Calculating Products of Decimals: IM 6.5.8
[url=https://im.kendallhunt.com/MS/teachers/1/5/8/preparation.html]“Calculating Products of Decimals”[/url] from IM Grade 6 by [url=https://www.geogebra.org/m/gus8ffvr]Open Up Resources[/url] and Illustrative Mathematics. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0 license[/url].
Table of Contents
- Lesson 6.5.8
- IM 6.5.8 Lesson: Calculating Products of Decimals
- Practice 6.5.8
- IM 6.5.8 Practice: Calculating Products of Decimals
IM 6.5.8 Lesson: Calculating Products of Decimals
Evaluate mentally.
[math]20\cdot5[/math][br]
[math]20\cdot\left(0.8\right)[/math][br]
[math]20\cdot\left(0.04\right)[/math][br]
[math]20\cdot\left(5.84\right)[/math][br]
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 above to calculate each product.
[math]\left(4.6\right)\cdot\left(0.9\right)[/math]
[math]\left(16.5\right)\cdot\left(0.7\right)[/math]
Use area diagrams to check your earlier calculations. For each problem:
[list][*]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.[/*][/list]
(4.6) · (0.9)
(16.5) · (0.7)
About how many centimeters are in 6.25 inches if 1 inch is about 2.5 centimeters?
Calculate each product. Show your reasoning. If you get stuck, consider drawing an area diagram to help.
[math]\left(5.6\right)\cdot\left(1.8\right)[/math]
[math]\left(0.008\right)\cdot\left(7.2\right)[/math]
A rectangular playground is 18.2 meters by 12.75 meters. Find its area in square meters.
A rectangular playground is 18.2 meters by 12.75 meters. If 1 meter is approximately 3.28 feet, what are the approximate side lengths of the playground in feet?
Write the following expressions as decimals.
[math]1-0.1[/math]
[math]1-0.1+10-0.01[/math]
[math]1-0.1+10-0.01+100-0.001[/math]
Describe the decimal that results as this process continues.[br]
What would happen to the decimal if all of the addition and subtraction symbols became multiplication symbols? Explain your reasoning.[br]
IM 6.5.8 Practice: Calculating Products of Decimals
Here are an unfinished calculation of (0.54) · (3.8) and 0.54-by-3.8 rectangle.
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 in the applet above.
What is [math]\left(0.54\right)\cdot\left(3.8\right)[/math]?
Explain how the product of 3 and 65 could be used to find [math]\left(0.03\right)\cdot\left(0.65\right)[/math].
Use vertical calculation to find the product: (5.4) · (2.4)
Use vertical calculation to find the product: (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: [math]7.4-0.0022[/math] or [math]7.39-0.0012[/math]? 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 below.