Expressing Ratios Numerically

Expressing Ratios Numerically




Mia used the following reasoning to determine which paint is redder:

"I think it will be difficult to compare the two ratios in the problem because the numbers are so large. Maybe if I find equivalent ratios that have smaller numbers, it will be easier to solve the problem.

"The ratio of red to yellow in the Sunset paint is 2416. This ratio is equivalent to the ratio 32.

"The ratio of red to yellow in the Apple paint is 4840. This ratio is equivalent to the ratio 65.

"It’s easy to compare 32 and 65. I know that 32 is greater than 65. So, the Sunset paint is redder than the Apple paint."

  • Talk to your partner about Mia's reasoning. Why is it more difficult to compare 2416 and 4840 than it is to compare 32 and 65?

Math Mission


Compare ratios using the simplest form of each ratio.

Find Equivalent Paint Ratios

Work Time

Find Equivalent Paint Ratios

Work with a partner.

  • Take turns finding and grouping cards that represent the same ratio of red paint to yellow paint.
  • Explain to your partner how you know that the cards represent the same ratio.
  • Your partner should either agree with your explanation or challenge it if your explanation is not correct, clear, or complete.
  • When you have finished grouping all the cards in a way that you both agree on, arrange the sets of cards in order from least to greatest (the least red to the most red).


Prepare a Presentation

Work Time

Prepare a Presentation

You arranged your sets of paint ratio cards from least to greatest in Task 3.

  • Show how you grouped the cards and how you put the sets in order.
  • Include an explanation of the method(s) you used.

Challenge Problem

A painter mixes 15-fluid-ounce samples of red, yellow, and brown paint in the ratio of 1 to 3 to 2 in order to check that the resulting color is right for his mural. This sample mixture contains 90 fluid ounces (6 × 15 fluid ounces).

  • For the mural, the painter needs 360 fluid ounces of paint in the same ratio (1:3:2). How many more fluid ounces of each color does he need?

Ask yourself:

How could you put the ratios on the cards in the same format to make them easier to compare?

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes as your classmates present their methods for putting the ratio cards into sets of equal ratios and ordering the sets.

As your classmates present, ask questions such as:

  • Did you and your partner have any disagreements about which cards represent the same ratio? If so, how did you resolve your disagreement?
  • Do you think simplifying ratios that are represented as fractions is a good strategy? Why or why not?
  • What do you think is the easiest way to tell whether two ratios are equivalent?
  • Did you rewrite any of the ratios to help you determine how to arrange them from least to greatest? If so, how did you rewrite the ratios?

Ratios in Simplest Form

Formative Assessment

Summary of the Math: Ratios in Simplest Form

Write a summary about using the simplest form of ratios and comparing ratios.

Check your summary.

  • Do you discuss why it is often easier to work with the simplest form of a ratio?
  • Do you explain how to find the simplest form of a ratio?
  • Do you describe how to compare and order ratios?

Reflect On Your Work

Work Time


Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

One way that I could figure out the relationship between the ratio 3:2 and the fraction 2718 is to …