Lesson 9: Equivalent Ratios6.AT.3

I can…

I can find and check equivalent ratios using multiplication and division.

Key words

• Equivalent Ratios — Ratios that compare quantities in the same relationship.
• Ratio — A way to compare two amounts, like 3 to 2.
• Rate — A ratio comparing two amounts with different units, like miles per hour.
• Proportion — A math sentence saying two ratios are equal.
• Simplify — To write a ratio with smaller numbers that still compares the same way. 6:8 and 3:4 are the same ratio.
• Ratio table — A table of equal ratios that shows a pattern.

Steps

1. Chef Montoya's soup serves 8 people, but she needs to serve 32.
2. I find the scale factor: 32 divided by 8 = 4.
3. The recipe uses 3 cups of tomatoes to 2 cups of broth, a 3:2 ratio.
4. I multiply both by 4: 3 x 4 = 12 cups of tomatoes, and 2 x 4 = 8 cups of broth.
5. So 3:2 and 12:8 are equivalent ratios, and the flavor stays the same.

Try it

At a farm stand, 3 pounds of apples cost $5. If every pound costs the same, what is the price of 12 pounds of apples?

Check your answer

$20

12 is 4 times 3, so the cost is 4 × $5 = $20. The ratio 3:5 scales to 12:20.

Sentence starter

I know ___ because ___.

Goal: I can explain my reasoning using the words equivalent ratios, rate, proportion, and simplify.