Lesson 5
Defining Equivalent Ratios
Problem 1
Each of these is a pair of equivalent ratios. For each pair, explain why they are equivalent ratios or draw a diagram that shows why they are equivalent ratios.
- \(4:5\) and \(8:10\)
- \(18:3\) and \(6:1\)
- \(2:7\) and \(10,\!000:35,\!000\)
Solution
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Problem 2
Explain why \(6:4\) and \(18:8\) are not equivalent ratios.
Solution
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Problem 3
Are the ratios \(3:6\) and \(6:3\) equivalent? Why or why not?
Solution
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Problem 4
This diagram represents 3 batches of light yellow paint. Draw a diagram that represents 1 batch of the same shade of light yellow paint.
![A discrete diagram for two quantities labeled "white paint, in cups" and "yellow paint, in cups". The data are as follows: white paint, 9 squares. yellow paint, 15 squares.](https://cms-im.s3.amazonaws.com/BHUhp4s8haXH5KiPof3947Pc?response-content-disposition=inline%3B%20filename%3D%226-6.2.B.PP_Image_8.png%22%3B%20filename%2A%3DUTF-8%27%276-6.2.B.PP_Image_8.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=20240630T181504Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b0c82395186f3deea8f24331744154918b861b9214872109745bcb3106c16076)
Solution
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(From Unit 2, Lesson 4.)Problem 5
In the fruit bowl there are 6 bananas, 4 apples, and 3 oranges.
- For every 4 __________________, there are 3 __________________.
- The ratio of __________________ to __________________ is \(6:3\).
- The ratio of __________________ to __________________ is 4 to 6.
- For every 1 orange, there are ______ bananas.
Solution
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(From Unit 2, Lesson 1.)Problem 6
Write fractions for points \(A\) and \(B\) on the number line.
![Number line, 7 evenly spaced tick marks, labeled zero, blank, A, blank, blank, B, blank, 1.](https://cms-im.s3.amazonaws.com/srDRSR1xLbBHnLivkj1JAnYr?response-content-disposition=inline%3B%20filename%3D%226-6.2.A1.PP.Image.Rev.0404.png%22%3B%20filename%2A%3DUTF-8%27%276-6.2.A1.PP.Image.Rev.0404.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=20240630T181504Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=3e86724b5f26e4231470768cd97df7246d3c78efc02b803771c092f06eeb8682)
Solution
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(From Unit 2, Lesson 1.)