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.

Select all the statements that correctly describe this diagram

A:

The ratio of cups of white paint to cups of green paint is 2 to 4.

B:

For every cup of green paint, there are two cups of white paint.

C:

The ratio of cups of green paint to cups of white paint is \(4:2\).

D:

For every cup of white paint, there are two cups of green paint.

E:

The ratio of cups of green paint to cups of white paint is \(2:4\).

Solution

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Problem 2

To make a snack mix, combine 2 cups of raisins with 4 cups of pretzels and 6 cups of almonds.

  1. Create a diagram to represent the quantities of each ingredient in this recipe.

  2. 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

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Problem 3

  1. A square is 3 inches by 3 inches. What is its area?
  2. A square has a side length of 5 feet. What is its area?
  3. The area of a square is 36 square centimeters. What is the length of each side of the square?

Solution

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(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.

 

Solution

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(From Unit 1, Lesson 11.)

Problem 5

Complete each equation with a number that makes it true.

  1. \(\frac18 \boldcdot 8 = \text{_______}\)
  2. \(\frac38 \boldcdot 8 = \text{_______}\)
  1. \(\frac18 \boldcdot 7 = \text{_______}\)
  2. \(\frac38 \boldcdot 7 = \text{_______}\)

Solution

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(From Unit 2, Lesson 1.)