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Learning Goal: Make tables of equivalent ratios and use them to compare and find missing values.

Vocabulary

equivalent ratiosRatios that show the same comparison, like 2:3 and 4:6.
ratio tableA table that lists equivalent ratios in rows or columns.
scaleTo multiply or divide both terms of a ratio by the same number.

What You Need to Know

  • Equivalent ratios show the same relationship. 1:2 = 2:4 = 3:6.
  • To make an equivalent ratio, multiply OR divide both terms by the same number.
  • Never add the same number to both terms — that changes the ratio.
  • A ratio table helps you see a pattern and find missing values.
  • You can multiply a whole column or row by the same number to fill a table.
  • To compare two ratios, scale them to a matching term.

Worked Example I Do — watch how it works

A recipe uses 2 cups of flour for every 3 eggs. Complete the ratio table for 6 cups of flour. How many eggs are needed?
  1. Step 1. Find how flour changed: 2 cups became 6 cups, so multiply by 3.
  2. Step 2. Whatever you do to flour, do to eggs. Multiply eggs by 3 too.
  3. Step 3. 3 eggs × 3 = 9 eggs.
Answer: 9 eggs (the ratio 2:3 scales to 6:9)

Guided Practice We Do — try it together

  1. 1. The ratio of dogs to cats is 3:4. If there are 12 dogs, how many cats?
    💡 Hint: 3 became 12, so multiply by 4. Do the same to 4.
  2. 2. Pencils to erasers is 5:2. If there are 6 erasers, how many pencils?
    💡 Hint: 2 became 6, so multiply by 3. Do the same to 5.
  3. 3. Is the ratio 4:6 equivalent to 6:9? Explain by scaling.
    💡 Hint: Simplify both. Divide each by their common factor.

Independent Practice You Do — show your work

  1. 1. The ratio of red to blue tiles is 2:5. If there are 10 red tiles, how many blue tiles?
  2. 2. A mix uses 3 cups water to 1 cup mix. For 9 cups of water, how many cups of mix?
  3. 3. Fill the table: 4:7, 8:?, 12:?. Find the two missing numbers.
  4. 4. Is 6:8 equivalent to 9:12? Answer yes or no.
  5. 5. Stickers to students is 7:3. For 21 stickers, how many students?

MCAP-Style Practice

Directions: Answer each item the way you would on the MCAP. For selected-response items, fill in the circle (○) next to the correct answer. For constructed-response items, enter your answer and show your work. Every item below assesses standard 6.RP.A.3a.
Item 1Selected Response6.RP.A.3a

Which ratio is equivalent to 3:5?

Select the correct answer.

Item 2Selected Response6.RP.A.3a

A ratio table shows 2:6, 4:12, 6:?. What is the missing number?

Select the correct answer.

Item 3Constructed Response6.RP.A.3a

The ratio of teachers to students is 1:18. Fill in: 4 teachers go with ____ students.

Enter your answer in the space provided. Show your work.

Enter your answer:
Teacher Answer Key (click to show)
Independent 125 blue tiles
Independent 23 cups of mix
Independent 314 and 21
Independent 4Yes (both simplify to 3:4)
Independent 59 students
Item 1 · 6.RP.A.3aC — Multiply both terms of 3:5 by 3 to get 9:15.
Item 2 · 6.RP.A.3aC — The ratio is 1:3, so 6 × 3 = 18.
Item 3 · 6.RP.A.3a72 — 18 × 4 = 72 students.
Neft Teacher · Grade 6 MCAP Mathematics Review · Standard 6.RP.A.3a