Unitary Method Calculator
Solve proportion and ratio problems with step-by-step solutions. Supports direct and inverse proportion.
If 5 Items → 100 Cost (₹), then 8 Items → ?
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What is the Unitary Method?
The unitary method is a fundamental math technique used to solve problems involving proportional relationships. The idea is simple: find the value of one unit first, then calculate for any number of units.
Direct Proportion
More → More
Example: If 5 notebooks cost ₹150
Step 1: 1 notebook = ₹150 ÷ 5 = ₹30
Step 2: 8 notebooks = ₹30 × 8 = ₹240
Inverse Proportion
More → Less
Example: If 6 workers finish a job in 12 days
Step 1: Total work = 6 × 12 = 72 worker-days
Step 2: 9 workers = 72 ÷ 9 = 8 days
How to Use This Calculator
- Choose Unitary Method or Ratio & Proportion tab
- For unitary method: select direct or inverse proportion
- Enter the known quantity, its value, and the target quantity
- Click "Calculate" to see the answer with step-by-step working
- Try the preset examples to understand different problem types
Tip for Students
Use the step-by-step solution to understand the working. Always ask yourself: "If I increase one quantity, does the other increase (direct) or decrease (inverse)?"
Frequently Asked Questions
What is the unitary method?
The unitary method is a mathematical technique where you first find the value of a single unit, then use it to find the value of any number of units. For example: if 5 pens cost ₹50, then 1 pen costs ₹10 (unitary value), so 8 pens cost ₹80.
What is the difference between direct and inverse proportion?
In direct proportion, when one quantity increases the other also increases (e.g. more items → more cost). In inverse proportion, when one quantity increases the other decreases (e.g. more workers → fewer days to complete a task).
How do you solve a ratio proportion problem?
Use cross multiplication. If A:B = C:D, then A × D = B × C. If you know three values, you can find the fourth by rearranging: D = (B × C) / A or C = (A × D) / B.
Where is the unitary method used in daily life?
The unitary method is used everywhere: calculating prices while shopping, recipe scaling, fuel consumption, work-time problems, speed-distance calculations, currency conversion, and many more real-life situations.
How to identify if a problem is direct or inverse proportion?
Ask: "If I increase one quantity, does the other increase too?" If yes, it is direct proportion. If the other decreases, it is inverse. Example: More speed → Less time (inverse). More quantity → More cost (direct).