4-5

1. Dividing Decimals and Integers by Decimals 4-5 Course 2 Warm Up Problem of the Day Lesson Presentation

2. Dividing Decimals and Integers by Decimals 4-5 Course 2 Warm Up Divide. 1.24.5 ÷ 7 2. 50.4 ÷ 6 3. 19.2 ÷ (–2) 4. 128.1 ÷ 21 3.5 8.4 –9.6 6.1

3. Dividing Decimals and Integers by Decimals 4-5 Course 2 Problem of the Day Place 20 pennies in a row on a table. Replace every fourth coin with a nickel. Now replace every third coin with a dime. Then replace every sixth coin with a quarter. What is the value of the 20 coins now on the table? $1.35

4. Dividing Decimals and Integers by Decimals 4-5 Course 2 Learn to divide decimals and integers by decimals.

5. Dividing Decimals and Integers by Decimals 4-5 Course 2 How many groups of 0.3 are in 0.6? This problem is equivalent to 0.6 ÷ 0.3. You can use a grid to model this division by circling groups of 0.3 and counting the number of groups. There are 2 groups of 0.3 in 0.6, so 0.6 ÷ 0.3 = 2.

6. Dividing Decimals and Integers by Decimals 4-5 Course 2 When you divide two numbers, you can multiply both numbers bythe same power of ten without changing the final answer. Multiply both 0.6 and 0.3 by 10: 0.6 · 10 = 6 and 0.3· 10 = 3 and 6÷ 3 = 2 0.6 ÷ 0.3 =2 By multiplying both powers by the same power of ten, you can make the divisor an integer. Dividing by an integer is much easier than dividing by a decimal.

7. Dividing Decimals and Integers by Decimals 4-5 Helpful Hint Multiply both numbers by the least power of ten that will make the divisor an integer. Course 2 Additional Example 1A: Dividing Decimals by Decimals Divide. A. 8.28 ÷ 4.6 Multiply both numbers by 10. 8.28 ÷ 4.6 = 82.8 ÷ 46 1. 8 ) 82.8 46 Divide as with whole numbers. 46 – 8 36 –36 8 0

8. Dividing Decimals and Integers by Decimals 4-5 Course 2 Additional Example 1B: Dividing Decimals by Decimals Divide. B. 18.48 ÷ (–1.75) 18.48 ÷ (–1.75) = 1848 ÷ 175 Multiply both numbers by 100. 1 0 .5 6 Use zeros as placeholders ) . 00 175 1848 Divide as with whole numbers. –175 0 9 8 –87 5 10 50 –10 50 0 The signs are different. 18.48 ÷ (–1.75) = –10.56

9. Dividing Decimals and Integers by Decimals 4-5 Course 2 Insert Lesson Title Here Try This: Example 1A Divide. A. 6.45 ÷ 0.5 6.45 ÷ 0.5 Multiply both numbers by10. = 64.5 ÷ 5 1 2 9 . ) 5 Divide as with whole numbers. 64.5 5 – 14 –10 5 4 –4 5 0

10. Dividing Decimals and Integers by Decimals 4-5 Course 2 Try This: Example 1B Divide. B. 16.48 ÷ (–2.06) Multiply both numbers by 100. 1648 ÷ (206) 16.48 ÷ (–2.06) = 8 ) 206 1,648 –1 648 Divide as with whole numbers. 0 16.48 ÷ (–2.06) = –8 The signs are different.

11. Dividing Decimals and Integers by Decimals 4-5 Course 2 Additional Example 2A: Dividing Integers by Decimals Divide. Estimate to check whether the answer is reasonable. A. 4 ÷ 1.25 Multiply both numbers by 100. 400 ÷ 125 4.00 ÷ 1.25 = . 3 2 ) 125 Use zero as a placeholder. 400 .0 Divide as with whole numbers. –375 25 0 –25 0 0 Estimate The answer is reasonable. 4 ÷ 1 = 4

12. Dividing Decimals and Integers by Decimals 4-5 Course 2 Additional Example 2B:Dividing Integers by Decimals Divide. Estimate to check whether the answer is Reasonable. B. –24 ÷ (–2.5) Multiply both numbers by 10. –24.0 ÷ (–2.5) = –240 ÷ (–25) 9 6 . ) 0 240 . Divide as with whole numbers. 25 – 225 0 15 – 15 0 0 Estimate –24 ÷ (–3) = 8 The answer is reasonable.

13. Dividing Decimals and Integers by Decimals 4-5 Course 2 Try This: Example 2A Divide. Estimate to check whether the answer is reasonable. A. 6 ÷ 1.25 Multiply both numbers by 100. 600 ÷ 125 6.00 ÷ 1.25 = . 4 8 ) 125 Use zero as a placeholder. 600 .0 Divide as with whole numbers. –500 100 0 –100 0 0 Estimate The answer is reasonable. 6 ÷ 1 = 6

14. Dividing Decimals and Integers by Decimals 4-5 Course 2 Try This: Example 2B Divide. Estimate to check whether the answer is Reasonable. B. –22 ÷ (–2.5) Multiply both numbers by 10. –22.0 ÷ (–2.5) = –220 ÷ (–25) 8 8 . ) 0 220 . Divide as with whole numbers. 25 –200 0 20 –20 0 0 Estimate –22 ÷ (–3) = 7 The answer is reasonable.

15. Dividing Decimals and Integers by Decimals 4-5 Course 2 Additional Example 3: Transportation Application Eric paid $229.25 to rent a car. The fee to rent the car was $32.75 per day. For how long did Eric rent the car? 229.25 ÷ 32.75 = 22,925 ÷ 3,275 Multiply both numbers by 100. 7 ) 22,975 3,275 Divide as with whole numbers. –22,975 0 Eric rented the car for 7 days.

16. Dividing Decimals and Integers by Decimals 4-5 Helpful Hint To calculate gas mileage, divide the number of miles driven by the number of gallons of gas used. Course 2 Insert Lesson Title Here Try This: Example 3 Jace took a trip in which he drove 350 miles. During the trip his truck used 12.5 gallons of gas. What was his truck’s gas mileage? 350.0 ÷ 12.5 = 3500 ÷ 125 Multiply both numbers by 100. 2 8 Divide as with whole numbers. ) 125 3500 –250 100 0 –1000 0 Jace’s truck’s gas mileage was 28 miles per gallon.

17. Dividing Decimals and Integers by Decimals 4-5 Course 2 Insert Lesson Title Here Lesson Quiz Divide. Estimate to check whether each answer is reasonable. 1. 78.2 ÷ 0.04 2. –9.72 ÷ 2.7 3. 18.88 ÷ 1.6 4. 19.5 ÷ 3.25 5. Jordan used 32.46 gallons of gas to drive his van 584.28 miles. How many miles did Jordan get per gallon? 1,995 –3.6 11.8 6 18