Neft Teacher · Learn It

Unit 3 · Standard 6.AT.3

Compare Ratio Relationships

Lesson 3-5 · Learn It — how the math works

Why we're learning this

Two friends used the paint shown to create shades of purple paint. Whose mixture contains the most blue paint?

✱ Math Workbench

Learn It

How do we compare two ratios?

To compare ratios fairly, make one amount the same in both, or find the unit rate (the amount for just 1). Then you can see which ratio is bigger.

Picture itSee what the math looks like before you read about it

Two chefs each mixed cocoa and milk to make the cups of hot cocoa shown. Each used a different ratio of cocoa to milk.
Where you see this in real lifeTwo chefs each mixed cocoa and milk to make the cups of hot cocoa shown. Each used a different ratio of cocoa to milk.

Watch me solve itI do — read one step at a time

The problem looks like this
Ratio table: Reyes 3 tbsp cocoa to 5 oz milk becomes 21 to 35; Tran 4 to 7 becomes 20 to 35. With 35 oz of milk, 21 is more than 20.ChefReyesReyes × 7TranTran × 5Cocoa (tbsp)321420Milk (oz)535735
  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 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 21:35.5 x 7 = 35
  4. For Tran: 7 x 5 = 35, so 4 x 5 = 20 tbsp, giving 20:35.7 x 5 = 35
  5. Now the milk is equal, so I cocoa: 21 > 20, so Chef Reyes's cocoa is more chocolatey.

Watch out — mistakes students make here

  • Find each price per muffin and compare — recompute both.
  • Compare the per-muffin costs; are $10/4 and $14/6 equal?
  • $6 for 3 and $9 for 5 do not give the same unit price. Divide each total by its number of mangoes to check.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. Store A sells 2 pens for $6. Store B sells 3 pens for $12. Which is the better deal?
  2. Find each , the price for 1 pen. Store A: 6 divided by 2 = $3 per pen.
  3. Store B: 12 divided by 3 = $4 per pen. Store A is cheaper at $3 per pen.

On your ownYou do — solve this one by yourself

Before you start, remember:

  • Then decide which chef's cocoa is more chocolatey.

Solve: Store A sells 3 mangoes for $6. Store B sells 5 mangoes for $9. Which store offers a better price per mango?

My answer

Stuck? Open one hint at a time.

Hint 1

The stores sell different counts for different prices — compare the price of ONE mango.

Hint 2

Divide dollars by mangoes for each store, then choose the store with the lower per-mango price.

Hint 3

Store A: divide 6 ÷ 3 for its price per mango. Store B: divide 9 ÷ 5. Compare the two prices.

Check my answer
✅ Answer: Store B
Store A: $6÷3 = $2.00 per mango. Store B: $9÷5 = $1.80 per mango. Store B has the better (lower) price per mango.

Turn & TalkSay it out loud with a partner

Reginald used 3 red and 3 blue cans; Anwar used 2 red and 3 blue. Why is 'who used more blue cans' a different question from 'whose paint is more blue'?

Try starting with:

  • I think ___ because ___.Pienso que ___ porque ___.
  • I agree / disagree with you because ___.Estoy / no estoy de acuerdo contigo porque ___.
Use these wordsCompare RatiosUnit rateEquivalent ratioCompareSimplify