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]