Illustrative Mathematics Unit 6.5, Lesson 8: Calculating Products of Decimals

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Illustrative Math
Grade 6

Let’s multiply decimals.

The following diagram shows how to use a product of whole numbers to find a product of decimals.

Evaluate mentally. 20 · 5
20 · (0.8)
20 · (0.04
20 · (5.84)

Scroll down the page for the solutions to the “Are you ready for more?” section.

A common way to find a product of decimals is to calculate a product of whole numbers, then place the decimal point in the product.
Here is an example for (2.5) · (1.2).
Use what you know about decimals and place value to explain why the decimal point of the product is placed where it is.
Use the method shown in the first question to calculate each product.
a. (4.6) · (0.9)
b. (16.5) · (10.7)
Use area diagrams to check your earlier calculations. For each problem:
Decompose each number into its base-ten units and write them in the boxes on each side of the rectangle. Write the area of each lettered region in the diagram. Then find the area of the entire rectangle. Show your reasoning.
a. (4.6) · (0.9)
b. (16.5) · (10.7)
About how many centimeters are in 6.25 inches if 1 inch is about 2.5 centimeters? Show your reasoning.

Calculate each product. Show your reasoning. If you get stuck, draw an area diagram to help.
a. (5.6) · (1.8)
b. (0.008) · (7.2)
A rectangular playground is 18.2 meters by 12.75 meters.
a. Find its area in square meters. Show your reasoning.
b. If 1 meter is approximately 3.28 feet, what are the approximate side lengths of the playground in feet? Show your reasoning.

Write the following expressions as decimals.
a. 1 - 0.1
b. 1 - 0.1 + 10 - 0.01
c. 1 - 0.1 + 10 - 0.01 + 100 = 0.001
- Show Answers
  
  a. 1 - 0.1 = 0.9
  b. 1 - 0.1 + 10 - 0.01 = 0.9 + 9.99 = 10.89
  c. 1 - 0.1 + 10 - 0.01 + 100 - 0.001 = 0.9 + 9.99 + 99.999 = 110.889
Describe the decimal that results as this process continues.
- Show Answers
  
  The value will keep increasing.
What would happen to the decimal if all of the positive and negative signs became multiplication symbols? Explain your reasoning.
- Show Answers
  
  1 · 0.1 · 10 · 0.01 · 100 · 0.001 · 1000 ·…
  = 1 · (0.1 · 10) · (0.01 · 100) · (0.001 · 1000) ·…
  = 1 · (0.1 · 10) · (0.01 · 100) · (0.001 · 1000) ·…
  = 1 · 1 · 1 · 1 · …. = 1

Here are an unfinished calculation of (0.54) · (3.8) and a 0.54-by-3.8 rectangle.
a. Which part of the rectangle has an area of 0.432? Which part of the rectangle has an area of 1.62? Show your reasoning. b. What is (0.54) · (3.8)?
Explain how the product of 3 and 65 could be used to find (0.03) · (0.65)
Use vertical calculation to find each product. a. (5.4) · (2.4) b. (1.67) · (3.5)
A pound of blueberries costs $3.98 and a pound of clementines costs $2.49. What is the combined cost of 0.6 pound of blueberries and 1.8 pounds of clementines? Round your answer to the nearest cent.
Complete the calculations so that each shows the correct sum or difference.
Which has a greater value: 7.4 - 0.0022 or 7.39 - 0.0012? Show your reasoning.
Andre is planting saplings (baby trees). It takes him 30 minutes to plant 3 saplings. If each sapling takes the same amount of time to plant, how long will it take Andre to plant 14 saplings? If you get stuck, consider using the table.

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

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