Lesson 7
Using Diagrams to Represent Multiplication
Let’s use area diagrams to find products.
Problem 1
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://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=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T162526Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=a76842ea7d6175a1e22b5fa0f148be8050c9018c19d621c78f336551b2999862)
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 2
Here is an area diagram that represents \((3.1) \boldcdot (1.4)\).
![Large rectangle divided into rectangles A and B. Length across top of rectangle A is 3 point 1. Width of rectangle A is 1. Width of rectangle B is 0 point 4.](https://cms-im.s3.amazonaws.com/2WETomx5jagJix2WgghNWuh8?response-content-disposition=inline%3B%20filename%3D%226-6.5.PP.Image.41.png%22%3B%20filename%2A%3DUTF-8%27%276-6.5.PP.Image.41.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T162526Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=26e133a67a8a3a911a03c625df895e3a8a7e846b1c5dcf5ce329c7253d86c7fa)
- Find the areas of sub-rectangles A and B.
- What is the area of the 3.1 by 1.4 rectangle?
Problem 3
Draw an area diagram to find \((0.36) \boldcdot (0.53)\). Label and organize your work so that it can be followed by others.
Problem 4
Find each product. Show your reasoning.
- \((2.5) \boldcdot (1.4)\)
- \((0.64) \boldcdot (0.81)\)
Problem 5
Complete the calculations so that each shows the correct sum.
![Four calculations with missing digits.](https://cms-im.s3.amazonaws.com/GjJBXHhA6Jh228uvU2FtP3Vs?response-content-disposition=inline%3B%20filename%3D%226-6.5.PP.Image.28a.png%22%3B%20filename%2A%3DUTF-8%27%276-6.5.PP.Image.28a.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T162526Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=d113c8ac25d25264b7457a4c8313056b69dedc185c403b338f8c731389816eb8)
Problem 6
Diego bought 12 mini muffins for $4.20.
- At this rate, how much would Diego pay for 4 mini muffins?
- How many mini muffins could Diego buy with $3.00? Explain or show your reasoning. If you get stuck, consider using the table.
number of mini muffins |
price in dollars |
---|---|
12 | 4.20 |