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

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 Course 2 4-5 Dividing Decimals and Integers by Decimals 6.1

3. 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 Course 2 4-5 Dividing Decimals and Integers by Decimals

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

5. 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. Course 2 4-5 Dividing Decimals and Integers by Decimals

6. When you divide two numbers, you can multiply both numbers by the same power of ten without changing the final answer. Multiply both 0.6 and 0.3 by 10: 0.6 · 10 = 6and0.3 · 10 = 3 0.6 ÷ 0.3 = 2 and6 ÷ 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. Course 2 4-5 Dividing Decimals and Integers by Decimals

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

8. Divide. Additional Example 1B: Dividing Decimals by Decimals B. 18.48 ÷ (–1.75) 18.48 ÷ (–1.75) =1848 ÷ 175Multiply both numbers by 100. ) 175 1848. 00 Use zeros as placeholders Divide as with whole numbers. 1 –175 98 0 0.5 –87 5 10 50 –10 50 0 18.48 ÷ (–1.75) = –10.56 6 The signs are different. Course 2 4-5 Dividing Decimals and Integers by Decimals

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

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

11. Divide. Estimate to check whether the answer is reasonable. Additional Example 2A: Dividing Integers by Decimals A. 4 ÷ 1.25 4.00 ÷ 1.25 = 400 ÷ 125 Multiply both numbers by 100. ) 125 400.0.0 Use zero as a placeholder. 3 –375 25 0 –25 0 0 Divide as with whole numbers. Estimate 4 ÷ 1 = 4 The answer is reasonable.. 2 Course 2 4-5 Dividing Decimals and Integers by Decimals

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

13. Divide. Estimate to check whether the answer is reasonable. Try This: Example 2A A. 6 ÷ 1.25 6.00 ÷ 1.25 = 600 ÷ 125 Multiply both numbers by 100. ) 125 600.0.0 Use zero as a placeholder. 4 –500 100 0 –100 0 0 Divide as with whole numbers. Estimate 6 ÷ 1 = 6 The answer is reasonable.. 8 Course 2 4-5 Dividing Decimals and Integers by Decimals

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

15. 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? Additional Example 3: Transportation Application 229.25 ÷ 32.75 =22,925 ÷ 3,275Multiply both numbers by 100. ) 3,275 22,975 Divide as with whole numbers. 7 –22,975 0 Eric rented the car for 7 days. Course 2 4-5 Dividing Decimals and Integers by Decimals

16. 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? Insert Lesson Title Here 350.0 ÷ 12.5 = 3500 ÷ 125 Multiply both numbers by 100. ) 125 3500 Divide as with whole numbers. 2 –250 100 8 0 –1000 0 Jace’s truck’s gas mileage was 28 miles per gallon. To calculate gas mileage, divide the number of miles driven by the number of gallons of gas used. Helpful Hint Course 2 4-5 Dividing Decimals and Integers by Decimals

17. 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? –3.6 1,995 Insert Lesson Title Here 11.8 6 18 Course 2 4-5 Dividing Decimals and Integers by Decimals