Year 8 Ratios and rates: free practice test with answers

Sample ratios and rates questions with answers

Try each one before you open the answer.

1. Simplifying ratios

   Simplify the ratio $45 : 60$.

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   Key idea: Divide both parts of the ratio by their highest common factor.

   1. The HCF of $45$ and $60$ is $15$
   2. $45 \div 15 : 60 \div 15 = 3 : 4$

   Answer: $3 : 4$

2. Solving ratio problems

   In a jar, the ratio of red jelly beans to green jelly beans is $3 : 5$. There are $24$ red jelly beans. How many green jelly beans are there?

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   Key idea: Find the value of one part, then multiply by the number of parts needed.

   1. $3$ parts $= 24$, so $1$ part $= 24 \div 3 = 8$.
   2. Green is $5$ parts: $5 \times 8 = 40$.

   Answer: $40$

3. Scale drawings

   A house plan has a scale of $1 : 200$. A wall is $4.5$ cm long on the plan. How long is the actual wall, in metres?

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   Key idea: A scale of $1 : 200$ means every length in real life is $200$ times the length on the plan.

   1. $4.5 \times 200 = 900$ cm
   2. $900$ cm $= 9$ m

   Answer: $9$ m

4. Introducing rates

   A car uses $45$ L of petrol to travel $540$ km. Find the rate of travel in kilometres per litre.

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   Key idea: A rate compares two different quantities; divide to find the amount per one unit.

   1. Kilometres per litre $= 540 \div 45$.
   2. $540 \div 45 = 12$ km/L.

   Answer: $12$ km/L

5. Solving rate problems

   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?

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   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.

6. Speed

   A cyclist travels 72 km in 3 hours. Find the cyclist's average speed in km/h.

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   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.

7. Ratios and rates and the unitary method

   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?

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   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.

Free worksheets for this chapter

Worked examples and a free PDF with answers for each topic.

• Year 8 speed, distance and time worksheet
• Year 8 rates worksheet
• Year 8 linear relations in real-life problems worksheet
• Year 8 time and time zones worksheet