Neft Teacher · Learn It

Unit 3 · Standard 6.AT.3

Equivalent Ratios

Lesson 3-9 · Learn It — how the math works

Why we're learning this

Chef Montoya is preparing her famous tomato soup for a school banquet. Her original recipe serves 8 people, but tonight she needs to serve 32 guests. She needs your help to scale the recipe without changing the flavor!

✱ Math Workbench

Learn It

What are equivalent ratios?

Equivalent ratios are ratios that mean the same thing. You make one by multiplying or dividing BOTH numbers by the same amount.

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

Chef Kowalski's spice mix uses 3 teaspoons of paprika for every 5 teaspoons of cumin. For a bigger batch she measures out 18 teaspoons of paprika and 30 teaspoons of cumin.
Where you see this in real lifeChef Kowalski's spice mix uses 3 teaspoons of paprika for every 5 teaspoons of cumin. For a bigger batch she measures out 18 teaspoons of paprika and 30 teaspoons of cumin.

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

The problem looks like this
Ratio table: 3 cups of tomatoes to 2 cups of broth is equivalent to 12 to 8, after multiplying both by 4.Tomatoes (cups)312Broth (cups)28
  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 .
  4. I multiply both by 4: 3 x 4 = 12 cups of tomatoes, and 2 x 4 = 8 cups of broth.3 x 4 = 12
  5. So 3:2 and 12:8 are , and the flavor stays the same.

Watch out — mistakes students make here

  • Find the scale factor: 5 × ? = 15, then scale the price too.
  • Recheck the multiplier; 15 ÷ 5 tells how much to scale.
  • Only the second number was multiplied here — the first part stayed at 2. In equivalent ratios both parts must be multiplied by the same factor.

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

Same steps, new numbers.

  1. A is 2:5. We want to make it bigger using a scale factor of 3.
  2. Multiply both by 3: 2 x 3 = 6 and 5 x 3 = 15.2 x 3 = 6
  3. So 2:5 and 6:15 are .

On your ownYou do — solve this one by yourself

Before you start, remember:

  • Multiply both ingredients by the same scale factor each time.

Solve: Marcus earns $45 for every 3 hours of work. How much does he earn in 8 hours?

My answer

Stuck? Open one hint at a time.

Hint 1

8 hours is not a whole-number multiple of 3 hours, so find what Marcus earns in ONE hour first.

Hint 2

Unit rate: divide the $45 by the 3 hours, then multiply that hourly pay by 8 hours.

Hint 3

Divide 45 ÷ 3 to get dollars per hour — then multiply that rate by 8.

Check my answer
✅ Answer: $120
Unit rate: $45 ÷ 3 = $15/hour. In 8 hours: $15 × 8 = $120.

Turn & TalkSay it out loud with a partner

Chef Montoya's soup serves 8 people, but she needs to serve 32. How many times bigger is the recipe, and what must she do to BOTH ingredients to keep the flavor?

Try starting with:

  • 32 is ___ times bigger than 8, so I multiply both by ___.32 es ___ veces más grande que 8, así que multiplico ambos por ___.
  • The flavor stays the same because ___.El sabor se mantiene igual porque ___.
Use these wordsEquivalent ratiosProportionRate