Inverse Proportion
When one quantity doubles, the other halves.
Key idea
When one quantity doubles, the other halves.
In depth
In inverse proportion, y = k/x: when one quantity doubles, the other halves, and the product xy stays constant. It models sharing a fixed total.
Worked example
6 workers finish in 10 days, so 60 worker-days of work in total. With 15 workers: 60 ÷ 15 = 4 days.
Formula
Real-world uses
- Working out how long a job takes with more workers
- Choosing gear ratios and the speed-time trade-off
Common mistake
Treating it as direct and multiplying instead of dividing.
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 Inverse Proportion?
When one quantity doubles, the other halves. It is a topic at the advanced level in Arithmetic & Number Sense.
What is the formula for Inverse Proportion?
The key formula is y = k/x.
Where is Inverse Proportion used in real life?
Real-world examples: Working out how long a job takes with more workers; Choosing gear ratios and the speed-time trade-off.
What should I learn before Inverse Proportion?
Make sure you are comfortable with Direct Proportion, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Inverse Proportion?
Treating it as direct and multiplying instead of dividing.
How can I practise Inverse 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 Inverse Proportion?
Move on to Scale Factor and Maps next.
Related advanced topics in Arithmetic & Number Sense
- Repeating Decimals – Decimals with a repeating block are rational and convertible to fractions.
- Compound Interest – Interest earned on principal and past interest.
- Rational Numbers – Numbers expressible as p/q with integers p, q, q≠0.
- Irrational Numbers – Real numbers that cannot be written as a fraction, such as √2 and π.
- Real Numbers – All rational and irrational numbers; the continuous number line.
- Square Roots of Non-squares – Approximate or simplify surds like √50 = 5√2.