Practice 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? 0 decimal places 1 decimal place 202 4 + 6072 0 1 + 0 = 1 decimal place 6274.4 A plane would use 6,274.4 pounds of fuel.