Recognizing and Testing Ratio Equivalence: Grade 8 Unit Mastery Quiz with Full Solutions

Grade 8 focus

This is a dedicated mastery quiz for the topic Recognizing and Testing Ratio Equivalence in Grade 8 ratios, rates, and proportions.

Use this record when the goal is to check whether a learner can:

• decide if two ratios are equivalent,
• justify the decision with a valid method,
• find missing values that preserve equivalence,
• interpret equivalence in tables and short contexts,
• distinguish equivalent ratios from merely similar-looking numbers.

For teaching, worked progression, and extra practice, use the linked records instead of reteaching here:

• rea.m08.number.ratios-rates-proportions.equivalent-ratios.recognizing-equivalence.practice-set
• rea.m08.number.ratios-rates-proportions.equivalent-ratios.unit-mastery-quiz
• rea.m08.number.ratios-rates-proportions.ratio-concepts.equivalent-ratios.unit-mastery-quiz

Quiz structure

• Questions: 10
• Total marks: 20
• Suggested time: 25-35 minutes
• Calculator: Not required

Student instructions

For each question, decide whether the ratios are equivalent or determine the missing value that makes them equivalent. Show your method clearly. You may use:

• simplification to lowest terms,
• multiplying or dividing both terms by the same non-zero number,
• a common scale factor,
• cross-products when appropriate.

A correct answer without reasoning earns at most 1 of 2 marks on justification questions.

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Questions

1. Basic recognition

Are the ratios 6:9 and 10:15 equivalent? Explain.

[2 marks]

2. Simplify and compare

Are 14/21 and 8/12 equivalent? Show how you know.

[2 marks]

3. Scale-factor recognition

Complete the statement with equivalent or not equivalent:

4:7 and 12:21 are __________.

Then justify your choice.

[2 marks]

4. Missing value in a ratio pair

Find x if 5:8 = x:24.

[2 marks]

5. Missing value with fractions written as ratios

Find y if 18/27 = y/12.

[2 marks]

6. Counterexample check

A student says: "9:12 and 12:15 are equivalent because both numbers in the second ratio are 3 more."

Is the student correct? Explain what is wrong or right about the reasoning.

[2 marks]

7. Table of values

A table shows red paint and blue paint mixed in a constant ratio.

Red	Blue
2	3
4	6
6	9
10	14

Which row does not match the same ratio as the first row? Justify.

[2 marks]

8. Choose all equivalent ratios

From the list below, choose all ratios equivalent to 3:5:

• 6:10
• 9:12
• 12:20
• 15:25
• 18:35

[2 marks]

9. Context question

A recipe uses flour and sugar in the ratio 4:1.

Recipe A uses 8 cups of flour and 2 cups of sugar. Recipe B uses 12 cups of flour and 4 cups of sugar.

Which recipe keeps the original ratio? Explain.

[2 marks]

10. Multi-step mastery question

Determine whether 16:24, 18:27, and 20:32 are all equivalent to each other.

State which are equivalent and which are not, and show your reasoning.

[2 marks]

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Full marking solutions

1. Basic recognition

6:9 = 2:3 after dividing both terms by 3.

10:15 = 2:3 after dividing both terms by 5.

Since both simplify to 2:3, the ratios are equivalent.

Marking:

• 1 mark for correct decision
• 1 mark for valid simplification or other correct justification

2. Simplify and compare

14/21 = 2/3 because both numerator and denominator divide by 7.

8/12 = 2/3 because both divide by 4.

Since both equal 2/3, they are equivalent.

Marking:

• 1 mark for correct simplification/comparison
• 1 mark for correct conclusion

3. Scale-factor recognition

4:7 to 12:21 is multiplying both terms by 3.

4 x 3 = 12 and 7 x 3 = 21.

So the ratios are equivalent.

Marking:

• 1 mark for writing equivalent
• 1 mark for identifying or demonstrating the scale factor of 3

4. Missing value in a ratio pair

5:8 = x:24

The second term goes from 8 to 24, which is x3. So the first term must also be multiplied by 3.

x = 5 x 3 = 15

So x = 15.

Marking:

• 1 mark for correct method
• 1 mark for x = 15

5. Missing value with fractions written as ratios

18/27 = y/12

First simplify 18/27:

18/27 = 2/3

So y/12 = 2/3.

To get denominator 12, multiply 3 by 4. Then multiply 2 by 4.

y = 8

So y = 8.

Alternative cross-product method: 18 x 12 = 27y 216 = 27y y = 8

Marking:

• 1 mark for correct setup or simplification
• 1 mark for y = 8

6. Counterexample check

The student is not correct.

Adding the same number to both terms does not preserve ratio equivalence. To test equivalence, both terms must be multiplied or divided by the same non-zero number.

Check by simplifying:

• 9:12 = 3:4
• 12:15 = 4:5

Since 3:4 and 4:5 are different, the ratios are not equivalent.

Marking:

• 1 mark for correct decision
• 1 mark for explaining that additive change is invalid and/or simplifying correctly

7. Table of values

The first row is 2:3.

Check each row:

• 4:6 = 2:3
• 6:9 = 2:3
• 10:14 = 5:7, not 2:3

So the row that does not match is 10 red and 14 blue.

Marking:

• 1 mark for identifying the incorrect row
• 1 mark for valid justification

8. Choose all equivalent ratios

Test each against 3:5:

• 6:10 divides by 2 to 3:5 -> equivalent
• 9:12 divides by 3 to 3:4 -> not equivalent
• 12:20 divides by 4 to 3:5 -> equivalent
• 15:25 divides by 5 to 3:5 -> equivalent
• 18:35 does not simplify to 3:5 -> not equivalent

Correct choices:

• 6:10
• 12:20
• 15:25

Marking:

• 2 marks for exactly all three correct and no incorrect choices
• 1 mark for two correct with no extra incorrect choice, or three correct plus one incorrect choice

9. Context question

Original ratio is 4:1.

Recipe A: 8:2 Divide both terms by 2: 8:2 = 4:1 So Recipe A keeps the ratio.

Recipe B: 12:4 Divide both terms by 4: 12:4 = 3:1 So Recipe B does not keep the ratio.

Therefore, Recipe A keeps the original ratio.

Marking:

• 1 mark for choosing Recipe A
• 1 mark for correct ratio check on both recipes

10. Multi-step mastery question

Simplify each ratio:

• 16:24 = 2:3 (divide by 8)
• 18:27 = 2:3 (divide by 9)
• 20:32 = 5:8 (divide by 4)

So:

• 16:24 and 18:27 are equivalent to each other
• 20:32 is not equivalent to them

They are not all equivalent.

Marking:

• 1 mark for correct simplifications
• 1 mark for correct final classification

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Mastery interpretation

Recommended mastery threshold

• 17-20 marks (85%-100%): Mastery
• 14-16 marks (70%-80%): Near mastery; assign targeted correction on weak item types
• 0-13 marks (below 70%): Not yet secure; return to guided practice before advancing

What mastery means here

A learner at mastery should be able to:

• test equivalence reliably using more than one valid method,
• solve missing-value equivalence questions without guessing,
• reject invalid additive reasoning,
• interpret equivalent ratios in tables and short contexts,
• explain why a ratio is or is not equivalent, not just state an answer.

Error diagnosis guide

• If errors cluster in Questions 1-3 or 8: the learner likely needs more fluency recognizing multiplicative scale factors.
• If errors cluster in Questions 4-5: the learner needs more work with missing values in equivalent ratios.
• If errors cluster in Questions 6-7 or 9: the learner may not yet distinguish multiplicative structure from additive change or context wording.
• If Question 10 is missed: the learner may recognize pairwise equivalence inconsistently when several ratios are presented together.

Short remediation map

After marking:

• For extra focused practice, use rea.m08.number.ratios-rates-proportions.equivalent-ratios.recognizing-equivalence.practice-set.
• For a broader end-of-unit assessment including proportions and other representations, use rea.m08.number.ratios-rates-proportions.equivalent-ratios.unit-mastery-quiz.
• For nearby work on simplification structure, compare with rea.m08.number.fraction-operations.equivalence.unit-mastery-quiz.