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 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 0.5 3 1 1.5 2.25 0.75 9

Sunshine State Standards MA.6.A.1.3 Solve real-world problems involving…division of…decimals. Also MA.6.A.1.1, MA.6.A.1.2. MA.6.A.5.3

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 Helpful Hint

Additional Example 1A: Dividing a Decimal by a Decimal Find the quotient. 5.2 ÷ 1.3 Multiply the divisor by 101, or 10 to make it a whole number. Multiply the dividend by the same power of 10. 1.3 5.2 4 Think: 1.3 x 10 = 13 5.2 x 10 = 52 13 52 Divide as with whole numbers. –52 5.2 ÷ 1.3 = 4

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

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

Check It Out: Example 1 Find the quotient. 51.2 ÷ 0.25 25 5120.00 204.8 0.25 51.2

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? 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.

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. Solve 3 First estimate the answer. You can use compatible numbers. 216.3 ÷ 10.5 200 ÷ 10 = 20

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

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

Understand the Problem Check It Out: Example 2 After driving 154.7 miles, the Changs filled up with 8.5 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 154.7 miles. They used 8.5 gallons of gas.

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. Solve 3 8.5 154.7 The Chang family averaged 18.2 miles per gallon.

Look Back 4 Use compatible numbers to estimate the quotient. 154.7 ÷ 8.5 → 160 ÷ 8 = 20 The answer is reasonable because 18.2 is close to the estimate of 20.