Comparing Ratios: Grade 8 Unit Mastery Quiz with Full Solutions

Position in the topic

This record is a dedicated assessment for the subtopic Comparing Ratios in Grade 8 Ratios, Rates and Proportions. It should be used after learners have studied the linked unit material on ratio concepts, equivalent ratios, and proportional reasoning.

Use these linked records for broader instruction and adjacent assessment:

• rea.m08.number.ratios-rates-proportions.ratio-concepts.unit-mastery-quiz for whole-unit assessment across ratio concepts and comparison.
• rea.m08.number.ratios-rates-proportions.equivalent-ratios.unit-mastery-quiz for equivalent-ratio and proportion fluency.
• rea.m08.number.ratios-rates-proportions.proportional-modeling.unit-mastery-quiz for richer proportional contexts.
• rea.m08.number.decimals-and-percents.percent-basics.unit-mastery-quiz when percent comparison is the more natural representation.

Grade 8 unit mastery quiz: Comparing Ratios

Recommended time: 35-45 minutes
Calculator: optional; not required
Total: 20 marks

Learning target

A learner demonstrates mastery when they can compare ratios by:

• rewriting to equivalent ratios,
• converting to unit rates or common denominators,
• comparing part-to-part and part-to-whole ratios correctly,
• justifying which representation is most efficient in a given context,
• avoiding invalid comparison shortcuts.

Questions

1. Direct comparison by simplification (2 marks)

Which ratio is greater: 8:12 or 10:14? Show your reasoning.

2. Equivalent-ratio table (2 marks)

A red-to-blue bead ratio is 3:5. Another bag has red-to-blue ratio 12:19. Which bag has the greater proportion of red beads? Explain.

3. Unit-rate comparison (2 marks)

Store A sells 6 granola bars for $4.50. Store B sells 8 granola bars for $5.76. Which store offers the better buy? Show the comparison clearly.

4. Same total, different part ratio (2 marks)

Class X has boys:girls = 7:9. Class Y has boys:girls = 11:13. Which class has the greater fraction of boys? Explain without using percentages if possible.

5. Ordering three ratios (2 marks)

Order these ratios from least to greatest:

• 4:7
• 5:8
• 7:12

6. Cross-multiplication justification (2 marks)

Without converting to decimals, determine whether 9:14 or 11:17 is greater. Show a valid comparison method.

7. Context: sports shooting accuracy (2 marks)

Player A made 18 shots out of 30 attempts. Player B made 22 shots out of 35 attempts. Who was more accurate? State the ratios compared and justify the answer.

8. Detecting a misconception (2 marks)

A student says: “Since 15 is bigger than 12 and 24 is bigger than 20, the ratio 15:24 must be greater than 12:20.” Is the student correct? Explain why or why not.

9. Missing value for equal comparison (2 marks)

Find x so that the ratios x:18 and 5:9 are equal. Then explain whether a ratio of 11:18 would be greater than, less than, or equal to 5:9.

10. Multi-step applied comparison (2 marks)

Two juice mixes are made as follows:

• Mix A: 4 cups concentrate and 10 cups water
• Mix B: 5 cups concentrate and 14 cups water Which mix is stronger in concentrate? Show a comparison that matches the context.

Complete marking key and full solutions

1. Direct comparison by simplification (2 marks)

Answer: 10:14 is greater.

Solution: 8:12 = 2:3 after dividing both terms by 4.
10:14 = 5:7 after dividing both terms by 2.

Compare 2/3 and 5/7. Cross-multiply: 2 x 7 = 14 and 3 x 5 = 15. Since 14 < 15, 2/3 < 5/7. So 8:12 < 10:14.

Marks:

• 1 mark for simplifying or writing as fractions.
• 1 mark for valid comparison and conclusion.

2. Equivalent-ratio table (2 marks)

Answer: The second bag, with ratio 12:19, has the greater proportion of red beads.

Solution: For 3:5, the red fraction is 3/(3+5) = 3/8. For 12:19, the red fraction is 12/(12+19) = 12/31.

Compare 3/8 and 12/31: 3 x 31 = 93 8 x 12 = 96 Since 93 < 96, 3/8 < 12/31. So the bag with ratio 12:19 has more red beads relative to its total.

Marks:

• 1 mark for setting up the correct part-to-whole comparison.
• 1 mark for correct comparison and conclusion.

3. Unit-rate comparison (2 marks)

Answer: Store B offers the better buy.

Solution: Find cost per bar.

Store A: $4.50 / 6 = $0.75 per bar.
Store B: $5.76 / 8 = $0.72 per bar.

Since $0.72 < $0.75, Store B is cheaper per bar.

Marks:

• 1 mark for a correct unit rate for one store.
• 1 mark for the second unit rate and conclusion.

4. Same total, different part ratio (2 marks)

Answer: Class Y has the greater fraction of boys.

Solution: For Class X, boys fraction is 7/(7+9) = 7/16.
For Class Y, boys fraction is 11/(11+13) = 11/24.

Compare: 7 x 24 = 168 16 x 11 = 176 Since 168 < 176, 7/16 < 11/24. So Class Y has the greater fraction of boys.

Marks:

• 1 mark for converting both part-to-part ratios to part-to-whole fractions.
• 1 mark for comparison and conclusion.

5. Ordering three ratios (2 marks)

Answer: 4:7 < 7:12 < 5:8

Solution: Write as fractions: 4:7 = 4/7, 5:8 = 5/8, 7:12 = 7/12.

Compare 4/7 and 7/12: 4 x 12 = 48, 7 x 7 = 49, so 4/7 < 7/12.

Compare 7/12 and 5/8: 7 x 8 = 56, 12 x 5 = 60, so 7/12 < 5/8.

Therefore 4:7 < 7:12 < 5:8.

Marks:

• 1 mark for two correct pairwise comparisons or equivalent decimal work.
• 1 mark for correct final order.

6. Cross-multiplication justification (2 marks)

Answer: 11:17 is greater.

Solution: Compare 9/14 and 11/17 using cross-products: 9 x 17 = 153 14 x 11 = 154 Since 153 < 154, 9/14 < 11/17. So 11:17 is greater.

Marks:

• 1 mark for valid setup of the cross-products.
• 1 mark for correct conclusion.

7. Context: sports shooting accuracy (2 marks)

Answer: Player B was more accurate.

Solution: Accuracy ratios are made shots : total attempts.

Player A: 18/30 = 3/5.
Player B: 22/35.

Compare 3/5 and 22/35: 3 x 35 = 105 5 x 22 = 110 Since 105 < 110, 3/5 < 22/35. So Player B had the higher shooting accuracy.

Marks:

• 1 mark for using the correct ratios from the context.
• 1 mark for valid comparison and conclusion.

8. Detecting a misconception (2 marks)

Answer: The student is not correct.

Solution: You cannot compare ratios by checking whether each individual number is larger. Ratios compare the relationship between the two numbers, not the numbers separately.

Compare: 15/24 = 5/8 and 12/20 = 3/5. Now compare 5/8 and 3/5: 5 x 5 = 25 8 x 3 = 24 Since 25 > 24, 5/8 > 3/5. So in this case 15:24 is greater, but not for the reason the student gave.

Marks:

• 1 mark for rejecting the incorrect reasoning.
• 1 mark for a valid comparison and corrected explanation.

9. Missing value for equal comparison (2 marks)

Answer: x = 10, and 11:18 is greater than 5:9.

Solution: Set the ratios equal: x/18 = 5/9 Multiply both sides by 18: x = 18 x 5 / 9 = 10

Now compare 11/18 and 5/9. Convert 5/9 to denominator 18: 5/9 = 10/18 Since 11/18 > 10/18, 11:18 is greater than 5:9.

Marks:

• 1 mark for finding x = 10.
• 1 mark for correct follow-up comparison.

10. Multi-step applied comparison (2 marks)

Answer: Mix A is stronger in concentrate.

Solution: “Stronger in concentrate” means compare concentrate as a fraction of the whole mixture.

Mix A total = 4 + 10 = 14, so concentrate fraction is 4/14 = 2/7.
Mix B total = 5 + 14 = 19, so concentrate fraction is 5/19.

Compare 2/7 and 5/19: 2 x 19 = 38 7 x 5 = 35 Since 38 > 35, 2/7 > 5/19. So Mix A is stronger.

Marks:

• 1 mark for choosing the correct contextual ratio to compare.
• 1 mark for correct computation and conclusion.

Score interpretation

• 18-20 marks: strong mastery; learner compares ratios flexibly and justifies method choice.
• 15-17 marks: secure overall; minor errors only.
• 12-14 marks: partial mastery; review part-to-whole comparisons and efficient methods.
• 0-11 marks: not yet mastered; revisit core instruction before moving on.

Recommended mastery threshold

Recommended threshold: 16/20 (80%), with at least:

• 1 correct contextual comparison question from Questions 7-10, and
• 1 correct justification question from Questions 6 or 8.

This threshold is appropriate because unit mastery in Grade 8 ratio comparison should include both computational fluency and reasoned method selection, not only answer-getting.

Common errors this quiz diagnoses

• Comparing only one term of each ratio.
• Comparing part-to-part ratios when the context requires part-to-whole.
• Treating larger raw numbers as automatically giving a larger ratio.
• Using cross-multiplication correctly but misinterpreting what the compared fractions represent.
• Comparing rates without first matching the unit.

Brief remediation guidance

• If Questions 1, 5, or 6 are weak: review equivalent ratios and fraction comparison.
• If Questions 2, 4, or 10 are weak: review the difference between part:part and part:whole.
• If Questions 3 or 7 are weak: review unit rates and interpreting context labels.
• If Question 8 is weak: explicitly confront invalid shortcut reasoning with counterexamples.