Lesson 6: Use Ratio Reasoning6.AT.3

I can…

I can use ratio reasoning to solve problems with proportions and scaling.

Key words

• Proportion — A math sentence saying two ratios are equal.
• Cross-multiply — Multiplying across two ratios to check if they are equal.
• Scale — To multiply or divide both parts of a ratio by the same number.
• Equivalent — Having the same value.
• Unit rate — A rate for just 1 of something. You find it by dividing.

Steps

1. Chef Reyes's recipe serves 8 people and uses 5 cups of tomatoes. The banquet has 120 guests.
2. I find the scale factor: 120 divided by 8 = 15.
3. I multiply the tomatoes by 15: 5 x 15 = 75 cups of tomatoes.
4. To check, I can cross-multiply 5/8 = 75/120: 5 x 120 = 600 and 8 x 75 = 600.
5. The cross products match, so 75 cups is correct.

Try it

A recipe calls for 6 cups of flour for every 15 cookies. How many cups of flour are needed to make 45 cookies?

Check your answer

18

Scale factor: 45 ÷ 15 = 3. Multiply flour by 3: 6 × 3 = 18 cups of flour.

Sentence starter

I know ___ because ___.

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