Concept Overview
Proportion explains how two quantities change together.
In direct proportion, both quantities increase or decrease together.
Direct & Inverse Proportion explained through a friendly whiteboard conversation, examples, visuals, and practice for school students.
Step 1
Notes
Step 2
Formulae
Step 3
Examples
Step 4
Practice
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Proportion explains how two quantities change together.
In direct proportion, both quantities increase or decrease together.
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A proportion is a statement that two ratios are equal.
Direct proportion means the ratio between two quantities stays constant. If notebooks double, total cost also doubles when each notebook has the same price.
Inverse proportion means the product of two quantities stays constant. If more workers do the same job, the time usually decreases.
The most important step is to decide whether the situation is direct or inverse before calculating.
Meaning: A ratio compares quantities. A proportion says two ratios are equal.
Definition: a::d means .
If 2 pens cost Rs 20 and 4 pens cost Rs 40, the ratios 2:20 and 4:40 show the same rate.
Meaning: Two quantities move in the same direction at a constant rate.
Definition: y is directly proportional to x if is constant.
If one pencil costs Rs 5, more pencils cost more money in the same ratio.
Meaning: One quantity increases while the other decreases.
Definition: y is inversely proportional to x if xy is constant.
If 4 workers finish a job faster than 2 workers, number of workers and time are inversely related when the work is fixed.
Meaning: The situation decides the method.
Definition: Direct means same direction. Inverse means opposite direction.
Cost and quantity are usually direct. Workers and time for fixed work are usually inverse.
Easy
Question: If 3 pencils cost Rs 24, find the cost of 6 pencils.
Medium
Question: y is directly proportional to x. If when , find y when .
Exam-level
Question: 6 workers finish a job in 12 days. How many days will 9 workers take for the same job?
Treating every proportion as direct
Why it happens: Direct proportion is learned first.
Correct approach: Ask whether both quantities move in the same direction.
Forgetting to find k
Why it happens: Students try to jump to the final answer.
Correct approach: Find the constant from the given pair first.
Mixing units
Why it happens: The numbers are copied without labels.
Correct approach: Convert units before forming ratios.
How do I know if it is direct?
If one quantity doubles and the other also doubles, it is direct proportion.
How do I know if it is inverse?
If one quantity doubles and the other becomes half, it is inverse proportion.
Is proportion the same as ratio?
No. A ratio compares quantities. A proportion says two ratios are equal.
Practise the same concept from this article. Your student profile may guide entitlement and follop recommendations, but it does not replace this concept.