Illustrative Math

Expressions and Equations

6

Unit 3

Lesson 20

Fractions and Decimals

Dividing Decimals by Decimals

Learning

Goal

6

Let’s divide decimals by
decimals.

Unit 3 ● Lesson 20

Warm-up

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

6

Find each quotient mentally.

80 ÷ 4

12 ÷ 4

1.2 ÷ 4

81.2 ÷ 4

Dividing by 4

Unit 3 ● Lesson 20 ● Activity 1

Warm-up

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

6

How did you mentally find the quotient of 81.2 ÷ 4?

Dividing by 4

Unit 3 ● Lesson 20 ● Activity 1

Open Ended

How did you mentally find the quotient of 81.2 divided by 4?

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

6

What do you notice? What do you wonder?

Dividends and Divisors

Unit 3 ● Lesson 20 ● Activity 2

Open Ended

What do you notice and/or what do you wonder?

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

6

Analyze the dividends, divisors, and quotients in the calculations, and then
answer the questions.

1.

Complete each sentence. In the calculations shown:

●Each dividend is ______ times the dividend to the left of it.

●Each divisor is ______ times the divisor to the left of it.

●Each quotient is _____________________ the quotient to the left of it.

Dividends and Divisors

Unit 3 ● Lesson 20 ● Activity 2

Fill in the Blanks

Fill in the Blanks

Fill in the Blanks

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

6

2.

Suppose we are writing a calculation to the right of
72,000 ÷ 3,000. Which expression has a quotient of 24? Be
prepared to explain your reasoning.

a.

72,000 ÷ 30,000

b.

720,000 ÷ 300,000

c.

720,000 ÷ 30,000

d.

720,000 ÷ 3,000

3.

Suppose we are writing a calculation to the left of 72 ÷ 3.
Write an expression that would also give a quotient of 24. Be
prepared to explain your reasoning.

Dividends and Divisors

Unit 3 ● Lesson 20 ● Activity 2

​Discuss with your group to find which

expression has a quotient of 24.

​

You have one minute to discuss. ​

​Work with your group to write an expression that would also give a quotient of 24.

You will have two minutes.​

​

Open Ended

Type your group's expression here.

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

6

4.

Decide which of the following expressions would have the
same value as 250 ÷ 10. Be prepared to share your
reasoning.

a.

250 ÷ 0.1

b.

25 ÷ 1

c.

2.5 ÷ 1

d.

2.5 ÷ 0.01

e.

2,500 ÷ 100

f.

0.25 ÷ 0.01

Dividends and Divisors

Unit 3 ● Lesson 20 ● Activity 2

Draw

Circle the expressions below that have the same value as 250 divided by 10.

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

6

4.

Decide which of the following expressions would have the
same value as 250 ÷ 10. Be prepared to share your
reasoning.

a.

250 ÷ 0.1

b.

25 ÷ 1

c.

2.5 ÷ 1

d.

2.5 ÷ 0.01

e.

2,500 ÷ 100

f.

0.25 ÷ 0.01

Dividends and Divisors

Unit 3 ● Lesson 20 ● Activity 2

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

6

What happens to the value of the quotient when both
the divisor and the dividend are multiplied by the same
power of 10? Use examples to show your thinking.

Dividends and Divisors

Unit 3 ● Lesson 20 ● Activity 2

​Discuss with a partner for one minute. Then you will have one minute to type your answer on the next slide.

Open Ended

What happens to the value of the quotient when both the divisor and the dividend are multiplied by the same power of 10? Use examples to show your thinking.

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

6

1.

Think of one or more ways to find 3 ÷ 0.12. Show your
reasoning.

2.

Find 1.8 ÷ 0.004. Show your reasoning. If you get stuck, think
about what equivalent division expression you could write.

3.

Diego said, “To divide decimals, we can start by moving the
decimal point in both the dividend and divisor by the same
number of places and in the same direction. Then we find
the quotient of the resulting numbers.”

Do you agree with Diego? Use the division expression
7.5 ÷ 1.25 to support your answer.

Placing Decimal Points in Quotients

Unit 3 ● Lesson 20 ● Activity 3

​Answer the above questions in your book on your own. When you are finished, sit quietly until the timer goes off. I will call on students to share their answers with the class after the timer has gone off.

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

6

Write a division expression that is equivalent to either
3 ÷ 0.12 or 1.8 ÷ 0.004 but has different decimal point
locations.

Placing Decimal Points in Quotients

Unit 3 ● Lesson 20 ● Activity 3

Open Ended

Write a division expression that is equivalent to either 3 ÷ 0.12 or 1.8 ÷ 0.004 but has different decimal point locations.

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

6

Find each quotient. Discuss your quotients with your group and
agree on the correct answers. Consult your teacher if the group
can't agree.

1.

106.5 ÷ 3

2.

58.8 ÷ 0.7

3.

257.4 ÷ 1.1

4.

Mai is making friendship bracelets. Each bracelet is made
from 24.3 cm of string. If she has 170.1 cm of string, how
many bracelets can she make? Explain or show your
reasoning.

Practicing Division with Decimals

Unit 3 ● Lesson 20 ● Activity 4

​Correct Answers

​1) 35.5

2) ​84

3) ​234

4) ​She can make 7 bracelets.

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

6

● Could the answer to the last question be found by

calculating the quotient of this expression:
24.3 ÷ 170.1?

● What would the quotient 24.3 ÷ 170.1 represent in

the context of the problem?

Practicing Division with Decimals

Unit 3 ● Lesson 20 ● Activity 4

Lesson Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

6

● What equivalent expression can we write to help us

find 18.4 ÷ 0.2?

● How might we find the quotient of 184 ÷ 2?

● Do we always multiply the dividend and divisor by

10? For example, what number should we multiply to
enable us to find 1.25 ÷ 0.005?

● Why is it helpful to multiply by a power of 10 instead

of another number that is not a power of 10?

Dividing Decimals by Decimals

Unit 3 ● Lesson 20

Learning
Targets

6

Unit 3 ● Lesson 20

● I can find the quotient of

two decimals.

● I know how multiplying

both the dividend and the
divisor by the same factor
affects the quotient.

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

6

Glossary

long division

Long division is a way to show the steps for dividing numbers in
decimal form. It finds the quotient one digit at a time, from left
to right.

For example, here is the long division for 57 ÷ 4.

Unit 3 ● Lesson 20

Cool-down

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

6

1. Write two division expressions that have the same

value as 36.8 ÷ 2.3.

2. Find the value of 36.8 ÷ 2.3. Show your reasoning.

The Quotient of Two Decimals

Unit 3 ● Lesson 20 ● Activity 5

​Complete the Cool Down on paper and turn in to the drawers when finished.

6

This slide deck is copyright 2021 by Kendall Hunt Publishing, https://im.kendallhunt.com/, and is licensed under the Creative
Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).

All curriculum excerpts are under the following licenses:

IM 6–8 Math™ was originally developed by Open Up Resources and authored by Illustrative Mathematics®, and is copyright
2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC
BY-NC 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.

Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics®, and are licensed under the
Creative Commons Attribution 4.0 International License (CC BY 4.0).

Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are
licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Adaptations and additions to create IM 6–8 Math Accelerated are copyright 2020 by Illustrative Mathematics®,
www.illustrativemathematics.org, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY
4.0).

The Illustrative Mathematics® name and logo are not subject to the Creative Commons license and may not be used without
the prior and express written consent of Illustrative Mathematics®.