Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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

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

Learn to divide decimals.

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 = 6 and 0.3 · 10 = 3 0.6 ÷ 0.3 = 2 and 6 ÷ 3 = 2 By multiplying both numbers 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.

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

Additional Example 1B: Dividing Decimals by Decimals Divide. 18.48 ÷ (–1.75) 18.48 ÷ (–1.75) = 1848 ÷ 175 Multiply both numbers by 100 to make the divisor an integer. 1 .5 6 Use zeros as placeholders 175 ) 1848 . 00 –175 Divide as with whole numbers. 9 8 –87 5 10 50 –10 50 18.48 ÷ (–1.75) = –10.56 The signs are different.

Check It Out: Example 1A Divide. 6.45 ÷ 0.5 6.45 ÷ 0.5 = 64.5 ÷ 5 Multiply both numbers by 10 to make the divisor an integer. 1 2 . 9 5 ) 64.5 Divide as with whole numbers. – 5 14 –10 4 5 –4 5

Check It Out: Example 1B Divide. 16.48 ÷ (–2.06) 16.48 ÷ (–2.06) = 1648 ÷ (206) Multiply both numbers by 100 to make the divisor an integer. 8 206 ) 1,648 –1 648 Divide as with whole numbers. 16.48 ÷ (–2.06) = –8 The signs are different.

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

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

Divide. Estimate to check whether each answer is reasonable. Check It Out: Example 2A Divide. Estimate to check whether each answer is reasonable. 6 ÷ 1.25 6.00 ÷ 1.25 = 600 ÷ 125 Multiply both numbers by 100. 4 . 8 125 ) 600 .0 Use zero as a placeholder. –500 Divide as with whole numbers. 100 0 –100 0 Estimate 6 ÷ 1 = 6 The answer is reasonable.

Divide. Estimate to check whether each answer is Reasonable. Check It Out: Example 2B Divide. Estimate to check whether each answer is Reasonable. –22 ÷ (–2.5) –22.0 ÷ (–2.5) = –220 ÷ (–25) Multiply both numbers by 10. 8 . 8 25 ) 220 . Divide as with whole numbers. –200 20 –20 0 Estimate –21 ÷ (–3) = 7 The answer is reasonable.

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 ) 3,275 22,975 Divide as with whole numbers. –22,975 Eric rented the car for 7 days.

Check It Out: 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 10. 2 8 Divide as with whole numbers. 125 ) 3500 –250 To calculate miles per gallon, divide the number of miles driven by the number of gallons of gas used. Helpful Hint 100 –1000 Jace’s truck’s gas mileage was 28 miles per gallon.

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

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

Lesson Quiz for Student Response Systems 1. Divide. 87.3 ÷ 0.09 A. 873 B. 970 C. 977 D. 1230

Lesson Quiz for Student Response Systems 2. Divide. –14.72 ÷ (3.2) A. –4.6 B. –5 C. –5.2 D. –5.6

Lesson Quiz for Student Response Systems 3. Divide. 19.98 ÷ 1.8 A. 11.4 B. 11.3 C. 11.2 D. 11.1

Lesson Quiz for Student Response Systems 4. Divide. 17.15 ÷ 2.45 A. 7 B. 8 C. 9 D. 10

Lesson Quiz for Student Response Systems 5. Chris drives at an average speed of 55.45 miles per hour. How long does it take for him to travel a distance of 388.15 miles? A. 6 hours B. 7 hours C. 8 hours D. 9 hours