What is the Rule of Three?
The Rule of Three is a mathematical method used to solve problems involving
proportional quantities. With it, you can find an unknown value
when three related values are known.
It is one of the most important techniques in basic mathematics, widely applied
in daily life for proportion, comparison, and estimation calculations.
Whenever there is a direct or inverse relationship between values—such as price, quantity,
time, distance, or output—the Rule of Three can be applied.
What is the Rule of Three used for?
The Rule of Three is used to calculate proportional values quickly, logically, and accurately,
and is applied in everyday, academic, and professional situations.
- Calculating proportional prices and discounts
- Unit conversions (kg, g, m, cm, liters, etc.)
- Adjusting cooking recipes
- Estimating time, distance, and speed
- Financial planning and expense tracking
- Calculations in construction, engineering, and manufacturing
In short, the Rule of Three is used whenever two or more quantities maintain
a proportional relationship with one another.
How does the Rule of Three work?
There are two main types of Rule of Three: the Simple Rule of Three
and the Compound Rule of Three. The difference between them lies in the number
of quantities involved in the problem.
1. Simple Rule of Three
The Simple Rule of Three is used when the problem involves only
two quantities, which may be directly or inversely proportional.
Directly proportional quantities:
when one increases, the other also increases.
Example:
The more hours worked, the higher the salary.
Inversely proportional quantities:
when one increases, the other decreases.
Example:
The more workers there are, the less time will be needed to complete a task.
Step-by-step guide to solving the Simple Rule of Three:
- Identify the quantities involved in the problem.
- Determine whether the relationship is direct or inverse.
- Set up the proportion correctly.
- Apply cross-multiplication.
- Solve the equation and find the unknown value.
2. Compound Rule of Three
The Compound Rule of Three is used when the problem involves
more than two proportional quantities.
Example:
If 4 machines produce 100 parts in 5 hours, how many parts will 6 machines produce in 3 hours?
In this case, we have three related quantities: number of machines,
working time, and number of parts produced.
How to solve the Compound Rule of Three:
- Analyze each quantity separately.
- Determine whether each relationship is direct or inverse.
- Set up the compound proportion.
- Perform the necessary multiplications and divisions.
Practical Rule of Three examples
Example 1: Fuel consumption
A car travels 300 km using 30 liters of fuel.
How many liters are required to travel 500 km?
Since distance and fuel consumption increase together, this is
a directly proportional relationship.
Example 2: Teamwork (inverse relationship)
10 workers build a wall in 8 days.
How many days would it take 20 workers to complete the same task?
More workers → fewer days → inversely proportional relationship.
Key tips for mastering the Rule of Three
- Always correctly identify the type of proportionality.
- Organize the data before setting up the proportion.
- Verify that the result makes practical sense.
- Use a Rule of Three calculator to speed up calculations.
Use our online Rule of Three calculator to get fast, free, and accurate results.