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Warm Up

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

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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. 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. 3 1 1.5 2.25 0.75 9

  4. 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

  5. Multiply the divisor by 101, or 10 to make it a whole number. Multiply the dividend by the same power of 10. Think: 1.3 x 10 = 13 5.2 x 10 = 52 Divide as with whole numbers. 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

  6. Multiply the divisor by 102, or 100, to make it a whole number. Multiply the dividend by the same power of 10. Think: 0.36 x 100 = 36 61.3 x 100 = 6,130 36 6,130.000 Additional Example 1B: Dividing a Decimal by a Decimal 61.3 ÷ 0.36 0.36 61.30

  7. Place the decimal point in the quotient. Divide as with whole numbers. When a repeating pattern occurs, show three dots or draw a bar over the repeating part of the quotient. __ 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

  8. Multiply the divisor by 101, or 10 to make it a whole number. Multiply the dividend by the same power of 10. Think: 1.1 x 10 = 11 6.6 x 10 = 66 Divide as with whole numbers. 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

  9. Multiply the divisor by 102, or 100, to make it a whole number. Multiply the dividend by the same power of 10. Think: 0.24 x 100 = 24 51.2 x 100 = 5,120 24 5120.00 Check It Out: Example 1B 51.2 ÷ 0.24 0.24 51.2 0

  10. Place the decimal point in the quotient. Divide as with whole numbers. 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

  11. 1 Understand the Problem Additional Example 2: Problem Solving Application After driving 216.3 miles, the Yorks 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.

  12. 2 Make a Plan 3 Solve 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

  13. 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 as with whole numbers. 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.

  14. 4 Look Back The answer is reasonable since 20.6 is close to the estimate of 20.

  15. 1 Understand the Problem Check It Out: Example 2 After driving 191.1 miles, the Changs 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.

  16. 2 Make a Plan 3 Solve 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

  17. 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 as with whole numbers. 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.

  18. 4 Look Back The answer is reasonable since 18.2 is close to the estimate of 19.

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