Rule of Three Pro
Professional calculator to solve direct and inverse proportion problems with step-by-step explanations
Simple Rule of Three
Solve problems of direct and inverse proportionality between two quantities.
Result
Detected proportion
Applied formula
Calculation steps
1. We identify that A is to B as C is to X
2. We apply the direct proportion formula
3. X = (10 × 7) / 5 = 14
Compound Rule of Three
Solve problems with more than two proportionally related quantities.
Result
Detected proportions
Quantity 1: Direct proportionality
Quantity 2: Direct proportionality
Applied formula
Calculation steps
1. We identify the proportional relationships
2. We apply the compound proportion formula
3. X = (10 × 4 × 12) / (5 × 8) = 12
Percentage Calculator
Calculate percentages, percentage increases and discounts.
Result
Calculation type
Applied formula
Calculation steps
1. Convert percentage to decimal: 15% = 0.15
2. Multiply by base value: 100 × 0.15 = 15
Learn About the Rule of Three
The rule of three is a fundamental mathematical tool that allows solving proportionality problems between quantities. It is widely used in everyday and professional situations.
Simple Direct Rule of Three
Applies when two quantities are directly proportional, meaning when one increases, the other also increases in the same proportion.
C → X ⇒ X = (B × C) / A
Simple Inverse Rule of Three
Applies when two quantities are inversely proportional, meaning when one increases, the other decreases in the same proportion.
C → X ⇒ X = (A × B) / C
Compound Rule of Three
Used when more than two proportionally related quantities are involved (can be direct or inverse).
Adjusts according to proportions
Practical Examples
If 5 apples cost $10, how much will 8 apples cost?
8 → X ⇒ X = (10 × 8) / 5 = $16
If 6 workers finish a job in 4 days, how long will 8 workers take?
8 → X ⇒ X = (6 × 4) / 8 = 3 days
If 5 machines make 100 pieces in 4 hours, how many pieces will 8 machines make in 6 hours?
(8 machines × 6 hrs → X) ⇒ X = (100 × 8 × 6) / (5 × 4) = 240 pieces
Frequently Asked Questions
To determine the type of proportion:
- Direct: If when one quantity increases, the other also increases (e.g., more products → higher cost).
- Inverse: If when one quantity increases, the other decreases (e.g., more workers → less time).
If in doubt, our auto mode will detect the relationship.
Simple rule of three: When there are only two related quantities (e.g., quantity and price).
Compound rule of three: When there are three or more related quantities (e.g., workers, hours and production).
Percentages are a special case of direct proportion where one of the quantities is always 100. For example:
X% → Part ⇒ Part = (Total value × X) / 100
Our percentage calculator automates these calculations.
