4-5 Dividing Decimals and Integers by Decimals

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm UpDivide.

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

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

Learn to divide decimals and integers by decimals.

Course 2

4-5 Dividing Decimals and Integers by Decimals

How many groups of 0.3 are in 0.6?

This problem is equivalent to 0.6 ÷ 0.3. You canuse a grid to model this division by circling groupsof 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

When you divide two numbers, you can multiply both numbers by the same power of ten withoutchanging 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 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

Divide.

Additional Example 1A: Dividing Decimals by Decimals

8.28 ÷ 4.6

) 82.8461.

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

Divide.

Additional Example 1B: Dividing Decimals by Decimals

B. 18.48 ÷ (–1.75)

18.48 ÷ (–1.75) = 1848 ÷ 175 Multiply both numbers by 100.

)175 1848 . 00 Use zeros as placeholdersDivide as with whole numbers.

1

–17598 0

0.5

–87 510 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

Try This: Example 1A

Divide.

Insert Lesson Title Here

6.45 ÷ 0.5

) 64.5 51

5–14

–10

A. 6.45 ÷ 0.5

2

4 5

.9

–4 50

Multiply both numbers by10.

Divide as with whole numbers.

= 64.5 ÷ 5

Course 2

4-5 Dividing Decimals and Integers by Decimals

Divide.

B. 16.48 ÷ (–2.06)

16.48 ÷ (–2.06) = 1648 ÷ (206)

)1,6482068

–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

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 Use zero as a placeholder.3

–37525 0

–25 0

0

Divide as with whole numbers.

Estimate4 ÷ 1 = 4 The answer is reasonable.

. 2

Course 2

4-5 Dividing Decimals and Integers by Decimals

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 2409

– 22515

.

.0

0

6

– 15 00

Estimate–24 ÷ (–3) = 8 The answer is reasonable.

Divide as with whole numbers.

Course 2

4-5 Dividing Decimals and Integers by Decimals

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 Use zero as a placeholder.4

–500100 0

–100 00

Divide as with whole numbers.

Estimate6 ÷ 1 = 6 The answer is reasonable.

. 8

Course 2

4-5 Dividing Decimals and Integers by Decimals

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 2208

–20020

.

.0

0

8

–20 00

Estimate–22 ÷ (–3) = 7 The answer is reasonable.

Divide as with whole numbers.

Course 2

4-5 Dividing Decimals and Integers by Decimals

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 ÷ 3,275 Multiply both numbersby 100.

)3,275 22,975 Divide as with whole numbers.

7

–22,9750

Eric rented the car for 7 days.

Course 2

4-5 Dividing Decimals and Integers by Decimals

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 3500Divide as with whole numbers.2

–250100

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

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