Equivalent Ratios and Proportions: Unit Mastery Quiz

Level: Grade 8 Number
Topic: Ratios, Rates and Proportions
Purpose: End-of-unit mastery check

This quiz is meant to assess whether a learner can recognize, generate, justify, and apply equivalent ratios and proportions across numerical, tabular, graphical, and word-problem settings.

For initial teaching and concept development, see:

• rea.m08.number.ratios-rates-proportions.equivalent-ratios.overview
• rea.m08.number.ratios-rates-proportions

For likely errors and repair strategies, see:

• rea.m08.number.ratios-rates-proportions.equivalent-ratios.misconceptions

Suggested Use

• Total marks: 30
• Suggested time: 35-45 minutes
• Calculator: not necessary
• Mastery threshold recommendation: 24/30 (80%), with at least:
  • success on most missing-value proportion questions, and
  • no major conceptual confusion between additive and multiplicative reasoning.

Achievement Interpretation

• 27-30: Strong mastery; ready to move confidently into unit rates and proportional applications.
• 24-26: Secure mastery; minor cleanup only.
• 18-23: Partial mastery; review needed before extension topics.
• 0-17: Not yet secure; revisit equivalent-ratio generation, proportion testing, and setup of missing-value equations.

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Quiz Questions

Question 1: Generate equivalent ratios (3 marks)

Write three ratios equivalent to 4:7.

Question 2: Simplify to lowest terms (3 marks)

Simplify 18:30 to its lowest terms.

Question 3: Are these ratios equivalent? (3 marks)

Determine whether 6:9 and 14:21 are equivalent. Show a method that justifies your answer.

Question 4: Missing value in a proportion (2 marks)

Solve for x:

5/8 = x/24

Question 5: Missing value with ratio notation (3 marks)

A recipe uses flour and sugar in the ratio 3:2. If there are 18 cups of flour, how many cups of sugar are needed to keep the ratio equivalent?

Question 6: Complete a ratio table (4 marks)

Complete the table.

Red beads	Blue beads
2	5
4	?
?	15
10	?

Question 7: Identify proportional pairs (3 marks)

Circle all pairs that form a proportion.

1. 3:5 and 9:15
2. 4:6 and 8:14
3. 7/9 and 21/27
4. 10:12 and 15:18

Question 8: Word problem with comparison (3 marks)

Store A sells juice boxes in packs of 6 for $4.50. Store B sells juice boxes in packs of 10 for $7.50. Are the prices proportional to the number of juice boxes? Explain.

Question 9: Graph/table interpretation (3 marks)

A table shows the relationship between notebooks and cost.

Notebooks	Cost ($)
2	3
4	6
6	9
9	13.5

1. Is the relationship proportional?
2. Write one proportion from the table.
3. Predict the cost of 12 notebooks.

Question 10: Multi-step application (3 marks)

A map scale uses the ratio 1 cm : 4 km. Two towns are 7 cm apart on the map.

1. What is the real distance?
2. A second map uses the equivalent ratio 2 cm : ? km. Fill in the missing value so the scale stays equivalent.

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Full Marking Solutions

Question 1 Solution (3 marks)

We need ratios equivalent to 4:7, so multiply both parts by the same number.

• 4:7 x 2 = 8:14
• 4:7 x 3 = 12:21
• 4:7 x 4 = 16:28

Answer: Examples include 8:14, 12:21, 16:28.

Marking:

• 1 mark for each correct equivalent ratio, up to 3 marks.

Question 2 Solution (3 marks)

Simplify 18:30 by dividing both terms by their greatest common factor, 6.

18 ÷ 6 : 30 ÷ 6 = 3:5

Answer: 3:5

Marking:

• 1 mark for identifying or using a common factor correctly
• 1 mark for dividing both terms correctly
• 1 mark for final simplified ratio 3:5

Question 3 Solution (3 marks)

Check whether 6:9 and 14:21 reduce to the same ratio.

6:9 = 2:3 because divide both terms by 3
14:21 = 2:3 because divide both terms by 7

Since both simplify to 2:3, they are equivalent.

Another valid method is cross products:

6 x 21 = 126
9 x 14 = 126

Since the cross products are equal, the ratios form a proportion.

Answer: Yes, they are equivalent.

Marking:

• 1 mark for a valid method
• 1 mark for correct computations
• 1 mark for correct conclusion

Question 4 Solution (2 marks)

Solve 5/8 = x/24.

Since 8 x 3 = 24, multiply the numerator by 3 too:

5 x 3 = 15

So x = 15.

Cross multiplication also works:

8x = 5 x 24 = 120
x = 120 ÷ 8 = 15

Answer: x = 15

Marking:

• 1 mark for correct setup or scaling idea
• 1 mark for correct answer 15

Question 5 Solution (3 marks)

The flour:sugar ratio is 3:2.

If flour is 18, then the scale factor is:

18 ÷ 3 = 6

Multiply the sugar part by 6:

2 x 6 = 12

Answer: 12 cups of sugar

Marking:

• 1 mark for finding scale factor 6
• 1 mark for applying it correctly to sugar
• 1 mark for correct final answer 12

Question 6 Solution (4 marks)

Start from the base ratio 2:5.

• If red beads are 4, that is 2 x 2, so blue beads are 5 x 2 = 10
• If blue beads are 15, that is 5 x 3, so red beads are 2 x 3 = 6
• If red beads are 10, that is 2 x 5, so blue beads are 5 x 5 = 25

Completed table:

Red beads	Blue beads
2	5
4	10
6	15
10	25

Answer: Missing values are 10, 6, and 25.

Marking:

• 1 mark for each correct missing entry (3 marks)
• 1 mark for preserving the same multiplicative relationship throughout

Question 7 Solution (3 marks)

Check each pair.

1. 3:5 and 9:15
9:15 simplifies to 3:5, so yes

2. 4:6 and 8:14
4:6 = 2:3, but 8:14 = 4:7, so no

3. 7/9 and 21/27
21/27 simplifies to 7/9, so yes

4. 10:12 and 15:18
10:12 = 5:6 and 15:18 = 5:6, so yes

Answer: Pairs 1, 3, and 4

Marking:

• 1 mark for identifying pair 1 correctly
• 1 mark for identifying pair 3 correctly
• 1 mark for identifying pair 4 correctly
• No penalty beyond those marks if pair 2 is also selected, unless teacher wants all-or-nothing on each item set

Question 8 Solution (3 marks)

Check whether the cost per juice box is constant.

Store A:

$4.50 ÷ 6 = $0.75 per box

Store B:

$7.50 ÷ 10 = $0.75 per box

Since both stores have the same cost per box, the prices are proportional to the number of juice boxes.

Answer: Yes. The relationship is proportional because both rates are $0.75 per juice box.

Marking:

• 1 mark for Store A computation
• 1 mark for Store B computation
• 1 mark for correct conclusion with explanation

Question 9 Solution (3 marks)

From the table:

• 2 notebooks -> $3
• 4 notebooks -> $6
• 6 notebooks -> $9
• 9 notebooks -> $13.5

Check the unit rate:

3 ÷ 2 = 1.5
6 ÷ 4 = 1.5
9 ÷ 6 = 1.5
13.5 ÷ 9 = 1.5

The unit rate is constant, so the relationship is proportional.

A valid proportion is:

2/3 = 4/6

To predict the cost of 12 notebooks:

12 x 1.5 = 18

Answers:

1. Yes, it is proportional.
2. Example: 2/3 = 4/6
3. 12 notebooks cost $18

Marking:

• 1 mark for identifying proportionality correctly
• 1 mark for a valid proportion from the table
• 1 mark for correct prediction $18

Question 10 Solution (3 marks)

Scale: 1 cm : 4 km

For 7 cm, multiply both parts by 7:

7 cm : 28 km

So the real distance is 28 km.

For the second map, keep the scale equivalent:

1 cm : 4 km
2 cm : 8 km

Answers:

1. 28 km
2. 8 km

Marking:

• 1 mark for scaling to 7 cm : 28 km
• 1 mark for real distance 28 km
• 1 mark for equivalent scale 2 cm : 8 km

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Answer Key Only

1. Any three equivalent ratios to 4:7, such as 8:14, 12:21, 16:28
2. 3:5
3. Yes
4. 15
5. 12
6. 10, 6, 25
7. 1, 3, 4
8. Yes
9. Yes; example 2/3 = 4/6; $18
10. 28 km; 8 km

What This Quiz Diagnoses

A learner meeting the mastery threshold should be able to:

• scale ratios multiplicatively in either direction
• simplify ratios and compare them reliably
• decide whether two ratios form a proportion
• solve missing-value proportion problems
• interpret equivalent ratios in tables and contexts
• explain answers using ratio structure, not guesswork

If the Learner Misses Several Questions

Use the error patterns to choose next steps.

• Errors in Questions 1, 2, or 6 usually mean the learner needs more work on scaling both terms by the same factor.
• Errors in Questions 3 or 7 often show confusion about equivalence testing.
• Errors in Questions 4, 5, or 10 suggest weakness in setting up missing-value proportions.
• Errors in Questions 8 or 9 may indicate the learner can compute but does not yet recognize proportional structure in context.

For targeted repair, link directly to rea.m08.number.ratios-rates-proportions.equivalent-ratios.misconceptions.