DO NOW Find the sum or difference. -2 + 6 2) -3 + (-4) 3) 7 + (-5) -2 + 6 2) -3 + (-4) 3) 7 + (-5) 4) -2 – 2 5) 76 – (-42) 6) -21 – 15

Learn to add and subtract decimals.

Next, they MUST HAVE the same decimal length. In order to add and subtract decimals, you must first line up the decimals Next, they MUST HAVE the same decimal length. To increase the number of decimal places, you can add zeros after the decimal. If a number does not have a decimal, put a decimal at the end of the number. Add zeros to hold the place value Ex: 23 23.0

66.8 + 4.0 70.8 Example: Find the sum. 66.8 + 4 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.

Example A Find the sum. 6.44 + 16 6.44 + 16.00 Line up the decimal points. Use zeros as placeholders. 22.44 Add.

–8.33 + (–10.972) Example A Find the sum. -8.33 – 10.972 8.330 +10.972 Line up the decimal points. Use zeros as placeholders. 19.302 Add. Use the sign of the two numbers. –19.302

Example A Find the sum. 3.6 + (–9.65) 3.6 – 9.65 9.65 - 3.60 Line up the decimal points. -6.05 Subtract. Answer is negative

When adding and subtracting with decimals, it is helpful to estimate your answer so that you know if you have done the operation correctly and which sign your answer will have.

Example B Find the difference. 5.34 – 2.08 5.34 Line up the decimal points. –2.08 3.26 Subtract.

Use zeros as placeholders. –15.911 Line up the decimal points. Example B Find the difference. 15.911 - 28 7 9 9 10 28.000 Use zeros as placeholders. –15.911 Line up the decimal points. -12.089 Subtract.

Find the difference. -32.6 – (-15.86) -32.6 + 15.86 32.60 Line up the decimal points. –15.86 -16.74 Subtract.

Extra Example During one month in the United States, 492.23 million commuter trips were taken on buses, and 26.331 million commuter trips were taken on light rail. What was the total number of trips taken on buses and light rail? Estimate to check whether your answer is reasonable. 492.230 +26.331 Use zero as a place holder. Line up the decimal points. 518.561 Add. The total number of trips was 518.561 million.

Extra Example In 1999, 143.66 million bushels of corn were grown in the United States. In 2000, the harvest yielded 169.831 million bushels. What was the total production for those two years? Estimate to check whether your answer is reasonable. 143.660 +169.831 Use zero as a place holder. Line up the decimal points. 313.491 Add. The total number of bushels was 313.491 million.

Lesson Quiz Find the sum. 2. –8.46 + (–19.2) 1. 6.98 + (-14.27) -7.29 –27.66 Find the difference. -6.72 – (-4.16) 4. -24 – 3.8 3. -27.8 -2.56

Lesson Quiz 5. Renee finished her first lap in the 200 m freestyle event in 28.76 seconds. She completed the second lap in 30.17 seconds. By how much did her time increase in the second lap? Estimate to check whether your answer is reasonable. 1.41 seconds

6. Identify the sum and then estimate to check whether the answer is reasonable. 7.86 + 12.16 A. 20.02; estimate: 8 + 12 = 20 B. 19.16; estimate: 8 + 12 = 20 C. 20.02; estimate: 7 + 12 = 19 D. 19.16; estimate: 7 + 12 = 19

7. Identify the sum and then estimate to check whether the answer is reasonable. –9.32 + (–18.1) A. –8.78; estimate: –9 + (–18) = –9 B. –27.42; estimate: –9 + (–18) = –9 C. –27.42; estimate: –9 + (–18) = –27 D. –8.78; estimate: –9 + (–18) = –27

8. Identify the difference and then estimate to check whether the answer is reasonable. 7.63 – 3.25 A. 4; estimate: 7 – 3 = 4 B. 4.22; estimate: 7 – 3 = 4 C. 4.32; estimate: 8 – 3 = 5 D. 4.38; estimate: 8 – 3 = 5

9. Identify the difference and then estimate to check whether the answer is reasonable. 35 – 2.7 A. 32; estimate: 35 – 3 = 32 B. 32.3; estimate: 35 – 3 = 32 C. 33; estimate: 35 – 2 = 33 D. 33.3; estimate: 35 – 2 = 33

10. Margaret took an exam that has two parts 10. Margaret took an exam that has two parts. She completed the first part in 17.55 minutes and the second part in 32.36 minutes. By how much did her time increase in the second part? Estimate to check whether the answer is reasonable. A. 16 min; estimate: 33 – 17 = 16 B. 15.11 min; estimate: 32 – 17 = 15 C. 14.81 min; estimate: 32 – 18 = 14 D. 10 min; estimate: 30 – 20 = 10