Directly Proportional and Inversely Proportional
Directly proportional means two amounts rise at the same rate, so doubling one doubles the other. For example, if 1 watermelon costs £4, then 2 cost £8. Inversely proportional is the opposite: doubling one halves the other.
Video Lesson
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Flashcards
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What Is Direct Proportionality?
- In direct proportion, doubling one value will double the other.
- If 1 watermelon costs £4, then 2 cost £8 and 4 cost £16.
What Is Inverse Proportionality?
- In inverse proportion, doubling one value will halve the other.
- For a task, 15 people take 2 hours, but 30 people only take 1 hour.
Spotting the Difference Quickly
- In direct proportion, the unit rate stays the same.
- In inverse proportion, the product of the two quantities stays the same.
Practice Questions
Test your understanding
At a supermarket, 3 watermelons cost £12 in total. How much would 7 watermelons cost if each watermelon costs the same?
Correct! 🎉 +10 pointsNot quite right
The cost of one watermelon is £ £4. For 7 watermelons, the total cost is 7 × £ £28.
A factory task takes 5 workers 6 hours to complete. How many hours will it take if 10 workers are available?
Correct! 🎉 +10 pointsNot quite right
The task requires a constant 30 work hours. With 10 workers, the time required is hours.
A construction job requires 8 workers and 15 days to complete. How many days would it take if only 5 workers are available?
Correct! 🎉 +20 pointsNot quite right
The task requires a constant work days. With 5 workers, the time required is days.
A train covers in 6 hours. How much time will it take to cover at the same speed?
Correct! 🎉 +20 pointsNot quite right
The speed of the train is . To cover , the time required is hours.
A car consumes 12 litres of fuel to travel . How far can the car travel with 18 litres of fuel?
Correct! 🎉 +20 pointsNot quite right
The car’s fuel efficiency is litre. With 18 litres of fuel, the car can travel .
A project requires 16 workers to complete in 12 days. How many more workers would be required to complete the project in 8 days?
Correct! 🎉 +30 pointsNot quite right
The task requires a constant worker-days. To complete it in 8 days, the total number of workers needed is . Subtracting the 16 workers already there, .
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Interactive Activity
Adjust the constant k to see how direct and inverse proportion affect a data table
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Students Also Ask
The questions students bump into most on this topic
The difference lies in how the two quantities change together. In direct proportion they change at the same rate, so doubling one doubles the other. In inverse proportion they change in opposite directions, so doubling one halves the other and their product stays the same.
Use the doubling test. If doubling one quantity doubles the other, the relationship is directly proportional. If doubling one quantity halves the other, it is inversely proportional. Checking this first is important, because it tells you which method to use to solve the question.
Find the unit rate first, which is the value of one item. Then multiply that unit rate by the quantity you need. For example, if 3 watermelons cost £12, then one watermelon costs £4. So 5 watermelons would cost £20 in total.
Find the constant product by multiplying the pair you know. Then divide it by the new quantity to find the missing value. For example, 5 workers take 6 hours, so the product is 30. This means 3 workers need 10 hours.
Buying watermelons is a direct proportion example, because the total cost rises at the same rate as the number you buy. A factory task is an inverse proportion example, because more workers means fewer hours, while the total work hours stay the same.