2. Dividing Decimals by Decimals

3. Divisor Quotient Remember! 0.15 0.75 5 Dividend Dividing Decimals by Decimals

4. To divide decimals, first write the divisor as a whole number. Multiply the divisor and dividend by the same power of ten. Remember! Dividing Decimals by Decimals

5. 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 Dividing Decimals by Decimals

6. Example: Dividing a Decimal by a Decimal Find the quotient. 5.2 ÷ 1.3 1.3 5.2 Multiply the divisor by 10 1, or 10 to make it a whole number. Multiply the dividend by the same power of 10. Think: 1.3 x 10 = 135.2 x 10 = 52Divide as with whole numbers. 13 52 4 –52 0 5.2 ÷ 1.3 = 4 Dividing Decimals by Decimals

7. Example: Dividing a Decimal by a Decimal 61.3 ÷ 0.36 0.36 61.30 Think: 0.36 x 100 = 36 61.3 x 100 = 6,130 Multiply the divisor by 10 2, or 100, to make it a whole number. Multiply the dividend by the same power of 10. 36 6,130.000 Dividing Decimals by Decimals

8. Example - Continued Place the decimal point in the quotient. Divide as with whole numbers. 36 6,130.000 7 -36 1 253 -252 10 -0 0 100.2 -72 -252 7 280 -252 280 7 28 61.3 ÷ 0.36 = 170.27 __ When a repeating pattern occurs, show three dots or draw a bar over the repeating part of the quotient. Dividing Decimals by Decimals

9. Check It Out Find the quotient. 51.2 ÷ 0.25 0.25 51.2 25 5120.00 204.8 Dividing Decimals by Decimals

10. Example: 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. Dividing Decimals by Decimals

11. 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 Dividing Decimals by Decimals

12. The York family averaged 20.6 miles per gallon. 105 2163.0 -210 2 63 -0 630 -630 0 0.6 Solve Continued 3 10.5 216.3 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. Dividing Decimals by Decimals

13. Look Back4 The answer is reasonable since 20.6 is close to the estimate of 20.

14. 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.

15. 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 8.5154.7 The Chang family averaged 18.2 miles per gallon.

16. Look Back4 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. Dividing Decimals by Decimals

17. 1. Identify the quotient. 72  0.9 A. 70 B. 79 C. 80 D. 90 Student Response Systems Dividing Decimals by Decimals

18. 2. Identify the quotient. 36.12  4.2 A. 8.6 B. 8.8 C. 9.5 D. 9.6 Student Response Systems Dividing Decimals by Decimals

19. 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 Student Response Systems Dividing Decimals by Decimals