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3-1 Adding and Subtracting Decimals DO NOW Find the sum or difference. 1) -2 + 6 2) -3 + (-4) 3) 7 + (-5) 4) -2 – 2 5) 76 – (-42) 6) -21 – 15 3-1 Adding and Subtracting Decimals Learn to add and subtract decimals. 3-1 Adding and Subtracting Decimals • 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 3-1 Adding and Subtracting Decimals Example: Find the sum. 66.8 + 4.0 70.8 66.8 + 4 Use zero as a placeholder so that both numbers have the same number of digits after their decimal points. Add each column just as you would add integers. Line up the decimal points. 3-1 Adding and Subtracting Decimals Example A Find the sum. 6.44 + 16 6.44 + 16.00 22.44 Line up the decimal points. Use zeros as placeholders. Add. 3-1 Adding and Subtracting Decimals Example A Find the sum. –8.33 + (–10.972) 8.330 +10.972 19.302 Line up the decimal points. Use zeros as placeholders. Add. –19.302 Use the sign of the two numbers. 3-1 Adding and Subtracting Decimals Example A Find the sum. 3.6 + (–9.65) 9.65 - 3.60 -6.05 Remember: Different signs – Eliminate! Line up the decimal points. Subtract. Answer has sign of ‘bigger number’ 3-1 Adding and Subtracting Decimals • Remember to be careful with your signs. Even if the operation is addition, if the signs are different you are going to subtract and take the sign of the larger number. • With subtraction problems, use KCS to make it an addition problem. 3-1 Adding and Subtracting Decimals Example B Find the difference. 5.34 – 2.08 5.34 –2.08 3.26 Line up the decimal points. Subtract. 3-1 Adding and Subtracting Decimals Example B Find the difference. 15.911 - 28 7 9 9 10 28.000 –15.911 -12.089 Use zeros as placeholders. Line up the decimal points. Subtract. 3-1 Adding and Subtracting Decimals Find the difference. -32.6 – (-15.86) -32.6 + 15.86 32.60 –15.86 -16.74 KCS Line up the decimal points. Subtract. 3-1 Adding and Subtracting Decimals 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 +26.331 518.561 Use zero as a place holder. Line up the decimal points. Add. The total number of trips was 518.561 million. 3-1 Adding and Subtracting Decimals 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 +169.831 313.491 Use zero as a place holder. Line up the decimal points. Add. The total number of bushels was 313.491 million. 3-1 Adding and Subtracting Decimals Lesson Quiz Find the sum. 1. 6.98 + (-14.27) -7.29 2. –8.46 + (–19.2) –27.66 Find the difference. 3. -6.72 – (-4.16) -2.56 4. -24 – 3.8 -27.8 3-1 Adding and Subtracting Decimals 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 3-1 Adding and Subtracting Decimals 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 3-1 Adding and Subtracting Decimals 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 3-1 Adding and Subtracting Decimals 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 3-1 Adding and Subtracting Decimals 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 3-1 Adding and Subtracting Decimals 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