Equivalent Fractions and Lowest Terms: Grade 8 Unit Mastery Quiz with Full Solutions

Purpose and scope

This record is a Grade 8 end-of-unit mastery quiz for Equivalent Fractions and Lowest Terms. It samples the full unit rather than reteaching it. Use it after instruction and practice on fraction equivalence, common factors, and simplification.

For adjacent topics, use these linked assessments instead of duplicating their content:

• Equivalent ratios and proportional reasoning: rea.m08.number.ratios-rates-proportions.equivalent-ratios.unit-mastery-quiz
• Fraction-decimal-percent conversion fluency: rea.m08.number.ratios-rates-proportions.percent-bridges.unit-mastery-quiz
• Percent foundations: rea.m08.number.decimals-and-percents.percent-basics.unit-mastery-quiz
• Decimal computation: rea.m08.number.decimals-and-percents.decimal-operations.unit-mastery-quiz

Mastery quiz

Recommended total: 20 marks
Suggested time: 25-35 minutes
Calculator: not required

Questions

1. Write three fractions equivalent to 3/5. (2 marks)

2. Reduce 18/24 to lowest terms. Show the factor used. (2 marks)

3. Are 14/21 and 2/3 equivalent? Justify your answer. (2 marks)

4. Fill in the missing number: 5/8 = ?/32. (2 marks)

5. Fill in the missing number: 27/45 = 3/?. (2 marks)

6. Circle all fractions equivalent to 4/6: 8/12, 12/18, 10/15, 6/10, 2/3. (2 marks)

7. A student says 12/16 in lowest terms is 6/8, so the simplification is finished. Explain why this is not yet lowest terms, then give the correct lowest-terms fraction. (2 marks)

8. Order these fractions from least to greatest: 3/4, 6/8, 2/3, 9/12. (2 marks)

9. Shade or describe a model that proves 3/4 = 9/12. Then explain the equivalence in words. (2 marks)

10. Solve the multi-part item. (4 marks) A recipe uses 15/20 cup of milk.

1. Write 15/20 in lowest terms.
2. Decide whether 12/16 cup is the same amount.
3. Decide whether 9/10 cup is the same amount. Explain each decision.

Full marking solutions

1. Write three fractions equivalent to 3/5. (2 marks)

Equivalent fractions are made by multiplying numerator and denominator by the same nonzero whole number.

• 3/5 x 2/2 = 6/10
• 3/5 x 3/3 = 9/15
• 3/5 x 4/4 = 12/20

Answer: examples include 6/10, 9/15, 12/20.

Marking:

• 1 mark for any two correct equivalents
• 1 mark for a third correct equivalent

2. Reduce 18/24 to lowest terms. Show the factor used. (2 marks)

Find a common factor of 18 and 24.

• Both are divisible by 6.
• 18/24 = (18 ÷ 6)/(24 ÷ 6) = 3/4

Check: 3 and 4 have no common factor greater than 1, so 3/4 is in lowest terms.

Answer: 3/4

Marking:

• 1 mark for dividing numerator and denominator by the same common factor
• 1 mark for correct lowest-terms result 3/4

3. Are 14/21 and 2/3 equivalent? Justify your answer. (2 marks)

Reduce 14/21:

• 14/21 = (14 ÷ 7)/(21 ÷ 7) = 2/3 Since both fractions reduce to 2/3, they are equivalent.

Answer: Yes, they are equivalent.

Marking:

• 1 mark for correct simplification or another valid method
• 1 mark for correct conclusion with justification

4. Fill in the missing number: 5/8 = ?/32. (2 marks)

The denominator changed from 8 to 32.

• 8 x 4 = 32 So multiply the numerator by 4 also:
• 5 x 4 = 20

Answer: 20

Marking:

• 1 mark for identifying the scale factor 4
• 1 mark for correct numerator 20

5. Fill in the missing number: 27/45 = 3/?. (2 marks)

Reduce 27/45:

• 27/45 = (27 ÷ 9)/(45 ÷ 9) = 3/5 So 27/45 = 3/5.

Answer: 5

Marking:

• 1 mark for valid simplification strategy
• 1 mark for correct denominator 5

6. Circle all fractions equivalent to 4/6: 8/12, 12/18, 10/15, 6/10, 2/3. (2 marks)

First reduce 4/6:

• 4/6 = 2/3 Now test each fraction:
• 8/12 = 2/3 yes
• 12/18 = 2/3 yes
• 10/15 = 2/3 yes
• 6/10 = 3/5 no
• 2/3 yes

Answer: 8/12, 12/18, 10/15, 2/3

Marking:

• 1 mark for identifying at least three correct fractions
• 1 mark for identifying all four correct fractions and excluding 6/10

7. A student says 12/16 in lowest terms is 6/8, so the simplification is finished. Explain why this is not yet lowest terms, then give the correct lowest-terms fraction. (2 marks)

12/16 = 6/8 is a correct simplification because both numbers were divided by 2. But it is not in lowest terms because 6 and 8 still have a common factor greater than 1.

• 6/8 = (6 ÷ 2)/(8 ÷ 2) = 3/4 Now 3 and 4 share no common factor greater than 1.

Answer: 6/8 is not lowest terms because numerator and denominator are still both divisible by 2. The correct lowest-terms fraction is 3/4.

Marking:

• 1 mark for explaining why 6/8 is not lowest terms
• 1 mark for correct final answer 3/4

8. Order these fractions from least to greatest: 3/4, 6/8, 2/3, 9/12. (2 marks)

Simplify or compare:

• 3/4 = 3/4
• 6/8 = 3/4
• 2/3 = 2/3
• 9/12 = 3/4 Since 2/3 < 3/4, the order is:
• 2/3, 3/4, 6/8, 9/12 The last three are equal, so any order among those three is acceptable if they are shown as equal in value.

Answer: 2/3 < 3/4 = 6/8 = 9/12

Marking:

• 1 mark for recognizing 6/8 and 9/12 as equivalent to 3/4
• 1 mark for correct ordered result

9. Shade or describe a model that proves 3/4 = 9/12. Then explain the equivalence in words. (2 marks)

One correct description:

• Draw one rectangle split into 4 equal parts and shade 3 parts.
• Draw an equal-sized rectangle split into 12 equal parts and shade 9 parts. These represent the same amount of the whole.

Numerically:

• 3/4 x 3/3 = 9/12

Answer: A correct area model or set model showing the same whole and the same shaded amount earns full credit. In words: multiplying numerator and denominator by the same number does not change the fraction's value.

Marking:

• 1 mark for a valid visual or verbal model
• 1 mark for correct explanation of why the fractions are equivalent

10. Recipe item. (4 marks)

A recipe uses 15/20 cup of milk.

Part 1: Write 15/20 in lowest terms.

• 15/20 = (15 ÷ 5)/(20 ÷ 5) = 3/4

Part 2: Is 12/16 cup the same amount?

• 12/16 = (12 ÷ 4)/(16 ÷ 4) = 3/4 So yes, 12/16 cup is the same as 15/20 cup.

Part 3: Is 9/10 cup the same amount?

• 15/20 = 3/4
• 9/10 stays 9/10 Since 3/4 is not equal to 9/10, they are not the same amount.

Answer:

1. 15/20 = 3/4
2. Yes, 12/16 is the same amount.
3. No, 9/10 is not the same amount.

Marking:

• 1 mark for correct lowest-terms form 3/4
• 1 mark for correctly identifying 12/16 as equivalent
• 1 mark for correctly identifying 9/10 as not equivalent
• 1 mark for clear justification using simplification or another valid equivalence method

Answer key summary

1. Any three correct equivalents of 3/5
2. 3/4
3. Yes
4. 20
5. 5
6. 8/12, 12/18, 10/15, 2/3
7. 3/4, with explanation
8. 2/3 < 3/4 = 6/8 = 9/12
9. Valid model plus explanation
10. 3/4; yes; no

Recommended mastery threshold

Recommended mastery threshold: 16/20 (80%), with these minimum conditions:

• The learner must correctly simplify fractions to lowest terms in routine items.
• The learner must correctly identify equivalence using either scaling or simplification.
• The learner must show at least one valid explanation or model, not only final answers.

A useful interpretation:

• 18-20: secure mastery
• 16-17: mastery achieved
• 13-15: near mastery; assign targeted review on lowest terms and equivalence tests
• 12 or below: revisit the unit before moving on

Common errors this quiz is designed to detect

• Simplifying only once and stopping too early, as in 12/16 -> 6/8
• Multiplying or dividing only the numerator, or only the denominator
• Treating larger denominators as automatically larger fractions
• Confusing “same simplified form” with “same denominator”
• Giving an answer without justification when equivalence must be shown

Remediation guidance

If a learner misses several items:

• Rebuild the idea that equivalent fractions name the same amount of the same whole.
• Practice finding the greatest common factor or at least repeated common factors when simplifying.
• Use strip, area, or set models before symbolic work if the error is conceptual.
• Then connect this record to the linked percent and ratio quiz records only after fraction equivalence is stable.