Ratio Remix Worksheet
Name: ___________________________ Date: _________________
Period: _______
Ratio Remix
Mastering Equivalent Ratios • Scaling & Proportions
Target Skill Identify & Generate Equivalent Ratios
Core Rule: Equivalent ratios have the same multiplicative relationship. Multiply or divide both terms by the same non-zero number (\(k\)).
\( \frac{a \times k}{b \times k} = \frac{a}{b} \)
1 Are They Equivalent?
Test each pair using scaling or simplification. Show your work!
A. \( 4 : 6 \) and \( 10 : 15 \)
Circle: YES NO
B. \( 5 : 8 \) and \( 20 : 36 \)
Circle: YES NO
C. \( 18 : 24 \) and \( 3 : 4 \)
Circle: YES NO
D. \( 7 : 9 \) and \( 28 : 45 \)
Circle: YES NO
2 Complete the Ratio Tables
Find the pattern or multiplier to fill in all missing values.
Table A: Teal Blast Paint Mix (Blue Cans to Yellow Cans) Ratio: 3 blue cans for every 2 yellow cans
| Blue Paint (\(B\)) | 3 | 6 | 9 | _____ | 18 | _____ |
|---|
| Yellow Paint (\(Y\)) | 2 | _____ | _____ | 8 | _____ | 20 |
Table B: Sugar Cookie Batches (Flour to Sugar) Ratio: 5 cups of flour for every 3 cups of sugar
| Flour (cups) | 5 | 10 | _____ | 25 | _____ | 45 |
|---|
| Sugar (cups) | 3 | _____ | 9 | _____ | 21 | _____ |
Ratio Remix • Equivalent Ratios Practice Page 1 of 2
Name: ___________________________ Ratio Remix • Page 2
3 Generate the Ratio Family
Multiply or divide to create 3 equivalent ratios for each base.
Base Ratio 2 : 7
Scale × 2 ___ : ___
Scale × 3 ___ : ___
Scale × 5 (or any \(k\)) ___ : ___
Base Ratio 4 : 9
Scale × 3 ___ : ___
Scale × 4 ___ : ___
Scale × 10 ___ : ___
Simplify First 18 : 24
Simplest Form (\(\div 6\)) ___ : ___
Scale Simplest × 4 ___ : ___
Scale Simplest × 7 ___ : ___
4 Real-World Ratio Challenges
Set up an equivalent ratio or ratio table and solve.
A. Smoothie Stand: A blended smoothie recipe requires 3 cups of strawberries for every 4 cups of yogurt. Elena is hosting a party and wants to make a mega-batch using 20 cups of yogurt. How many cups of strawberries does Elena need?
Final Answer:
_______ cups of strawberries
B. Hiking Trail: On a topographic hiking map, every 2 inches on the paper represents an actual trail distance of 7 miles. If Jayden plans to hike a section that measures 10 inches on the map, what is the actual trail distance?
Final Answer:
_______ miles on the trail
5 The Ratio Detective (Error Analysis)
Critical Thinking
Maya's Claim: "The ratio 4 : 7 is equivalent to 8 : 11 because I added 4 to each number: \(4 + 4 = 8\) and \(7 + 4 = 11\)."
Explain Maya's mistake:
Correct equivalent ratio:
\( 4 : 7 = \) ____ : ____
Ratio Remix • Equivalent Ratios Practice Page 2 of 2
Ratio Remix Answer Key
Teacher Reference ANSWER KEY • Scoring & Solutions
Standard: 6.RP.A.1, 6.RP.A.3a
Ratio Remix • Key
Worked Solutions • Pacing • Misconception Alerts
Grading Guide Total: 25 Points Possible
1 Are They Equivalent? Solutions
2 pts each (1 pt choice, 1 pt work)
A. \( 4 : 6 \) and \( 10 : 15 \)
YES NO
• Simplified: \( \frac{4\div 2}{6\div 2} = \frac{2}{3} \) and \( \frac{10\div 5}{15\div 5} = \frac{2}{3} \)
• Cross-prod: \( 4 \times 15 = 60 \); \( 6 \times 10 = 60 \) ✓
B. \( 5 : 8 \) and \( 20 : 36 \)
YES NO
• Scaling: \( 5 \times 4 = 20 \), but \( 8 \times 4 = 32 \neq 36 \)
• Cross-prod: \( 5 \times 36 = 180 \neq 8 \times 20 = 160 \) ✗
C. \( 18 : 24 \) and \( 3 : 4 \)
YES NO
• Simplifying: \( \frac{18 \div 6}{24 \div 6} = \frac{3}{4} \) (Exact match)
• Scaling up: \( 3 \times 6 = 18 \) and \( 4 \times 6 = 24 \) ✓
D. \( 7 : 9 \) and \( 28 : 45 \)
YES NO
• Scaling: \( 7 \times 4 = 28 \), but \( 9 \times 4 = 36 \neq 45 \)
• Cross-prod: \( 7 \times 45 = 315 \neq 9 \times 28 = 252 \) ✗
2 Ratio Tables Solutions
1 pt per missing cell (10 pts total)
Table A: Teal Blast Paint Mix (Unit Multiplier: \(\times 1.5\) or \(3 : 2\)) Key: Highlighted answers bolded
| Blue Paint (\(B\)) | 3 | 6 | 9 | 12 | 18 | 30 |
|---|
| Yellow Paint (\(Y\)) | 2 | 4 | 6 | 8 | 12 | 20 |
Work / Reasoning: When \(Y=8\), factor is \(8\div 2=4\), so \(B=3\times 4=\mathbf{12}\). When \(Y=20\), factor is \(20\div 2=10\), so \(B=3\times 10=\mathbf{30}\).
Table B: Sugar Cookie Batches (Base Ratio \(5 : 3\)) Key: Highlighted answers bolded
| Flour (cups) | 5 | 10 | 15 | 25 | 35 | 45 |
|---|
| Sugar (cups) | 3 | 6 | 9 | 15 | 21 | 27 |
Work / Reasoning: When Sugar=9, factor is 3 (\(9\div 3\)), so Flour=\(5\times 3=\mathbf{15}\). When Flour=25, factor is 5, Sugar=\(3\times 5=\mathbf{15}\).
Teacher Resource • Ratio Remix Solutions Page 1 of 2
