**Learning Targets:**

- I can use place value and fractions to reason about multiplication of decimals.

**Related Pages**

Illustrative Math

Grade 6

Let’s look at products that are decimals.

Illustrative Math Unit 6.5, Lesson 5 (printable worksheets)

The following diagram shows how to use place value and fractions to reason about multiplication of decimals.

- In which equation is the value of the largest?

x · 10 = 810

x · 10 = 81

x · 10 = 8.1

x · 10 = 0.81 - How many times the size of 0.81 is 810?

Work with a partner to answer the following questions. One person should answer the questions labeled “Partner A,” and the other should answer those labeled “Partner B.” Then compare the results.

- Find each product or quotient. Be prepared to explain your reasoning.
Partner A

a. 250 · 1/10

b. 250 · 1/100

c. 48 ÷ 10

d. 48 ÷ 100

Partner B

a. 250 ÷ 10

b. 250 ÷ 100

c. 48 · 1/10

d. 48 · 1/100 - Use your work in the previous problems to find 720 · (0.1) and 720 · (0.01). Explain your reasoning. Pause here for a class discussion.
- Find each product. Show your reasoning.

a. 36 · (0.1)

b. (14.5) · (0.1)

c. (1.8) · (0.1)

d. 54 · (0.01)

e. (9.2) · (0.01) - Jada says: “If you multiply a number by 0.001, the decimal point of the number moves three places to the left.” Do you agree with her statement? Explain your reasoning.

- Select all expressions that are equivalent to (0.6) · (0.5). Be prepared to explain your reasoning.

a. 6 · (0.1) · 5 · (0.1)

b. 6 · (0.01) · 5 · (0.01)

c. 6 · 1/10 · 5 · 1/10

d. 6 · 1/1,000 · 5 · 1/100

e. 6 · (0.001) · 5 · (0.01)

f. 6 · 5 · 1/10 · 1/10

g. 6/10 · 5/10 - Find the value of (0.6) · (0.5). Show your reasoning.
- Find the value of each product by writing and reasoning with an equivalent expression with fractions.

a. (0.3) · (0.02)

b. (0.7) · (0.05)

Ancient Romans used the letter I for 1, V for 5, X for 10, L for 50, C for 100, D for 500, and M for 1,000.

Write a problem involving merchants at an agora, an open-air market, that uses multiplication of numbers written with Roman numerals.

- a. Find the product of each number and 1/100.

122.1

11.8

1350.1

1.704

b. What happens to the decimal point of the original number when you multiply it by 1/100? Why do you think that is? Explain your reasoning. - Which expression has the same value as (0.06) · (0.154)? Select all that apply.

A. 6 · 1/100 · 154 · 1/1,000

B. 6 · 154 · 1/100,000

C. 6 · (0.1) · 154 · (0.01

D. 6 · 154 · (0.00001

E. 0.00924 - Calculate the value of each expression by writing the decimal factors as fractions, then writing their product as a decimal. Show your reasoning.

a. (0.01) · (0.02)

b. (0.3) · (0.2)

c. (1.2) · 5

d. (0.9) · (1.1)

e. (1.5) · 2 - Write three numerical expressions that are equivalent to (0.0004) · (0.005).
- Calculate each sum.

a. 33.1 + 1.95

b. 1.075 + 27.105

c. 0.401 + 9.28 - Calculate each difference. Show your reasoning.

a. 13.2 - 1.78

b. 23.11 - 0.376

c. 0.9 - 0.245 - On the grid, draw a quadrilateral that is not a rectangle that has an area of 18 square units. Show how you know the area is 18 square units.

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.