Lesson 2
Representing Ratios with Diagrams
Problem 1
Here is a diagram that describes the cups of green and white paint in a mixture.
![Four squares labeled green paint, cups, and two squares labeled white paint, cups.](https://cms-im.s3.amazonaws.com/CAVJKM8kkmziDBueLrAMfoW8?response-content-disposition=inline%3B%20filename%3D%226-6.2.A.PP_Image_4.png%22%3B%20filename%2A%3DUTF-8%27%276-6.2.A.PP_Image_4.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T233005Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=69579446318ae5171c6c38c5460514c07228299b08c7cd0873920af9ae143685)
Select all the statements that correctly describe this diagram
The ratio of cups of white paint to cups of green paint is 2 to 4.
For every cup of green paint, there are two cups of white paint.
The ratio of cups of green paint to cups of white paint is \(4:2\).
For every cup of white paint, there are two cups of green paint.
The ratio of cups of green paint to cups of white paint is \(2:4\).
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 2
To make a snack mix, combine 2 cups of raisins with 4 cups of pretzels and 6 cups of almonds.
-
Create a diagram to represent the quantities of each ingredient in this recipe.
-
Use your diagram to complete each sentence.
- The ratio of __________________ to __________________ to __________________ is ________ : ________ : ________.
- There are ________ cups of pretzels for every cup of raisins.
- There are ________ cups of almonds for every cup of raisins.
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 3
- A square is 3 inches by 3 inches. What is its area?
- A square has a side length of 5 feet. What is its area?
- The area of a square is 36 square centimeters. What is the length of each side of the square?
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
(From Unit 1, Lesson 17.)Problem 4
Find the area of this quadrilateral. Explain or show your strategy.
![A blue quadrilateral in the shape of a kite. Two smaller sides span across 3 squares. Two longer sides span across 5 squares.](https://cms-im.s3.amazonaws.com/D1g5uQt466D8KEHPVbUQT3Qw?response-content-disposition=inline%3B%20filename%3D%226-6.1.D.PP_Image_5.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.D.PP_Image_5.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T233005Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=007be67cbd2fc24ec1e8ef40ba90f435a73ff9abf03030395f62cd35cd1544a9)
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
(From Unit 1, Lesson 11.)Problem 5
Complete each equation with a number that makes it true.
- \(\frac18 \boldcdot 8 = \text{_______}\)
- \(\frac38 \boldcdot 8 = \text{_______}\)
- \(\frac18 \boldcdot 7 = \text{_______}\)
- \(\frac38 \boldcdot 7 = \text{_______}\)
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
(From Unit 2, Lesson 1.)