Lesson 16
Methods for Multiplying Decimals
Let’s look at some ways we can represent multiplication of decimals.
Problem 1
Write three numerical expressions that are equivalent to \((0.0004) \boldcdot (0.005)\).
Problem 2
Find each product. Show your reasoning.
- \((1.2) \boldcdot (0.11)\)
- \((0.34) \boldcdot (0.02)\)
- \(120 \boldcdot (0.002)\)
Problem 3
You can use a rectangle to represent \((0.3) \boldcdot (0.5)\).
- What must the side length of each square represent for the rectangle to correctly represent \((0.3) \boldcdot (0.5)\)?
- What area is represented by each square?
- What is \((0.3) \boldcdot (0.5)\)? Show your reasoning.
![A rectangle area model. The rectangle is partitioned into 15 identical squares. There are 5 rows of 3 squares in each row.](https://staging-cms-im.s3.amazonaws.com/Vgc1qkr59cEZnL5bLX53Ei1A?response-content-disposition=inline%3B%20filename%3D%226-6.5.C2.Image.07.png%22%3B%20filename%2A%3DUTF-8%27%276-6.5.C2.Image.07.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T073247Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=7ca720ad3ee1b4490deaa6ea14f8024d7d567230dfa3870fde0537eb36b7852e)
Problem 4
Here is a rectangle that has been partitioned into four smaller rectangles.
![Rectangle divided into 4 smaller rectangles labeled A, B, C, D. Length across top is 3.4 and width is 2.6.](https://staging-cms-im.s3.amazonaws.com/rsdrBadPomWR6LLzpg2gKCUn?response-content-disposition=inline%3B%20filename%3D%226-6.5.PP.Image.36.1.png%22%3B%20filename%2A%3DUTF-8%27%276-6.5.PP.Image.36.1.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T073247Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=abc2d13743e066a2644c5f05ec1fe44a1816835e26e1f76f2d8cc2ce55129527)
For each expression, choose the sub-rectangle whose area, in square units, matches the expression.
- \(3 \boldcdot (0.6)\)
- \((0.4) \boldcdot 2\)
- \((0.4) \boldcdot (0.6)\)
- \(3 \boldcdot 2\)
Problem 5
Find the value of \(\frac{49}{50}\div\frac{7}{6}\) using any method.
Problem 6
Calculate each difference. Show your reasoning.
- \(13.2 - 1.78\)
- \(23.11 - 0.376\)
- \(0.9 - 0.245\)