Direct Proportion
When one quantity doubles, the other doubles too.
Key idea
When one quantity doubles, the other doubles too.
In depth
In direct proportion, y = kx: when x doubles, y doubles. The ratio y/x stays constant. Its graph is a straight line through the origin.
Worked example
If 5 kg of rice cost 15, then k = 3 per kg and 8 kg costs 24.
Formula
Real-world uses
- Calculating how much paint covers a bigger wall
- Cost of petrol for a longer trip at a fixed price per litre
Common mistake
Calling any increasing relationship direct. A line that does not pass through the origin is not direct proportion.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Direct Proportion?
When one quantity doubles, the other doubles too. It is a topic at the intermediate level in Arithmetic & Number Sense.
What is the formula for Direct Proportion?
The key formula is y = kx.
Where is Direct Proportion used in real life?
Real-world examples: Calculating how much paint covers a bigger wall; Cost of petrol for a longer trip at a fixed price per litre.
What should I learn before Direct Proportion?
Make sure you are comfortable with Rates and Unit Rates, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Direct Proportion?
Calling any increasing relationship direct. A line that does not pass through the origin is not direct proportion.
How can I practise Direct Proportion?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Direct Proportion?
Move on to Inverse Proportion next.
Related intermediate topics in Arithmetic & Number Sense
- Long Multiplication – Multiply by each digit of the multiplier, shift by place value, then add partial products.
- Long Division – Divide, multiply, subtract and bring down repeatedly to get the quotient.
- Factors and Multiples – Factors divide a number exactly; multiples are its products with whole numbers.
- Divisibility Rules – Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
- Prime Numbers – A prime has exactly two positive divisors: 1 and itself.
- Composite Numbers – Numbers greater than 1 with more than two factors.