Lesson 11.3 · 25 min
Inverse Proportion
When one quantity goes up the other goes down in step: the product stays the same.
In this lesson you will learn to…
- Recognise when two quantities are inversely proportional
- Solve problems by finding the constant product
- Write the relationship as or
- Tell direct and inverse proportion apart
Why this matters
More workers finish a job sooner. A faster car makes the same journey in less time. Wider buckets fill a tank in fewer trips. These are all inverse proportion — and the same one-line method solves every one.
Direct or inverse?
| Situation | Type |
|---|---|
| 6 taps fill a tank in 20 minutes | inverse — more taps, less time |
| 30 pounds = 41.70 dollars | direct — more pounds, more dollars |
| 4 friends clean a house in 1 hour | inverse |
| Rectangles with the same area: length and width | inverse — is constant |
Check the direction. Before calculating, ask: should the answer be bigger or smaller? 4 builders instead of 10 must take longer, so 15 days is sensible; 2.4 days is not.
Two changes at once
10 minutes to fill a 200-litre tank with 4 taps; how long for 500 litres with 2 taps? Change one thing at a time. With 4 taps, 500 litres takes minutes (direct). With 2 taps it takes twice as long: 50 minutes (inverse).
Key rules and formulas
Inverse proportion
Two quantities are inversely proportional if, when one is doubled, the other is halved (when one is tripled, the other is divided by 3).The product is constant
10 builders take 6 days: that is builder-days of work, whoever does it.Method
Multiply the two known values to find the total amount of "work", then divide by the new value.
Worked examples
Builders
Try it yourself first, then reveal the solution one step at a time.
Speed and time
Try it yourself first, then reveal the solution one step at a time.
A formula
Try it yourself first, then reveal the solution one step at a time.
Practice: inverse proportion
9 questions
Question 1 of 9Type the answerFoundation It takes 10 builders 6 days to build a wall. How long would 4 builders take?daysQuestion 2 of 9Match the pairs Is each pair directly or inversely proportional?Pick an answer, then choose the row it belongs to. You can also drag it.
- Number of taps and time to fill a tank
- English pounds and US dollars
- Number of friends and time to clean a house
- Laps run and total time at a steady pace
Question 3 of 9Type the answer It takes 8 machines 6 minutes to complete a job. How long will it take 12 machines?minutesQuestion 4 of 9Type the answer It takes 15 buckets of 4 litres to fill a fish tank. How many 6-litre buckets are needed?Question 5 of 9Type the answer Sanjay travels at 50 km/h for 30 minutes. How many minutes would the same journey take at 75 km/h?minutesQuestion 6 of 9Complete the table is inversely proportional to . When , . Complete the table.m b 20 36 5 60 Question 7 of 9Multiple choice Which equation shows inverse proportion between and ?Question 8 of 9Type the answer is inversely proportional to . When , . Find when .Question 9 of 9Step by stepChallenge Two changes at once.It takes 10 minutes to fill a 200-litre tank using 4 taps. How long would it take to fill a 500-litre tank using 2 taps?- With 4 taps, how long does 500 litres take? (direct proportion)minutes