Equivalent Ratios and Simplification: Grade 8 Unit Mastery Quiz with Full Solutions

Grade 8 unit mastery quiz

This record is a focused assessment for Grade 8 Number: Ratios, Rates and Proportions, Ratio Concepts and Comparison, Equivalent Ratios and Simplification. It is meant to be used after instruction and practice on the topic. For reteaching, wider unit review, or proportion-focused assessment, use the linked records rather than relying on this quiz alone.

Coverage

This quiz samples whether a learner can:

• recognize equivalent and non-equivalent ratios;
• generate equivalent ratios by scaling up or down;
• simplify ratios to lowest terms;
• solve for missing values in equivalent ratios;
• compare ratios by simplifying or scaling to a common form;
• interpret equivalent ratios in simple contexts.

Format and marks

• 10 questions
• 20 marks total
• Suggested time: 30-40 minutes
• Calculators: not necessary

Quiz

Question 1 (2 marks)

Are the ratios 6:9 and 10:15 equivalent? Show how you know.

Question 2 (2 marks)

Write three ratios equivalent to 4:7.

Question 3 (2 marks)

Simplify the ratio 18:24 to lowest terms.

Question 4 (2 marks)

Simplify 30 cm : 45 cm to lowest terms.

Question 5 (2 marks)

Find the missing value: 5:8 = 20:x.

Question 6 (2 marks)

Find the missing value: x:21 = 4:7.

Question 7 (2 marks)

A recipe uses red paint and blue paint in the ratio 2:5. If 12 cups of red paint are used, how many cups of blue paint are needed to keep the ratio equivalent?

Question 8 (2 marks)

Which is greater: 8:12 or 10:18? Explain by simplifying or rewriting both ratios.

Question 9 (3 marks)

A class has 14 boys and 21 girls.

1. Write the ratio of boys to girls.
2. Simplify it.
3. Write one different equivalent ratio.

Question 10 (3 marks)

A student says, "To simplify a ratio, subtract the same number from both parts." For example, they simplify 12:18 to 6:12 by subtracting 6.

Explain why this method does not always work, and then correctly simplify 12:18.

Full marking key and solutions

Question 1 solution (2 marks)

6:9 = 2:3 because both parts divide by 3.

10:15 = 2:3 because both parts divide by 5.

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

Marking:

• 1 mark for simplifying or scaling one ratio correctly
• 1 mark for correct conclusion with justification

Question 2 solution (2 marks)

Equivalent ratios are made by multiplying both parts by the same number.

Examples:

• 8:14 (multiply by 2)
• 12:21 (multiply by 3)
• 16:28 (multiply by 4)

Any three correct examples earn full credit.

Marking:

• 2 marks for three correct equivalent ratios
• 1 mark if only two are correct

Question 3 solution (2 marks)

Simplify 18:24.

The greatest common factor of 18 and 24 is 6.

Divide both parts by 6:

• 18 ÷ 6 = 3
• 24 ÷ 6 = 4

So the simplified ratio is 3:4.

Marking:

• 1 mark for a valid common-factor step
• 1 mark for 3:4

Question 4 solution (2 marks)

30 cm : 45 cm

Because the units are the same, simplify the numbers:

• divide both by 15
• 30 ÷ 15 = 2
• 45 ÷ 15 = 3

So the simplified ratio is 2:3.

Marking:

• 1 mark for correct simplification process
• 1 mark for 2:3

Question 5 solution (2 marks)

5:8 = 20:x

From 5 to 20 is ×4, so multiply 8 by 4:

• x = 8 × 4 = 32

So x = 32.

Marking:

• 1 mark for identifying the scale factor
• 1 mark for 32

Question 6 solution (2 marks)

x:21 = 4:7

From 7 to 21 is ×3, so multiply 4 by 3:

• x = 12

So x = 12.

Marking:

• 1 mark for identifying the scale factor
• 1 mark for 12

Question 7 solution (2 marks)

Red : Blue = 2:5

If red is 12, then the scale factor is:

• 12 ÷ 2 = 6

So blue must be:

• 5 × 6 = 30

So 30 cups of blue paint are needed.

Marking:

• 1 mark for correct scale factor or setup
• 1 mark for 30

Question 8 solution (2 marks)

Simplify both ratios.

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

10:18 = 5:9 because divide both by 2.

Compare 2:3 and 5:9.

Rewrite 2:3 with denominator-part 9:

• 2:3 = 6:9

Now compare 6:9 and 5:9. Since 6:9 is greater than 5:9, 8:12 is greater.

Marking:

• 1 mark for simplifying both ratios correctly
• 1 mark for correct comparison and conclusion

Question 9 solution (3 marks)

1. Boys to girls: 14:21
2. Simplify by dividing both by 7: 2:3
3. One equivalent ratio: for example 4:6 or 6:9

Marking:

• 1 mark for 14:21
• 1 mark for 2:3
• 1 mark for one correct equivalent ratio

Question 10 solution (3 marks)

The method "subtract the same number from both parts" does not preserve equivalence in general. Equivalent ratios are made by multiplying or dividing both parts by the same non-zero number, not by subtracting.

For example:

• 12:18 = 2:3
• if we subtract 6 from both parts, we get 6:12 = 1:2

Since 2:3 and 1:2 are different ratios, subtraction changed the ratio.

Correct simplification of 12:18:

• divide both parts by 6
• 12 ÷ 6 = 2
• 18 ÷ 6 = 3

So the correct simplified ratio is 2:3.

Marking:

• 1 mark for explaining that subtraction does not preserve ratio equivalence
• 1 mark for a correct counterexample or comparison
• 1 mark for correct simplification to 2:3

Mastery threshold recommendation

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

• one correct simplification in lowest terms;
• one correct missing-value solution using equivalence;
• one correct explanation/justification response.

Interpretation

• 18-20: secure mastery
• 16-17: meets unit mastery
• 13-15: developing; assign targeted correction on simplification and scaling
• 0-12: reteach equivalent-ratio structure before moving on

Common error signals to watch for

• Treating ratios as additive instead of multiplicative
• Simplifying only one part of a ratio
• Using different scale factors on the two parts
• Forgetting that same-unit ratios can be simplified directly
• Believing subtraction preserves equivalence

Use with linked records

• Use the broader Ratio Concepts and Comparison mastery quiz for whole-unit checking across this topic family.
• Use the Equivalent Ratios and Proportions quiz when the learner is ready for more formal proportional reasoning, tables, and broader missing-value structures.
• Use the Equivalent Fractions and Lowest Terms quiz if the learner's difficulty comes from weak equivalence/simplification foundations rather than ratio meaning itself.