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Determine Equivalent Ratios Using Tables

Use ratio tables to generate and reason about equivalent ratios by multiplying or dividing both quantities.

6.AT.A.3a · Ratios & Rates
Level
Guided practice with vocabulary support

🟠 Level 0 — Extra Support

Sentence starters: “First, I…” · “The answer is… because…” · “I know this because…”
W

Warm-Up

2 questions
Warm-Up 1
Which pair of ratios is equivalent?
Vocabulary: Equivalent ratios are ratios that name the same comparison. You can multiply or divide both parts of a ratio by the same number.
✓Correct! 2:3 and 4:6 are equivalent because 2×2=4 and 3×2=6.
✗Multiply both parts of 2:3 by 2: 2×2=4, 3×2=6 → 4:6. The answer is B.
Warm-Up 2
Complete the ratio table. If the ratio of cups of flour to batches is 3:1, how many cups for 4 batches?
Hint: In a ratio table, multiply both quantities by the same number. 3 cups × 4 = ?
Cups for 4 batches =
✓Correct! 3 × 4 = 12 cups of flour.
✗Multiply 3 cups by 4 batches: 3 × 4 = 12 cups.
P

Practice

5 questions
Practice 1
Complete the missing values in the ratio table.
Strategy: Find the multiplier between the first row and each column. Multiply both quantities by that number.
Red 2 4 6 ?
Blue 5 10 15 ?
Red =
Blue =

Sentence frame: "I multiplied both ___ and ___ by ___ to get ___ and ___."

✓Correct! 2×4=8 red and 5×4=20 blue.
✗The pattern is ×2, ×3, ×4. Red: 2×4=8. Blue: 5×4=20.
Practice 2
A recipe uses 2 cups of sugar for every 5 cups of flour. How many cups of sugar are needed for 20 cups of flour?
Strategy: 5 cups × ? = 20 cups. Find the multiplier: 20 ÷ 5 = 4. Then multiply sugar by the same number: 2 × 4 = ?
Show your work:

Sentence frame: "I multiplied both parts by ___ because 5 × ___ = 20, so sugar = 2 × ___ = ___."

✓Correct! Multiplier = 4. Sugar = 2 × 4 = 8 cups.
✗20 ÷ 5 = 4. Multiply sugar: 2 × 4 = 8. The answer is B.
Practice 3
Are the ratios 6:9 and 10:15 equivalent?
Strategy: Simplify both ratios by dividing by their GCF. If they simplify to the same ratio, they are equivalent.
Show your simplification:

Sentence frame: "6:9 simplifies to ___:___ and 10:15 simplifies to ___:___. They are ___."

✓Correct! 6:9 = 2:3 and 10:15 = 2:3. They are equivalent.
✗Simplify: 6÷3=2, 9÷3=3 → 2:3. And 10÷5=2, 15÷5=3 → 2:3. They are equivalent.
Practice 4
Complete the ratio table for the ratio 3:7.
Strategy: Multiply both parts by 2, 3, and 5 to fill in each column.
A 3 6 ? ?
B 7 14 ? ?
Column 3: A = , B =
Column 4: A = , B =

Sentence frame: "I multiplied 3 and 7 by ___ to get ___ and ___, and by ___ to get ___ and ___."

✓All correct! ×3 → 9:21 and ×5 → 15:35.
✗Column 3: 3×3=9, 7×3=21. Column 4: 3×5=15, 7×5=35.
Practice 5
The ratio of boys to girls on a team is 4:5. If there are 20 girls, how many boys are on the team?
Strategy: Girls went from 5 to 20. What did you multiply by? 20 ÷ 5 = 4. Multiply boys by the same: 4 × 4 = ?
Explain your reasoning:

Sentence frame: "I divided ___ by ___ to find the multiplier = ___. Then ___ × ___ = ___ boys."

✓Correct! Multiplier = 4. Boys = 4 × 4 = 16.
✗20 ÷ 5 = 4 (multiplier). Boys: 4 × 4 = 16. The answer is C.
★

Challenge

1 question
Challenge
A ratio table shows the relationship between lemonade mix and water. The ratio is 3 scoops of mix to 8 cups of water. If you have 15 scoops of mix, how many cups of water do you need? Complete the table.
Think about it: 15 ÷ 3 = 5, so the multiplier is 5. Multiply water by 5: 8 × 5 = ?
Mix (scoops) 3 6 9 12 15
Water (cups) 8 16 24 32 ?
Water for 15 scoops = cups
Show your work:

Sentence frame: "The multiplier is ___ ÷ ___ = ___. Water = ___ × ___ = ___ cups."

✓Excellent! 15 ÷ 3 = 5. Water = 8 × 5 = 40 cups.
✗15 ÷ 3 = 5. Water = 8 × 5 = 40 cups.