Lesson 5: Compare Ratio Relationships6.AT.3

I can…

I can compare ratios by finding unit rates or using equivalent ratios.

Key words

• Compare Ratios — Decide which ratio is greater, less, or equal by using equivalent ratios or unit rates.
• Unit rate — A rate for just 1 of something, like cost for 1 item.
• Equivalent ratio — Two ratios that mean the same thing.
• Compare — To look at ratios and see which is bigger, smaller, or equal.
• Simplify — To write a ratio with smaller numbers that still compares the same way. 6:8 and 3:4 are the same ratio.
• Common denominator — A bottom number that two fractions can share so you can compare them.
• Common multiple — A number that both terms can be scaled to.
• Least common multiple — The smallest common multiple of two numbers.
• Benchmark — A shared amount you scale both choices to so you can compare them.

Steps

1. Chef Reyes uses 3 tbsp cocoa for 5 oz milk (3:5). Chef Tran uses 4 tbsp for 7 oz milk (4:7).
2. I cannot compare yet because the milk amounts are different.
3. I scale both to 35 oz of milk. For Reyes: 5 x 7 = 35, so 3 x 7 = 21 tbsp, giving 21:35.
4. For Tran: 7 x 5 = 35, so 4 x 5 = 20 tbsp, giving 20:35.
5. Now the milk is equal, so I compare cocoa: 21 > 20, so Chef Reyes's cocoa is more chocolatey.

Try it

Art Shop A sells 3 paintbrushes for $10. Art Shop B sells 4 paintbrushes for $13. Which shop charges less for one paintbrush?

Check your answer

Art Shop B

Art Shop A: $10 ÷ 3 ≈ $3.33 per paintbrush. Art Shop B: $13 ÷ 4 = $3.25 per paintbrush. Art Shop B has the lower price.

Sentence starter

I know ___ because ___.

Goal: I can explain my comparison using the words unit rate, equivalent ratio, compare, and common denominator.