3-6 Dividing by Decimals Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

3-6 Dividing by Decimals

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


Warm UpDivide.

1. 4.8 ÷ 2

2. 16.1 ÷ 7

3. 0.36 ÷ 3

4. 25.28 ÷ 4

2.42.3

0.12

6.32


Problem of the Day

In the following magic square, 3.375 is the product of the numbers in every row, column, and diagonal. Fill in the missing numbers.

4.5 0.25

0.5

3

1 1.5 2.25

0.75 9


MA.6.A.1.3 Solve real-world problems involving…division of…decimals.

Also MA.6.A.1.1, MA.6.A.1.2. MA.6.A.5.3

Sunshine State Standards


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


Additional Example 1A: Dividing a Decimal by a Decimal

Find the quotient.

5.2 ÷ 1.3

1.3 5.2 Multiply the divisor by 101, or 10 to make it a whole number. Multiply the dividend by the same power of 10.

Think: 1.3 x 10 = 13 5.2 x 10 = 52

Divide as with whole numbers. 13 52

4

–520

5.2 ÷ 1.3 = 4


Additional Example 1B: 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 102, or 100, to make it a whole number. Multiply the dividend by the same power of 10.

36 6,130.000


Additional Example 1B Continued

Place the decimal point in the quotient. Divide as with whole numbers.

36 6,130.0007

-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.


Check It Out: Example 1

Find the quotient.

51.2 ÷ 0.25

0.25 51.2 25 5120.00204.8


Additional Example 2: 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?

11 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.


22 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.

Solve33

First estimate the answer. You can use compatible numbers.

216.3 ÷ 10.5 200 ÷ 10 = 20


The York family averaged 20.6 miles per gallon.

105 2163.0-210

2

63 -0630

-630

0

0

.6

Solve Continued33

10.5 216.3Multiply 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.


Look Back44

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


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?

11 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.


22 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.

Solve33

8.5 154.7

The Chang family averaged 18.2 miles per gallon.


Look Back44

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.


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson Quiz

Find each quotient.

1. 49 ÷ 0.7

2. 21.63 ÷ 2.1

3. 38.43 ÷ 6.1

4. 16.9 ÷ 5.2

5. John spent $13.44 renting 4 videos for the

weekend. What was the cost per video?

10.3

70

6.3

3.25

$3.36


1. Identify the quotient.

72 0.9

A. 70

B. 79

C. 80

D. 90




36.12 4.2

A. 8.6

B. 8.8

C. 9.5

D. 9.6




51.51 5.1

A. 10.1

B. 10

C. 5.1

D. 5




26.35 6.2

A. 4.25

B. 4.5

C. 4.75

D. 5



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


Documents

3-6 Dividing by Decimals Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes