Grade 8 Percent Bridges and Conversions: Unit Mastery Quiz with Full Solutions

Use of this record

This is an end-of-unit assessment record for Grade 8 Percent Bridges and Conversions. For teaching, review, and graduated practice, use [rea.m08.number.ratios-rates-proportions.percent-bridges.practice-set] rather than this quiz. For broader ratio comparison language and notation, see [rea.m08.number.ratios-rates-proportions.ratio-concepts.unit-mastery-quiz].

What this quiz assesses

A learner is ready for mastery if they can:

• convert among percent, decimal, fraction, and ratio forms;
• simplify when appropriate;
• interpret a percent as “out of 100” and as a multiplicative comparison;
• move both directions, including from ratios and fractions back to percent;
• solve short application questions without confusing the whole and the part.

Quiz structure

• 10 questions
• 20 marks total
• Suggested time: 25 to 35 minutes
• Calculator: not required

Questions

1. Convert to decimal and fraction. (2 marks)

Write 37% as:

• a decimal
• a fraction in simplest form

2. Convert to percent and ratio. (2 marks)

Write 0.84 as:

• a percent
• a ratio in simplest whole-number form

3. Convert all forms. (2 marks)

Write 3/5 as:

• a decimal
• a percent
• a ratio of whole numbers

4. Convert a non-benchmark fraction. (2 marks)

Write 7/20 as:

• a decimal
• a percent

5. Move from ratio to percent. (2 marks)

A class survey shows the ratio of students who walk to school to total students is 9:25.

• Write this as a fraction.
• Write this as a percent.

6. Identify equivalent forms. (2 marks)

Which one of the following is not equivalent to the others?

• 45%
• 0.45
• 9/20
• 45/1000 Explain briefly.

7. Find the percent of a quantity. (2 marks)

What is 15% of 240? Show a conversion or percent-bridge method.

8. Find the whole from a percent. (2 marks)

18 is 30% of what number?

9. Compare two forms in context. (2 marks)

A sports club says 62% of its members attended an event. Another report says the attendance ratio was 31:50. Are these statements equivalent? Show why.

10. Multi-step conversion and interpretation. (4 marks)

A water bottle is 3/4 full.

• Write 3/4 as a decimal.
• Write 3/4 as a percent.
• If the bottle holds 800 mL, how many millilitres of water are in it?
• How many millilitres are still needed to fill it completely?

Full marking key and solutions

1. 37% as decimal and fraction. (2 marks)

• Decimal: 0.37 (1 mark)
• Fraction: 37/100 (1 mark)

Solution: 37% means 37 out of 100, so 37% = 37/100 = 0.37. 37/100 is already in simplest form because 37 is prime.

2. 0.84 as percent and ratio. (2 marks)

• Percent: 84% (1 mark)
• Ratio: 84:100 = 21:25 (1 mark)

Solution: To convert a decimal to a percent, multiply by 100: 0.84 = 84%. As a ratio, 84% means 84:100. Simplify by dividing both terms by 4: 84:100 = 21:25.

3. 3/5 in all forms. (2 marks)

• Decimal: 0.6 (1 mark)
• Percent: 60% (1 mark)
• Ratio: 3:5 (accepted within either mark if shown correctly)

Solution: 3/5 = 0.6. Then 0.6 = 60%. As a ratio of whole numbers, the fraction 3/5 corresponds to 3:5.

4. 7/20 as decimal and percent. (2 marks)

• Decimal: 0.35 (1 mark)
• Percent: 35% (1 mark)

Solution: Convert to a denominator of 100 or divide: 7/20 = 35/100 = 0.35. So the percent is 35%.

5. Ratio 9:25 to fraction and percent. (2 marks)

• Fraction: 9/25 (1 mark)
• Percent: 36% (1 mark)

Solution: 9:25 means 9 out of 25, so the fraction is 9/25. Convert to percent: 9/25 = 36/100 = 36%.

6. Identify the non-equivalent form. (2 marks)

• Not equivalent: 45/1000 (1 mark)
• Explanation: 45% = 45/100 = 0.45 = 9/20, but 45/1000 = 0.045 = 4.5% (1 mark)

Solution: Check each form:

• 45% = 45/100
• 45/100 = 0.45
• 9/20 = 45/100 = 0.45
• 45/1000 = 0.045 So 45/1000 is not equivalent.

7. Find 15% of 240. (2 marks)

• Correct answer: 36 (2 marks, or 1 for setup and 1 for arithmetic)

Solution 1: 15% = 0.15 0.15 x 240 = 36

Solution 2 using a percent bridge: 10% of 240 = 24 5% of 240 = 12 15% = 10% + 5% So 24 + 12 = 36.

8. 18 is 30% of what number? (2 marks)

• Correct answer: 60 (2 marks, or 1 for setup and 1 for solution)

Solution: Let the whole be x. 30% of x = 18 0.30x = 18 x = 18 / 0.30 = 60 Check: 30% of 60 = 18.

9. Compare 62% and 31:50. (2 marks)

• Yes, they are equivalent. (1 mark)
• Justification: 31/50 = 62/100 = 62% (1 mark)

Solution: Convert the ratio to a fraction: 31:50 = 31/50. Now convert to percent: 31/50 = 62/100 = 62%. So the two statements match.

10. Multi-step conversion and interpretation. (4 marks)

• Decimal: 0.75 (1 mark)
• Percent: 75% (1 mark)
• Amount of water: 600 mL (1 mark)
• Amount needed to fill: 200 mL (1 mark)

Solution: 3/4 = 0.75 So 3/4 = 75%. To find the water in the bottle: 0.75 x 800 = 600 So there are 600 mL in the bottle. To fill it completely: 800 - 600 = 200 So 200 mL are still needed.

Score interpretation

• 18-20 marks: strong mastery
• 16-17 marks: secure overall understanding; review any errors before moving on
• 13-15 marks: partial mastery; more practice needed on conversions or percent-of-quantity problems
• 0-12 marks: revisit the unit lesson flow and complete additional guided practice

Recommended mastery threshold

Recommended threshold: 16/20 (80%).

Reasoning:

• A learner at this level usually shows reliable two-way conversion among forms.
• Small errors may remain, but the core ideas are stable enough for later work with rates, discounts, tax, percent change, and algebraic percent equations.
• A score below 16/20 often means the learner is still mixing up part, whole, and percent, or is not yet fluent enough with equivalent forms.

Common error patterns to check during marking

• Writing 37% = 37 instead of 0.37 or 37/100
• Forgetting to simplify ratios or fractions
• Converting 0.45 to 0.45% instead of 45%
• Treating a:b as a/b without checking what the ratio compares
• In percent-of-quantity questions, multiplying by the wrong decimal or subtracting from the whole when no decrease is asked for

Record links

• Core graduated practice: [rea.m08.number.ratios-rates-proportions.percent-bridges.practice-set]
• Related ratio assessment language: [rea.m08.number.ratios-rates-proportions.ratio-concepts.unit-mastery-quiz]