Lesson 8Calculating Products of Decimals
Learning Goal
Let’s multiply decimals.
Learning Targets
I can describe and apply a method for multiplying decimals.
I know how to use a product of whole numbers to find a product of decimals.
Warm Up: Number Talk: Twenty Times a Number
Problem 1
Evaluate mentally.
Activity 1: Calculating Products of Decimals
Problem 1
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
Use what you know about decimals and place value to explain why the decimal point of the product is placed where it is.
Problem 2
Use the method shown in the first question to calculate each product.
Problem 3
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.
Problem 4
About how many centimeters are in 6.25 inches if 1 inch is about 2.5 centimeters? Show your reasoning.
Activity 2: Practicing Multiplication of Decimals
Problem 1
Calculate each product. Show your reasoning. If you get stuck, consider drawing an area diagram to help.
Problem 2
A rectangular playground is 18.2 meters by 12.75 meters.
Find its area in square meters. Show your reasoning.
If 1 meter is approximately 3.28 feet, what are the approximate side lengths of the playground in feet? Show your reasoning.
Are you ready for more?
Problem 1
Write the following expressions as decimals.
Problem 2
Describe the decimal that results as this process continues.
Problem 3
What would happen to the decimal if all of the addition and subtraction symbols became multiplication symbols? Explain your reasoning.
Lesson Summary
We can use
Since 8.4 is 84 tenths and 4.3 is 43 tenths, then:
Write each decimal factor as a product of a whole number and a fraction.
Multiply the whole numbers.
Multiply the fractions.
Multiply the products of the whole numbers and fractions.
We know multiplying by fractions such as