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Warm Up

Learn to divide whole numbers and decimals by decimals with helpful hints and examples. Practice solving problems and understand the concept of division. Quiz included.

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Warm Up

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  2. Warm Up Divide. 1.4.8 ÷ 2 2. 16.1 ÷ 7 3. 0.36 ÷ 3 4. 25.28 ÷ 4 2.4 2.3 0.12 6.32

  3. 3 1 1.5 2.25 0.75 9 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. Learn to divide whole numbers and decimals by decimals.

  5. 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 = 7

  6. Multiply the divisor and dividend by the same power of ten. There is one decimal place in the divisor. Multiply by 101, or 10. Think: 1.3 x 10 = 13 5.2 x 10 = 52 Divide. Additional Example 1A: Dividing a Decimal by a Decimal Find the quotient. 5.2 ÷ 1.3 1.3 5.2 4 13 52 –52 0 5.2 ÷ 1.3 = 4

  7. 36 6,130.000 Think: 0.36 x 100 = 36 61.3 x 100 = 6,130 Make the divisor a whole number by multiplying the divisor and dividend by 102, or 100. Additional Example 1B: Dividing a Decimal by a Decimal 61.3 ÷ 0.36 0.36 61.30

  8. __ When a repeating pattern occurs, show three dots or draw a bar over the repeating part of the quotient. Place the decimal point in the quotient. Divide. 61.3 ÷ 0.36 = 170.27 Additional Example 1B Continued 0 .2 1 7 7 7 36 6,130.000 -36 253 -252 10 -0 100 -72 280 -252 280 -252 28

  9. 1 Multiply the divisor and dividend by the same power of ten. There is one decimal place in the divisor. Multiply by 10 , or 10. Think: 1.1 x 10 = 11 6.6 x 10 = 66 Divide. Check It Out: Example 1A Find the quotient. 6.6 ÷ 1.1 1.1 6.6 6 11 66 -66 0 6.6 ÷ 1.1 = 6

  10. 24 5120.00 Think: 0.24 x 100 = 24 51.2 x 100 = 5,120 Make the divisor a whole number by multiplying the divisor and dividend by 102, or 100. Check It Out: Example 1B 51.2 ÷ 0.24 0.24 51.2 0

  11. __ Divide. When a repeating pattern occurs, show three dots or draw a bar over the repeating part of the quotient. 51.2 ÷ 0.24 = 213.3 Check It Out: Example 1B Continued 2 .3 1 3 3 24 5,120.00 -48 32 -24 80 -72 80 -72 80 -72 8

  12. 1 Understand the Problem 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? 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.

  13. 3 Solve Make a Plan 2 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. First estimate the answer. You can use compatible numbers. 216.3 ÷ 10.5 200 ÷ 10 = 20

  14. 3 Multiply the divisor and dividend by 10. Think: 10.5 x 10 = 105 216.3 x 10 = 2,163 Place the decimal point in the quotient. Divide. Solve Continued 10.5 216.3 2 .6 0 105 2163.0 -210 63 -0 630 -630 0 The York family averaged 20.6 miles per gallon.

  15. The answer is reasonable since 20.6 is close to the estimate of 20. 4 Look Back

  16. 1 Understand the Problem 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? 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.

  17. 3 Solve Make a Plan 2 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. First estimate the answer. You can use compatible numbers. 191.1 ÷ 10.5 190 ÷ 10 = 19

  18. 3 Multiply the divisor and dividend by 10. Think: 10.5 x 10 = 105 191.1 x 10 = 1,911 Place the decimal point in the quotient. Divide. Solve Continued 10.5 191.1 1 .2 8 105 1911.0 -105 861 -840 210 -210 0 The Chang family averaged 18.2 miles per gallon.

  19. The answer is reasonable since 18.2 is close to the estimate of 19. 4 Look Back

  20. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  21. Lesson Quiz Find each quotient. 1. 49 ÷ 0.7 2. 21.63 ÷ 2.1 3. 38.43 ÷ 6.1 4. 16.9 ÷ 5.2 5. John spent $13.44 renting 4 videos for the weekend. What was the cost per video? 70 10.3 6.3 3.25 $3.36

  22. Lesson Quiz for Student Response Systems 1. Identify the quotient. 72  0.9 A. 70 B. 79 C. 80 D. 90

  23. Lesson Quiz for Student Response Systems 2. Identify the quotient. 36.12  4.2 A. 8.6 B. 8.8 C. 9.5 D. 9.6

  24. Lesson Quiz for Student Response Systems 3. Identify the quotient. 51.51  5.1 A. 10.1 B. 10 C. 5.1 D. 5

  25. Lesson Quiz for Student Response Systems 4. Identify the quotient. 26.35  6.2 A. 4.25 B. 4.5 C. 4.75 D. 5

  26. Lesson Quiz for Student Response Systems 5. Dee bought 5 cups of iced tea for $4.85. What was the cost per cup? A. $0.66 B. $0.69 C. $0.95 D. $0.97

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