Dividing Decimals By Decimals

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Examples and steps for dividing multi-digit numbers with decimals

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Dividing Decimals By Decimals

  1. 1. 3-7 Dividing by Decimals Warm Up Problem of the Day Lesson PresentationCourse 1
  2. 2. 3-7 Dividing by Decimals Warm Up Divide. 1. 4.8 ÷ 2 2.4 2. 16.1 ÷ 7 2.3 3. 0.36 ÷ 3 0.12 4. 25.28 ÷ 4 6.32Course 1
  3. 3. 3-7 Dividing by Decimals Problem of the Day In the following magic square, 3.375 is the product of the numbers in every row, column, and diagonal. Fill in the missing numbers. 4.5 0.25 3 1 1.5 2.25 0.75 9 0.5Course 1
  4. 4. 3-7 Dividing by Decimals Learn to divide whole numbers and decimals by decimals.Course 1
  5. 5. 3-7 Dividing by Decimals Helpful Hint Multiplying the divisor and the dividend by the same number does not change the quotient. 42 ÷ 6 = 7 ×10 × 10 420 ÷ 60 = 7 × 10 × 10 4,200 ÷ 600 = 7Course 1
  6. 6. 3-7 Dividing by Decimals Additional Example 1A: Dividing a Decimal by a Decimal Find the quotient. 5.2 ÷ 1.3 Multiply the divisor and dividend by 1.3 5.2 the same power of ten. 4 There is one decimal place in the 13 52 divisor. Multiply by 101, or 10. –52 0 Think: 1.3 x 10 = 13 5.2 x 10 = 52 Divide. 5.2 ÷ 1.3 = 4Course 1
  7. 7. 3-7 Dividing by Decimals Additional Example 1B: Dividing a Decimal by a Decimal 61.3 ÷ 0.36 Make the divisor a whole number 0.36 61.30 by multiplying the divisor and dividend by 102, or 100. Think: 0.36 x 100 = 36 36 6,130.000 61.3 x 100 = 6,130Course 1
  8. 8. 3-7 Dividing by Decimals Additional Example 1B Continued 1 70.2 77 36 6,130.000 -36 Place the decimal point in the 253 quotient. Divide. -252 10 -0 When a repeating pattern 100 occurs, show three dots or -72 draw a bar over the repeating 280 part of the quotient. -252 280 __ -252 61.3 ÷ 0.36 = 170.27 28Course 1
  9. 9. 3-7 Dividing by Decimals Check It Out: Example 1A Find the quotient. 6.6 ÷ 1.1 Multiply the divisor and dividend by 1.1 6.6 the same power of ten. 6 There is one decimal place in the 11 66 1 divisor. Multiply by 10 , or 10. -66 0 Think: 1.1 x 10 = 11 6.6 x 10 = 66 Divide. 6.6 ÷ 1.1 = 6Course 1
  10. 10. 3-7 Dividing by Decimals Check It Out: Example 1B 51.2 ÷ 0.24 Make the divisor a whole number 0.24 51.2 0 by multiplying the divisor and dividend by 102, or 100. Think: 0.24 x 100 = 24 24 5120.00 51.2 x 100 = 5,120Course 1
  11. 11. 3-7 Dividing by Decimals Check It Out: Example 1B Continued 2 13.3 3 24 5,120.00 -48 Divide. 32 -24 80 -72 When a repeating pattern 80 occurs, show three dots or -72 draw a bar over the repeating 80 part of the quotient. -72 8 __ 51.2 ÷ 0.24 = 213.33Course 1
  12. 12. 3-7 Dividing by Decimals Additional Example 2: Problem Solving Application After driving 216.3 miles, the York’s filled up with 10.5 gallons of gas. On average, how many miles did they drive per gallon of gas? 1 Understand the Problem The answer will be the average number of miles per gallon. List the important information: They drove 216.3 miles. They used 10.5 gallons of gas.Course 1
  13. 13. 3-7 Dividing by Decimals 2 Make a Plan Solve a simpler problem by replacing the decimals in the problem with whole numbers. If they drove 10 miles using 2 gallons of gas, they averaged 5 miles per gallon. You need to divide miles by gallons to solve the problem. 3 Solve First estimate the answer. You can use compatible numbers. 216.3 ÷ 10.5 200 ÷ 10 = 20Course 1
  14. 14. 3-7 Dividing by Decimals 3 Solve Continued Multiply the divisor and dividend 10.5 216.3 by 10. Think: 10.5 x 10 = 105 216.3 x 10 = 2,163 2 0.6 105 2163.0 Place the decimal point in the -210 quotient. Divide. 63 -0 630 -630 0 The York family averaged 20.6 miles per gallon.Course 1
  15. 15. 3-7 Dividing by Decimals 4 Look Back The answer is reasonable since 20.6 is close to the estimate of 20.Course 1
  16. 16. 3-7 Dividing by Decimals Check It Out: Example 2 After driving 191.1 miles, the Chang’s filled up with 10.5 gallons of gas. On average, how many miles did they drive per gallon of gas? 1 Understand the Problem The answer will be the average number of miles per gallon. List the important information: They drove 191.1 miles. They used 10.5 gallons of gas.Course 1
  17. 17. 3-7 Dividing by Decimals 2 Make a Plan Solve a simpler problem by replacing the decimals in the problem with whole numbers. If they drove 10 miles using 2 gallons of gas, they averaged 5 miles per gallon. You need to divide miles by gallons to solve the problem. 3 Solve First estimate the answer. You can use compatible numbers. 191.1 ÷ 10.5 190 ÷ 10 = 19Course 1
  18. 18. 3-7 Dividing by Decimals 3 Solve Continued Multiply the divisor and dividend 10.5 191.1 by 10. Think: 10.5 x 10 = 105 191.1 x 10 = 1,911 1 8.2 Place the decimal point in the 105 1911.0 quotient. Divide. -105 861 -840 210 -210 0 The Chang family averaged 18.2 miles per gallon.Course 1
  19. 19. 3-7 Dividing by Decimals 4 Look Back The answer is reasonable since 18.2 is close to the estimate of 19.Course 1
  20. 20. 3-7 Dividing by Decimals Insert Lesson Title Here Lesson Quiz Find each quotient. 1. 49 ÷ 0.7 70 2. 21.63 ÷ 2.1 10.3 3. 38.43 ÷ 6.1 6.3 4. 16.9 ÷ 5.2 3.25 5. John spent $13.44 renting 4 videos for the weekend. What was the cost per video? $3.36Course 1

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