Interpreting Unit Rates in Context: Graded Practice Set (Grade 8)

This Grade 8 practice set targets one specific skill: interpreting what a unit rate means in context, not just calculating it. It provides a graded sequence of 24 problems, a complete answer key, and full solutions for the hardest eight problems, while linking to the broader unit-rate lesson, worked examples, misconceptions, and general practice set for re-teaching and extension.

Position in the unit

This record is a focused practice set for Grade 8 learners who already know how to compute a unit rate but still need practice deciding what the rate means, which unit belongs in the answer, and whether the answer actually matches the question asked.

Use these companion records instead of repeating their content here:

For broader mixed unit-rate practice: [rea.m08.number.ratios-rates-proportions.unit-rates.practice-set]
For fully modeled interpretation examples: [rea.m08.number.ratios-rates-proportions.unit-rates.interpret-unit-rates.worked-examples]
For common mistakes and repair strategies: [rea.m08.number.ratios-rates-proportions.unit-rates.misconceptions]
For the larger unit context and applications: [rea.m08.number.ratios-rates-proportions.unit-rates.rate-applications.overview]

How to use this set

For each problem, do all of the following:

Identify the two quantities being compared.
Decide which quantity should be "per 1".
Compute the unit rate if needed.
State the meaning in a full sentence with units.
Check that your sentence answers the actual question.

Difficulty tags

Core: straightforward interpretation of a given or easy-to-find unit rate
Bridge: requires choosing the correct orientation of the rate or comparing meanings
Stretch: includes misleading wording, two-step reasoning, or decision-making in context

Problems

Core

A car travels 180 km in 3 hours. What does the unit rate mean in this situation?
Tag: Core
A pack of 8 granola bars costs $6.40. Find the unit rate and interpret it in context.
Tag: Core
Liam reads 45 pages in 3 hours. Interpret the unit rate in context.
Tag: Core
A water bottle holds 750 mL and costs $1.50. What is the cost per 100 mL, and what does it mean?
Tag: Core
A baker uses 12 cups of flour to make 16 muffins. Interpret the unit rate in cups of flour per muffin.
Tag: Core
A cyclist rides 54 km in 2 hours. State the unit rate and its meaning.
Tag: Core
A streaming plan costs $18 for 6 months. What is the monthly cost, and what does it represent?
Tag: Core
A jug pours 2.4 L of juice into 6 glasses equally. Find and interpret the unit rate.
Tag: Core

Bridge

210 words are typed in 5 minutes. Is it more useful here to say 42 words per minute or 1/42 minute per word? Explain briefly.
Tag: Bridge
A 15 kg bag of rice costs $24. Should the unit rate be written as dollars per kilogram or kilograms per dollar if you want to compare grocery prices? Find the better unit rate and interpret it.
Tag: Bridge
Nora walks 3.6 km in 45 minutes. Find a unit rate and explain what it tells you about her walking.
Tag: Bridge
A machine fills 96 bottles in 8 minutes. Interpret the unit rate in the most natural way for production.
Tag: Bridge
A 500 g container of yogurt costs $3.25, and a 750 g container costs $4.50. Find the better buy and justify using unit rates in context.
Tag: Bridge
A bus uses 18 L of fuel to travel 150 km. Interpret a useful unit rate for fuel efficiency in context.
Tag: Bridge
A student earns $35 for 4 hours of tutoring. Another earns $52 for 6 hours. Who earns at a greater hourly rate, and what does that comparison mean?
Tag: Bridge
A recipe uses 3/4 cup of sugar for 6 muffins. Interpret the unit rate in context.
Tag: Bridge

Stretch

A tap fills 10 L in 4 minutes. Maya says, "The unit rate is 2.5, so the tap fills 2.5 minutes each litre." Identify the error and give the correct interpretation.
Tag: Stretch
A 12-pack of juice boxes costs $7.80. A 20-pack costs $12.40. One student says the 20-pack is a better buy because it has more juice boxes. Use unit rates to decide and interpret the result correctly.
Tag: Stretch
A runner completes 9 km in 50 minutes. Find both kilometres per minute and minutes per kilometre. Which unit rate is more useful if the runner wants to predict how long 1 km will take? Interpret your answer.
Tag: Stretch
A printer produces 150 pages in 6 minutes. How long should 25 pages take at the same rate? Show how the unit rate helps answer the question, then interpret the result.
Tag: Stretch
A 2.5 kg bag of apples costs $8.25. A 4 kg bag costs $12.60. Which is the better buy? Then explain what your unit rate means in words, not just numbers.
Tag: Stretch
A canoe travels 18 km downstream in 2 hours and 12 km upstream in 2 hours. Compare the two unit rates and explain what the comparison suggests about the river current.
Tag: Stretch
A school club prints 300 posters for $126. Another print shop charges $0.39 per poster. Which option is cheaper for 300 posters, and what does each unit rate tell you in context?
Tag: Stretch
A water tank is drained at a constant rate: 84 L are removed in 7 minutes. After 3 more minutes at the same rate, a student says, "Since the unit rate is 12, there must be 12 L left." Explain why this interpretation is wrong, and state what the unit rate actually tells you. Then determine how many litres are removed in 10 minutes total.
Tag: Stretch

Answer key

60 km/h; the car travels 60 kilometres each hour.
$0.80 per bar; each granola bar costs 80 cents.
15 pages per hour; Liam reads 15 pages each hour.
$0.20 per 100 mL; every 100 mL costs 20 cents.
0.75 cup per muffin; each muffin uses 3/4 cup of flour? No. Check: 12/16 = 0.75, so each muffin uses 3/4 cup of flour.
27 km/h; the cyclist rides 27 kilometres each hour.
$3 per month; the plan costs $3 for each month.
0.4 L per glass; each glass gets 0.4 L of juice.
42 words per minute is more useful; it tells typing speed directly.
$1.60 per kilogram; this tells the cost of 1 kg, which is the standard way to compare prices.
0.08 km per minute or 4.8 km/h; Nora walks 0.08 km each minute, or 4.8 km each hour.
12 bottles per minute; the machine fills 12 bottles each minute.
Better buy: 750 g container. Unit prices: $0.0065/g and $0.006/g, or $6.50/kg and $6.00/kg.
0.12 L per km or 12 L per 100 km; the bus uses 0.12 litre for each kilometre traveled.
First student: $8.75/h; second student: about $8.67/h. The first student earns slightly more per hour.
1/8 cup per muffin; each muffin uses one-eighth of a cup of sugar.
Error: wrong units. Correct interpretation: 2.5 L per minute, meaning the tap fills 2.5 litres each minute.
Same unit price: $0.65 per juice box; neither is a better buy.
0.18 km/min and about 5.56 min/km; minutes per kilometre is more useful for predicting time for 1 km.
25 pages should take 1 minute; the printer prints 25 pages each minute.
Better buy: 4 kg bag. Unit prices: $3.30/kg and $3.15/kg; the 4 kg bag costs less for each kilogram of apples.
Downstream: 9 km/h; upstream: 6 km/h; the canoe moves faster downstream, suggesting the current helps downstream travel and slows upstream travel.
First shop: $126/300 = $0.42 per poster. Second shop: $0.39 per poster. The second shop is cheaper; it charges 39 cents for each poster instead of 42 cents.
The unit rate 12 means 12 L per minute removed, not 12 L left. In 10 minutes, 120 L are removed.

Full solutions for the hardest third

17. Tap-filling error

We are told 10 L are filled in 4 minutes.

Step 1: Find the unit rate.

10 / 4 = 2.5
So the tap fills 2.5 L per minute.

Step 2: Check Maya's statement.

Maya said, "2.5 minutes each litre."
That uses the wrong units.
2.5 came from dividing litres by minutes, so the units are L/min, not min/L.

Step 3: State the correct interpretation.

The tap fills 2.5 litres each minute.

Final answer: Maya reversed the units. The correct unit rate is 2.5 L/min, meaning the tap adds 2.5 litres of water every minute.

18. Comparing two pack sizes

Find the cost per juice box for each pack.

Step 1: 12-pack.

$7.80 / 12 = $0.65 per juice box.

Step 2: 20-pack.

$12.40 / 20 = $0.62? Check carefully.
12.40 / 20 = 0.62

This means the original quick answer must be corrected.

Step 3: Compare.

12-pack: $0.65 per box
20-pack: $0.62 per box

Step 4: Interpret.

The 20-pack costs 62 cents for each juice box.
The 12-pack costs 65 cents for each juice box.
Since 62 cents is less than 65 cents, the 20-pack is the better buy.

Final answer: The 20-pack is the better buy. It costs about $0.62 per juice box, compared with $0.65 per juice box for the 12-pack.

19. Two useful unit rates from one situation

The runner completes 9 km in 50 minutes.

Step 1: Find kilometres per minute.

9 / 50 = 0.18
So the speed is 0.18 km/min.

Interpretation:

The runner covers 0.18 kilometre each minute.

Step 2: Find minutes per kilometre.

50 / 9 ≈ 5.56
So the pace is about 5.56 min/km.

Interpretation:

The runner takes about 5.56 minutes for each kilometre.

Step 3: Decide which is more useful.

If the goal is to predict how long 1 km will take, then minutes per kilometre is better.
It directly answers the time-for-1-km question.

Final answer: 0.18 km/min and about 5.56 min/km. The more useful rate for predicting 1 km time is 5.56 min/km, meaning the runner takes a little more than 5.5 minutes to run 1 kilometre.

20. Using the unit rate to answer a time question

A printer produces 150 pages in 6 minutes.

Step 1: Find the production rate.

150 / 6 = 25
So the printer makes 25 pages per minute.

Step 2: Use the interpretation.

If it prints 25 pages every minute, then printing 25 pages takes 1 minute.

Step 3: State the result in context.

At the same rate, 25 pages should take 1 minute.

Final answer: The unit rate is 25 pages per minute, so 25 pages should take 1 minute.

21. Better buy for apples

Compare cost per kilogram.

Step 1: First bag.

$8.25 / 2.5 = $3.30 per kg

Step 2: Second bag.

$12.60 / 4 = $3.15 per kg

Step 3: Compare the rates.

$3.15/kg is less than $3.30/kg
So the 4 kg bag is the better buy.

Step 4: Interpret in words.

The 2.5 kg bag costs $3.30 for each kilogram of apples.
The 4 kg bag costs $3.15 for each kilogram of apples.

Final answer: The 4 kg bag is the better buy because it has the lower unit price, $3.15 per kilogram.

22. Downstream versus upstream

Find each speed.

Step 1: Downstream rate.

18 km / 2 h = 9 km/h

Step 2: Upstream rate.

12 km / 2 h = 6 km/h

Step 3: Compare and interpret.

Downstream travel is faster: 9 km each hour.
Upstream travel is slower: 6 km each hour.
This suggests the river current helps the canoe move downstream and resists its motion upstream.

Final answer: Downstream speed is 9 km/h, upstream speed is 6 km/h. The comparison suggests the current increases speed downstream and decreases speed upstream.

23. Comparing two printing options

Step 1: Find the first shop's unit rate.

126 / 300 = 0.42
So the first shop charges $0.42 per poster.

Step 2: Write the second shop's unit rate.

The second shop already charges $0.39 per poster.

Step 3: Compare.

$0.39 < $0.42
So the second shop is cheaper per poster.

Step 4: Check total for 300 posters.

Second shop total: 300 x 0.39 = 117
So the second shop would cost $117.
First shop costs $126.

Step 5: Interpret.

First shop: each poster costs 42 cents.
Second shop: each poster costs 39 cents.

Final answer: The second shop is cheaper. Its unit rate is $0.39 per poster, so 300 posters cost $117, which is less than $126.

24. Interpreting a draining rate correctly

We are told 84 L are removed in 7 minutes.

Step 1: Find the unit rate.

84 / 7 = 12
The unit rate is 12 L per minute.

Step 2: Interpret the rate.

This does not tell us how much water is left in the tank.
It tells us how much water is removed each minute.

Step 3: Explain the student's error.

The student treated the number 12 as an amount remaining.
But a unit rate must be interpreted with its units.
12 means 12 litres removed per minute.

Step 4: Find the amount removed in 10 minutes total.

12 x 10 = 120

Final answer: The interpretation "12 L left" is wrong because the unit rate means 12 L removed each minute. In 10 minutes, 120 L are removed.

Quick self-check prompts

Use these after each question:

Did I say what happens for 1 unit?
Did I keep the units in the correct order?
Did I answer in per hour, per item, per kilogram, or another unit that matches the question?
If I reversed the rate, would the sentence still make sense?

Common repair note

If you got the number right but the meaning wrong, revisit the worked-examples and misconceptions records linked at the top. In this topic, the most common failure is interpreting the quotient without its units.