Illustrative Mathematics Unit 6.5, Lesson 5: Decimal Points in Products

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Illustrative Math
Grade 6

Lesson 5: Decimal Points in Products

Let’s look at products that are decimals.

Illustrative Math Unit 6.5, Lesson 5 (printable worksheets)

Lesson 5 Summary

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

Lesson 5.1 Multiplying by 10

1. In which equation is the value of the largest?
   x · 10 = 810
   x · 10 = 81
   x · 10 = 8.1
   x · 10 = 0.81
   
2. How many times the size of 0.81 is 810?

• See Video for Whole Lesson

Lesson 5.2 Fractionally Speaking: Powers of Ten

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.

1. 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
   
2. 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.
3. 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)
   
4. 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.

Lesson 5.3 Fractionally Speaking: Multiples of Powers of Ten

1. 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
   
2. Find the value of (0.6) · (0.5). Show your reasoning.
3. 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)
   
   

Are you ready for more?

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.

Lesson 5 Practice Problems

1. 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.
   
2. 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
   
3. 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
   
4. Write three numerical expressions that are equivalent to (0.0004) · (0.005).
5. Calculate each sum.
   a. 33.1 + 1.95
   b. 1.075 + 27.105
   c. 0.401 + 9.28
   
6. Calculate each difference. Show your reasoning.
   a. 13.2 - 1.78
   b. 23.11 - 0.376
   c. 0.9 - 0.245
   
7. 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.
   
   
   
   

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