Year 8 - Rates - Free practice

Year 8 Rates Worksheets & Practice Tests

Q: What's a rate in maths?

A comparison of two quantities with different units. Speed is a rate (km per hour), so is unit price ($ per kg), density (kg per m^3), and pay (dollars per hour).

Q: How do students convert between rate units?

Convert each unit separately. To go from km/h to m/s: km to m is x 1000, h to s is /3600, so the rate gets multiplied by 1000/3600 = 5/18. So 36 km/h = 36 x 5/18 = 10 m/s.

Q: What's the difference between a ratio and a rate?

A ratio compares two quantities with the same units (3 boys to 5 girls). A rate compares two quantities with different units (50 km in 2 hours). The arithmetic looks similar but the interpretation differs.

Q: What real-world problems use rates in Year 8?

Speed, density, currency exchange, fuel consumption, water flow, and unit pricing for shopping comparisons. These worksheets pull from a mix so students get fluent across contexts.

Speed, density, unit pricing - the everyday rate problems.

Quick answer

What are rates and how do you use them to solve problems?

A rate compares two quantities with different units, such as km/h, $/kg or people/km². To solve rate problems, write the rate as a fraction and multiply or divide to find the missing quantity. For example, at 60 km/h for 2.5 hours, distance = 60 × 2.5 = 150 km.

Generate a free maths worksheet

Six questions across Foundation, Standard and Extension, with full worked solutions, written to the Australian Curriculum.

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Worked examples

Year 8 rates: worked examples

Three examples, from a standard question to a worded problem. Have a go at each one before you open the solution.

Example 1 · Finding speed using distance and time
A cyclist travels 72 km in 3 hours. Find the cyclist's average speed in km/h.
Show worked solution
Key idea: Speed is a rate that compares distance to time. Use $\text{speed} = \dfrac{\text{distance}}{\text{time}}$ .
1. Write the formula: $\text{speed} = \frac{\text{distance}}{\text{time}}$
2. Substitute the known values: $\text{speed} = \frac{72}{3}$
3. Calculate: $\text{speed} = 24 \text{ km/h}$
4. Check: $24 \times 3 = 72$ km. ✓
Answer: The cyclist's average speed is 24 km/h.
Example 2 · Best-buy comparison using unit pricing
Orange juice is sold in two sizes. A 600 mL bottle costs $3.00 and a 1.5 L bottle costs $6.60. Which size is the better buy?
Show worked solution
Key idea: Convert both options to the same unit, then find the cost per millilitre (unit price) for each. The lower unit price is the better buy.
1. Convert 1.5 L to millilitres: $1.5 \text{ L} = 1500 \text{ mL}$
2. Unit price of the 600 mL bottle: $\frac{300}{600} = 0.50 \text{ cents/mL}$
3. Unit price of the 1500 mL bottle: $\frac{660}{1500} = 0.44 \text{ cents/mL}$
4. Compare: $0.44 < 0.50$ , so the 1.5 L bottle has the lower unit price.
Answer: The 1.5 L bottle is the better buy at 0.44 cents/mL.
Example 3 · Multi-step rate problem: road trip fuel cost
Priya drives from Melbourne to Ballarat, a distance of 112 km. Her car uses fuel at a rate of 8 litres per 100 km. Petrol costs $2.10 per litre. How much does the petrol for this trip cost in total?
Show worked solution
Key idea: Use the fuel rate to find the total litres used, then use the price rate to find the total cost.
1. Find the fuel used for 112 km using the rate of 8 litres per 100 km: $\text{fuel} = \frac{8}{100} \times 112 = 8.96 \text{ litres}$
2. Find the total cost using 210 cents per litre (keeping numbers as plain amounts): $\text{cost} = 8.96 \times 2.10 = 18.816$
3. Round to the nearest cent: $18.816 \approx 18.82$
Answer: The petrol for the trip costs $18.82.

Common mistakes

Where students usually lose marks

Dividing in the wrong order for speed

Speed $= \dfrac{\text{time}}{\text{distance}} = \dfrac{3}{72} = 0.04\overline{1}$ km/h

Always divide distance by time, not the other way around. Check that your answer is a reasonable speed: 0.04 km/h for a cyclist makes no sense.

Comparing prices without matching units

Comparing $3.00 for 600 mL directly with $6.60 for 1.5 L and concluding the cheaper price means the better buy.

You must find the price for the same amount (such as per mL or per 100 mL) before comparing. Convert all quantities to the same unit first.

Forgetting to convert units before calculating a rate

Converting km/h to m/s by dividing only by 3600, giving $72 \div 3600 = 0.02$ m/s instead of 20 m/s.

To convert km/h to m/s, multiply by 1000 (km to m) and divide by 3600 (hours to seconds): $\frac{\times 1000}{\div 3600} = \times \frac{1000}{3600} = \times \frac{5}{18}$

Using the wrong operation in a multi-step rate problem

Adding the fuel rate and the distance instead of multiplying: $8 + 112 = 120$ litres.

Read what each rate means carefully. 'Litres per 100 km' means you multiply the rate by the number of hundreds of kilometres travelled: $\dfrac{8}{100} \times 112$ .

Try one yourself

Your turn

A 750 g box of cereal costs $4.50 and a 1.2 kg box of the same cereal costs $6.96. What is the unit price of the cheaper box in cents per 100 g? Give your answer in cents per 100 g, correct to 1 decimal place.

Got a different rates question wrong? Upload it to Tuterly and get the worked solution and a fresh one to practise, free.

About this worksheet

Why we built it

Rates are the secret backbone of physics, chemistry and even senior economics. Year 8 introduces them properly - distance/time, unit price, density. These worksheets give your student practice setting up the right ratio every time, then converting units cleanly.

What's covered

Sub-skills your student will practise

✓Speed = distance / time problems
✓Unit pricing and best-buy comparisons
✓Density and similar rate-based quantities
✓Converting between rate units (km/h to m/s, $/kg to $/g)
✓Multi-step word problems involving rates

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Frequently asked

Questions parents ask about rates

What's a rate in maths?