Ratios and Rates Practice Test
Build confidence one level at a time. Start with ratio foundations, then progress through simplifying, sharing quantities, unit rates, speed conversions and challenging mixed problems.
- 8 progressive levels
- 67 original questions
- Instant answer checks
- Hints and full working
Your answers and checked results are saved automatically in this browser.
Level 1
Ratio Foundations and Equivalent Ratios
0/8
Level 2
Simplifying Ratios and Converting Units
0/8
Level 3
Dividing Quantities in a Given Ratio
0/8
Level 4
Scale, Proportion and Ratio Applications
0/8
Level 5
Unit Rates Practice
0/8
Level 6
Rate Word Problems and the Unitary Method
0/8
Level 7
Speed and Rate Conversions
0/10
Level 8
Challenging Ratios and Rates Problems
0/9
How to Solve Ratios and Rates
Ratios and rates become much easier when you use a consistent method. Instead of memorising a different rule for every question, first identify what is being compared, make the units suitable, find the value of one part or one unit, and then scale that value to the amount required.
This article explains that strategy through clear examples, including simplifying ratios, dividing quantities, solving unit-rate problems, working with speed and converting between units such as kilometres per hour and metres per second.
Ratio and Rate: What Is the Difference?
A ratio compares the relative sizes of two or more quantities. For example, a ratio of red marbles to blue marbles of 3:5 means that for every 3 red marbles, there are 5 blue marbles.
A rate also compares quantities, but the quantities usually have different units. Examples include 60 kilometres per hour, $4.50 per kilogram and 20 pages per minute.
| Ratio | Rate |
|---|---|
| Compares relative quantities | Compares quantities using different units |
| Examples: 3:5, 2:7:9 | Examples: 60 km/h, $8/kg, 12 L/min |
| Find the value of one part | Find the value for one unit |
The Five-Step Method
- Identify the quantities. Decide exactly what is being compared.
- Keep the correct order. A ratio of cats to dogs is written cats:dogs, not dogs:cats.
- Make the units consistent. Convert metres to centimetres, hours to minutes or kilograms to grams when needed.
- Find one part or one unit. Divide by the known number of parts or units.
- Scale and check. Multiply to find the required amount, then check the order, units and total.
Important: The word per means “for each” and usually tells you to divide. For example, kilometres per hour means kilometres divided by hours.
How to Simplify Ratios
To simplify a ratio, divide every term by the same common factor. Before doing this, make sure all quantities are written in the same unit.
Example 1: Simplifying a whole-number ratio
Simplify 18:24.
18 ÷ 6 : 24 ÷ 6
= 3:4
Answer: 3:4
Example 2: Convert the units first
Simplify 1 metre : 40 centimetres.
100:40
Divide both terms by 20
= 5:2
Answer: 5:2
Common mistake: Do not write 1 m : 40 cm as 1:40. The units are different, so the quantities must be converted before the ratio is simplified.
How to Find Equivalent Ratios
Equivalent ratios describe the same comparison. To create one, multiply or divide every term by the same number.
Example: Finding a missing value
Complete the equivalent ratio 5:8 = 20:x.
Therefore, 8 × 4 = 32
x = 32
Answer: 5:8 = 20:32
Equivalent ratios are formed by multiplication or division. Adding the same number to both terms does not preserve the ratio.
How to Divide a Quantity in a Ratio
When a total amount is divided in a ratio, add the ratio parts first. This tells you how many equal parts make up the whole amount.
Example: Divide $420 in the ratio 2:3:5
Value of one part = $420 ÷ 10 = $42
First share = 2 × $42 = $84
Second share = 3 × $42 = $126
Third share = 5 × $42 = $210
Answer: $84, $126 and $210
Check: $84 + $126 + $210 = $420. The shares must add back to the original total.
When One Quantity Is Known
Do not add the ratio parts automatically. First decide what the known number represents.
Example: One side of the ratio is given
The ratio of boys to girls is 3:5. There are 40 girls. How many boys are there?
1 part = 40 ÷ 5 = 8
Boys = 3 parts
3 × 8 = 24
Answer: 24 boys
Here, 40 represents only the girls, so it corresponds to 5 parts. You would add 3 + 5 only if the question gave the total number of students.
When the Difference Is Known
If the difference between two quantities is given, find the difference between their ratio parts first.
Example: Two numbers are in the ratio 5:8 and differ by 21
3 parts = 21
1 part = 21 ÷ 3 = 7
First number = 5 × 7 = 35
Second number = 8 × 7 = 56
Answer: 35 and 56
Always ask whether the given amount represents the total, one quantity or the difference. That decision determines the correct method.
How to Solve Rate Problems
The most reliable method for rates is the unitary method. Find the amount for one unit, then multiply by the number of units required.
Example 1: Find a unit rate
A vehicle travels 360 kilometres in 8 hours. Find its average speed.
360 ÷ 8 = 45
Answer: 45 km/h
Example 2: Use the unit rate
At 45 km/h, how far will the vehicle travel in 5 hours?
45 × 5 = 225
Answer: 225 km
Example 3: Find the time
A machine produces 24 items per minute. How long will it take to produce 600 items?
600 ÷ 24 = 25
Answer: 25 minutes
Quick decision: To find a total amount, multiply by the rate. To find the number of units or the time taken, divide by the rate.
Speed, Distance and Time
Speed = Distance ÷ Time Distance = Speed × Time Time = Distance ÷ SpeedThe units must match before using these formulas. If the speed is measured in kilometres per hour, the time must be written in hours.
Example: Time must be converted first
An aircraft travels at 720 km/h for 20 minutes. Find the distance travelled.
Distance = 720 × 1/3
= 240 km
Answer: 240 km
Converting Kilometres per Hour and Metres per Second
Use the facts that 1 kilometre equals 1000 metres and 1 hour equals 3600 seconds.
km/h ÷ 3.6 = m/s m/s × 3.6 = km/hExample 1: Convert 72 km/h to m/s
Answer: 20 m/s
Example 2: Convert 15 m/s to km/h
Answer: 54 km/h
Converting Other Rates
For other rate conversions, convert the top and bottom units separately. Keep the units visible so that they guide the calculation.
Example 1: Convert 3 L/min to mL/s
1 minute = 60 seconds
3000 ÷ 60 = 50
Answer: 50 mL/s
Example 2: Convert 250 m/min to km/h
15,000 ÷ 1000 = 15 km/h
Answer: 15 km/h
How to Solve Scale Problems
A scale ratio is usually written as drawing length : actual length. Both sides must first be interpreted using the same unit.
Example: Map scale
A map has a scale of 1:50,000. Two locations are 4 cm apart on the map. Find the actual distance.
= 200,000 cm
= 2000 m
= 2 km
Answer: 2 km
Common Mistakes
Reversing the ratio: 3:5 is not the same as 5:3. Follow the order stated in the question.
Using different units: Convert the quantities before simplifying or comparing them.
Changing only one term: Every ratio term must be multiplied or divided by the same number.
Adding the parts at the wrong time: Add the parts when a total is being shared, not whenever you see a ratio.
Reversing a rate: Kilometres per litre means kilometres divided by litres.
Ignoring time conversions: A rate per hour requires time in hours.
Leaving out units: A rate answer is incomplete without its unit.
Final Problem-Solving Checklist
- What quantities are being compared?
- What order should they be written in?
- Do the units need to be converted?
- Does the known amount represent the total, one part or a difference?
- Can I find one part or one unit first?
- Should I multiply or divide next?
- Does the answer have the correct unit?
- Can I check it against the original information?
The Strategy to Remember
Understand the comparison → match the units → find one part or one unit → scale to the required amount → check the answer.
Once this process becomes familiar, ratio and rate problems stop feeling like separate rules. They become a sequence of small, logical steps that can be used for simple questions, word problems, speed calculations, scale drawings and unit conversions.
