Ratio, proportion and rate
Cambridge IGCSE Mathematics (0580) · Unit 1: Number · 18 flashcards
Ratio, proportion and rate is topic 1.5 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 1 — Number , alongside Types of number, Fractions, decimals and percentages and Operations and order of operations. In one line: A rate is a ratio that compares two quantities with different units.
This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator.
The deck below contains 18 flashcards — 2 definitions, 2 key concepts and 1 application card — covering the precise wording mark schemes reward. Use the 2 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.
'rate' and give an example
A rate is a ratio that compares two quantities with different units.
Questions this Ratio, proportion and rate deck will help you answer
- › Explain how to determine the 'best buy' when comparing prices of different sized items.
- › A map has a scale of 1:50000. What real-world distance, in kilometers, is represented by 4 cm on the map?
- › What is the difference between direct proportion and inverse proportion?
Simplify the ratio 24:36:18.
Find the greatest common factor (GCF) of the numbers. The GCF of 24, 36, and 18 is 6. Divide each number by the GCF: 24/6 : 36/6 : 18/6 = 4:6:3. Therefore, the simplified ratio is 4:6:3.
Divide £420 in the ratio 2:3:7.
Add the ratio numbers: 2+3+7 = 12. Divide the total amount by the sum: £420 / 12 = £35. Multiply each ratio number by this value: 2*£35 : 3*£35 : 7*£35 = £70 : £105 : £245. The amounts are £70, £105, and £245.
If y is directly proportional to x, and y=10 when x=2, find y when x=5.
Direct proportion means y = kx, where k is a constant. First find k: 10 = k * 2, so k = 5. Now find y when x=5: y = 5 * 5 = 25. Therefore, y = 25.
If y is inversely proportional to x, and y=6 when x=4, find y when x=3.
Inverse proportion means y = k/x, where k is a constant. First find k: 6 = k / 4, so k = 24. Now find y when x=3: y = 24 / 3 = 8. Therefore, y = 8.
Define 'rate' and give an example.
A rate is a ratio that compares two quantities with different units.
A car travels 150 km in 2 hours. Calculate its average speed.
Speed is calculated as distance divided by time. Speed = 150 km / 2 hours = 75 km/h. Therefore, the average speed of the car is 75 km/h.
Explain how to determine the 'best buy' when comparing prices of different sized items.
Calculate the unit price for each item (price per unit of measure,
A map has a scale of 1:50000. What real-world distance, in kilometers, is represented by 4 cm on the map?
1 cm on the map represents 50000 cm in reality. So 4 cm represents 4 * 50000 cm = 200000 cm. Convert cm to km: 200000 cm = 2000 m = 2 km. Therefore, 4 cm on the map represents 2 km in reality.
Define 'proportion'.
A proportion is a statement that two ratios are equal. It is often used to solve problems where one quantity changes in relation to another, maintaining a constant relationship.
Convert 500 US dollars to British pounds (£) if the exchange rate is £1 = $1.25.
To convert USD to GBP, divide the USD amount by the exchange rate. £ = $500 / $1.25 = £400. Therefore, $500 is equivalent to £400.
Divide 240 in the ratio 3:5. Show your working.
Total parts = 3 + 5 = 8
Value of one part = 240 ÷ 8 = 30
First share = 3 × 30 = 90
Second share = 5 × 30 = 150
Check: 90 + 150 = 240 ✓
Method: always find the total number of parts first, then divide.
A map has a scale of 1:25000. Two towns are 8 cm apart on the map. What is the actual distance in kilometres?
Map distance = 8 cm
Scale = 1:25000, so actual = 8 × 25000 = 200,000 cm
Convert to km: 200,000 ÷ 100,000 = 2 km
Alternatively: 200,000 cm → 2000 m → 2 km
Remember: to convert cm to km, divide by 100,000 (or divide by 100 for metres, then by 1000 for km).
If y is directly proportional to x, and y = 12 when x = 4, find y when x = 7.
Direct proportion means y = kx (where k is a constant).
Find k: 12 = k × 4, so k = 3
Now find y when x = 7:
y = 3 × 7 = 21
Alternatively: y/x is constant, so y/7 = 12/4, giving y = 7 × 3 = 21.
If y is inversely proportional to x², and y = 8 when x = 3, find y when x = 6.
Inverse proportion with x² means y = k/x²
Find k: 8 = k/3² = k/9, so k = 72
Now find y when x = 6:
y = 72/6² = 72/36 = 2
Note: when x doubles from 3 to 6, y decreases by a factor of 4 (not 2) because y is inversely proportional to x² (squared).
A car travels 180 km in 2.5 hours. Calculate its average speed.
Speed = distance / time
Speed = 180 / 2.5 = 72 km/h
Alternatively: 2.5 hours = 2 hours 30 minutes. In 2 hours the car covers 144 km, then in 0.5 hours it covers 36 km, totalling 180 km at 72 km/h.
Remember: average speed uses total distance ÷ total time, not the average of different speeds.
The exchange rate is 1 euro = 1.18 US dollars. Convert 350 euros to US dollars.
350 euros × 1.18 = 413 US dollars
To go from euros to dollars, multiply by 1.18.
To go from dollars to euros, divide by 1.18.
Tip: always check your answer makes sense. Since 1 euro > 1 dollar, the number of dollars should be larger than the number of euros.
A recipe for 6 people uses 450 g of flour. How much flour is needed for 10 people?
Method (unitary method):
Flour for 1 person = 450 ÷ 6 = 75 g
Flour for 10 people = 75 × 10 = 750 g
Alternatively (ratio method):
6 people : 450 g = 10 people : x g
x = (10/6) × 450 = 750 g
The unitary method (find the value for 1, then multiply) works for all proportion questions.
What is the difference between direct proportion and inverse proportion?
Direct proportion: as one quantity increases, the other increases at the same rate. y = kx. Graph is a straight line through the origin.
Key Questions: Ratio, proportion and rate
Define 'rate' and give an example.
A rate is a ratio that compares two quantities with different units.
Define 'proportion'.
A proportion is a statement that two ratios are equal. It is often used to solve problems where one quantity changes in relation to another, maintaining a constant relationship.
Tips to avoid common mistakes in Ratio, proportion and rate
- ● Before solving, identify the type of proportionality (direct or inverse) and use the corresponding formula.
- ● Before diving into complex calculations, carefully reread the question to catch any direct relationships.
- ● Before applying a ratio, make sure you understand which quantity corresponds to each part of the ratio.
More topics in Unit 1 — Number
Ratio, proportion and rate sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.
Cambridge syllabus keywords to use in your answers
These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.
Key terms covered in this Ratio, proportion and rate deck
Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.
Related Mathematics guides
Long-read articles that go beyond the deck — cover the whole subject's common mistakes, high-yield content and revision pacing.
How to study this Ratio, proportion and rate deck
Start in Study Mode, attempt each card before flipping, then rate Hard, Okay or Easy. Cards you rate Hard come back within a day; cards you rate Easy push out to weeks. Your progress is saved in your browser, so come back daily for 5–10 minute reviews until every card reads Mastered.
Study Mode
Space to flip • ←→ to navigate • Esc to close
You're on a roll!
You've viewed 10 topics today
Create a free account to unlock unlimited access to all revision notes, flashcards, and study materials.
You're all set!
Enjoy unlimited access to all study materials.
Something went wrong. Please try again.
What you'll get:
- Unlimited revision notes & flashcards
- Track your study progress
- No spam, just study updates