Rule of Three Calculator
Usage Instructions:
Objective: Calculate the unknown value X based on the Rule of Three, where Value A corresponds to Value B, and Value C corresponds to X.
Steps:
- Enter Value A: Input the first known value (A).
- Enter Value B: Input the second known value (B) that corresponds to A.
- Enter Value C: Input the known value (C) that corresponds to X.
- Click the "Calculate X" Button: After entering all values, click the "Calculate X" button to get the unknown value X.
- View the Result: The calculated value X will be displayed in the results section.
The Rule of Three is a mathematical principle used to solve problems involving proportions. It helps find an unknown value when three values are known and they are in a proportional relationship. Here’s a detailed guide on how to use the Rule of Three:
What is the Rule of Three?
The Rule of Three is based on the concept of direct or inverse proportionality. If three quantities are known, you can find the fourth quantity if the quantities are proportional.
Types of Proportionality:
- Direct Proportionality:
- When two quantities increase or decrease together.
- Example: If 5 apples cost $10, how much would 8 apples cost?
- Inverse Proportionality:
- When one quantity increases as the other decreases.
- Example: If 4 workers can complete a task in 6 days, how many days will it take 6 workers to complete the same task?
How to Use the Rule of Three
1. Direct Proportionality
- Formula:
- (Value 1 / Value 2) = (Value 3 / Value 4)
- Steps:
- Set up the proportion using the known values.
- Cross-multiply to solve for the unknown value.
- Example Calculation:
- Problem: If 5 apples cost $10, how much do 8 apples cost?
- Setup:
- 5 apples / $10 = 8 apples / X dollars
- Solve:
- (5 × X) = (8 × 10)
- 5X = 80
- X = 16
- Answer: 8 apples cost $16.
2. Inverse Proportionality
- Formula:
- (Value 1 × Value 2) = (Value 3 × Value 4)
- Steps:
- Set up the inverse proportion using the known values.
- Solve for the unknown value.
- Example Calculation:
- Problem: If 4 workers can complete a task in 6 days, how many days will it take 6 workers?
- Setup:
- 4 workers × 6 days = 6 workers × X days
- Solve:
- 24 = 6X
- X = 4
- Answer: It will take 6 workers 4 days to complete the task.
Quick Reference Table
Here’s a table showing how the Rule of Three applies to different scenarios:
| Known Values | Unknown Value Calculation | Example Result |
|---|---|---|
| 5 apples, $10 | 8 apples / X dollars | $16 |
| 4 workers, 6 days | 6 workers / X days | 4 days |
| 10 liters, $30 | 15 liters / X dollars | $45 |
| 2 machines, 5 hours | 3 machines / X hours | 3.33 hours |
Why Use the Rule of Three?
- Problem Solving: Quickly solves problems involving proportions in various fields such as finance, engineering, and everyday tasks.
- Practical Applications: Useful for budgeting, scaling recipes, adjusting project timelines, and more.
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