Applying Unit Rates to Solve Problems: Grade 8 Unit Mastery Quiz with Full Solutions

Grade 8 scope and purpose

This record is a focused mastery quiz for Grade 8 Ratios, Rates and Proportions: Applying Unit Rates to Solve Problems. It does not reteach the full ideas of finding unit rates, interpreting unit-rate language, or mixed unit-rates assessment; use the linked records for those broader purposes.

Use this quiz after learners can already:

• compute a unit rate from a ratio;
• read units correctly (for example, dollars per kilogram, kilometres per hour, pages per minute);
• compare rates fairly by rewriting them as per 1 unit.

Links to adjacent records

Use these records before or alongside this quiz:

• rea.m08.number.ratios-rates-proportions.unit-rates.unit-mastery-quiz for a broader mixed assessment across the whole unit-rates topic.
• rea.m08.number.ratios-rates-proportions.unit-rates.rate-language.unit-mastery-quiz for precision with rate wording and unit structure.
• rea.m08.number.ratios-rates-proportions.equivalent-ratios.unit-mastery-quiz when a learner still struggles to scale ratios reliably.

Quiz structure

Total: 20 marks
Recommended time: 30-40 minutes
Calculator: Optional unless your program specifies otherwise.

Award full marks for correct reasoning, not just the final number. Units must be shown where appropriate.

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Questions

1. Grocery price comparison (2 marks)

A 2.5 kg bag of rice costs $8.75. What is the cost per kilogram?

2. Travel time from speed (2 marks)

A cyclist travels at 18 km/h. At that rate, how far will the cyclist travel in 2.5 hours?

3. Best buy: juice boxes (2 marks)

Store A sells 6 juice boxes for $4.50. Store B sells 10 juice boxes for $7.20. Which store offers the better price per juice box?

4. Earnings problem (2 marks)

A student earns $51 for 4 hours of work. If the rate stays constant, how much will the student earn in 7 hours?

5. Multi-step copying problem (2 marks)

A machine prints 45 pages in 3 minutes.

1. What is its unit rate in pages per minute?
2. At that rate, how long will it take to print 120 pages?

6. Walking distance decision (2 marks)

Mina walks 1.8 km in 24 minutes.

1. What is Mina's walking speed in km per minute?
2. Can Mina walk 4.5 km in 1 hour at the same rate?

7. Comparing pet food prices with different package sizes (2 marks)

Brand X: 3.2 kg for $19.84
Brand Y: 4.5 kg for $27.45

Which brand is cheaper per kilogram?

8. Water usage application (2 marks)

A faucet fills 15 litres in 4 minutes.

1. What is the unit rate in litres per minute?
2. How many litres will it fill in 18 minutes?

9. Reading rate with interpretation (2 marks)

Noah reads 42 pages in 35 minutes.

1. Find Noah's unit rate in pages per minute.
2. Estimate how many pages Noah would read in 50 minutes at the same rate.

10. Taxi fare comparison (4 marks)

Taxi Company P charges $18 for a 12 km trip.
Taxi Company Q charges $22.50 for a 15 km trip.

1. Find each company's cost per kilometre.
2. Which company is cheaper per kilometre?
3. Using your answer, estimate the cost of a 20 km trip with the cheaper company.

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Full marking solutions

1. Grocery price comparison

Cost per kilogram = 8.75 / 2.5 = 3.5

So the rice costs $3.50 per kg.

Marks:

• 1 mark for dividing cost by kilograms
• 1 mark for correct unit rate with units

2. Travel time from speed

Distance = rate x time
Distance = 18 x 2.5 = 45

So the cyclist travels 45 km.

Marks:

• 1 mark for correct multiplication setup
• 1 mark for correct distance with units

3. Best buy: juice boxes

Store A: 4.50 / 6 = 0.75
Store B: 7.20 / 10 = 0.72

Store A costs $0.75 per box.
Store B costs $0.72 per box.

Since 0.72 < 0.75, Store B is the better buy.

Marks:

• 1 mark for both unit prices
• 1 mark for correct comparison and decision

4. Earnings problem

Hourly rate = 51 / 4 = 12.75

For 7 hours: 12.75 x 7 = 89.25

So the student earns $89.25 in 7 hours.

Marks:

• 1 mark for finding $12.75 per hour
• 1 mark for correct total earnings

5. Multi-step copying problem

1. Unit rate: 45 / 3 = 15

The machine prints 15 pages per minute.

2. Time for 120 pages: 120 / 15 = 8

It will take 8 minutes.

Marks:

• 1 mark for 15 pages/min
• 1 mark for 8 minutes

6. Walking distance decision

1. Speed in km per minute: 1.8 / 24 = 0.075

So Mina walks 0.075 km/min.

2. In 1 hour, Mina walks for 60 minutes.

Distance in 60 minutes = 0.075 x 60 = 4.5

So Mina can walk 4.5 km in 1 hour exactly.

Marks:

• 1 mark for the unit rate
• 1 mark for correct conclusion with supporting calculation

7. Comparing pet food prices

Brand X: 19.84 / 3.2 = 6.20
Brand Y: 27.45 / 4.5 = 6.10

Brand X costs $6.20 per kg.
Brand Y costs $6.10 per kg.

Since 6.10 < 6.20, Brand Y is cheaper per kilogram.

Marks:

• 1 mark for both unit prices
• 1 mark for correct cheaper brand

8. Water usage application

1. Unit rate: 15 / 4 = 3.75

The faucet fills 3.75 L/min.

2. In 18 minutes: 3.75 x 18 = 67.5

It fills 67.5 L in 18 minutes.

Marks:

• 1 mark for 3.75 L/min
• 1 mark for 67.5 L

9. Reading rate with interpretation

1. Unit rate: 42 / 35 = 1.2

Noah reads 1.2 pages per minute.

2. In 50 minutes: 1.2 x 50 = 60

Noah would read about 60 pages in 50 minutes.

Marks:

• 1 mark for 1.2 pages/min
• 1 mark for correct estimate/application

10. Taxi fare comparison

1. Cost per kilometre:

Company P: 18 / 12 = 1.50
Company Q: 22.50 / 15 = 1.50

So both companies charge $1.50 per km.

2. Which is cheaper?

Neither. They cost the same per kilometre.

3. Cost of a 20 km trip:

1.50 x 20 = 30

A 20 km trip would cost $30.00 with either company.

Marks:

• 2 marks for both correct unit rates
• 1 mark for correct comparison
• 1 mark for correct 20 km estimate

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Answer key summary

1. $3.50 per kg
2. 45 km
3. Store B
4. $89.25
5. 15 pages/min, 8 min
6. 0.075 km/min, Yes, 4.5 km in 60 min
7. Brand Y
8. 3.75 L/min, 67.5 L
9. 1.2 pages/min, 60 pages
10. P = $1.50/km, Q = $1.50/km, same cost, $30

Mastery threshold recommendation

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

• the learner must correctly solve at least 7 of 10 questions;
• the learner must show correct unit-rate reasoning on at least 2 comparison questions (3, 7, or 10);
• the learner should lose no more than 1 mark total for missing or incorrect units.

Interpretation guidance

• 18-20 marks: Secure mastery. The learner can apply unit rates in routine and mildly non-routine contexts.
• 16-17 marks: Meets mastery. Minor arithmetic or notation errors may remain, but reasoning is sound.
• 12-15 marks: Developing. The learner can often compute a unit rate but is inconsistent when using it to make decisions.
• Below 12 marks: Not yet secure. Revisit finding unit rates, matching units, and deciding whether to multiply or divide after the unit rate is known.

Common error patterns to watch for

• Dividing the wrong way around, such as computing kg per dollar when the question asks for dollars per kg.
• Comparing package prices directly instead of comparing price per 1 item or per 1 kg.
• Finding a correct unit rate but then using the wrong operation afterward.
• Omitting units, which can hide whether the rate has been interpreted correctly.

Suggested next links

After this quiz, use the broader unit assessment record for mixed unit-rate fluency across contexts, or the rate-language record if errors came from misreading units rather than from calculation.