Rule of Three – Simple Explanation and How It Works
Master proportions with clear examples and step-by-step methods. Perfect for students, teachers, and everyday problem-solving.
Try the Calculator →What is the Rule of Three?
The rule of three is a simple math method used to find an unknown value when you know three related values. It’s based on the idea of proportion—when two ratios are equal.
If 3 apples cost 6 pesos, how much do 5 apples cost?
You know: 3 apples → 6 pesos
You want to find: 5 apples → ? pesos
The rule of three helps you solve this quickly and accurately. It’s also called:
- Cross multiplication
- Proportion method
- Direct proportion (when both values increase together)
What Is It Used For?
The rule of three is used in everyday situations where quantities are related proportionally.
Shopping
Calculate prices for different quantities of products
Cooking
Adjust recipe ingredients for more or fewer servings
Travel
Estimate fuel costs or travel time for different distances
Currency Exchange
Convert money between different currencies
How Does It Work?
The rule of three works by setting up a proportion between two ratios and solving for the unknown value.
When you have a proportion like this:
A is to B as C is to X
You can find X using the rule of three formula.
The Rule of Three Formula
Where:
- A = First known value
- B = Second known value (related to A)
- C = Third known value
- X = Unknown value (what you’re solving for)
You can also write it as a proportion:
A : B = C : X
Worked Example: Step-by-Step
Let’s solve a real problem using the rule of three.
If 4 notebooks cost 100 pesos, how much do 7 notebooks cost?
A = 4 notebooks
B = 100 pesos
C = 7 notebooks
X = ? pesos
X = (B × C) ÷ A
X = (100 × 7) ÷ 4
X = 700 ÷ 4
X = 175
7 notebooks cost 175 pesos
Common Mistakes to Avoid
Make sure you match the correct values. A and C should be the same type (e.g., both quantities), and B and X should be the same type (e.g., both prices).
The basic rule of three works for direct proportions only. If one value increases while the other decreases (inverse proportion), you need a different approach.
Always include units (pesos, kilos, hours, etc.) to avoid confusion and ensure your answer makes sense.
Always verify: Does the answer make logical sense? If 4 items cost 100, should 7 items cost more or less?
Real-Life Use Cases
Construction & DIY
If 2 bags of cement cover 10 square meters, how many bags do you need for 35 square meters?
Medicine & Health
If a patient needs 5ml of medicine per 10kg of body weight, how much does a 65kg patient need?
School & Study
If you read 30 pages in 45 minutes, how long will it take to read 80 pages at the same speed?
Art & Design
If a design uses 3 colors for every 5 elements, how many colors are needed for 20 elements?
Frequently Asked Questions
The rule of three is a math method to find an unknown value when you know three related values. It uses proportion: if A relates to B the same way C relates to X, you can find X.
Use it when two quantities are directly proportional—meaning when one increases, the other increases in the same ratio. Common examples: pricing, recipes, speed/distance, and conversions.
Direct proportion: both values increase or decrease together (more items = more cost). Inverse proportion: one increases while the other decreases (more workers = less time).
Yes! For example, if 20% of 50 is 10, what is 35% of 50? Set it up as: 20 is to 10 as 35 is to X.
Yes, they’re the same concept. Cross multiplication is the technique used to solve the proportion equation in the rule of three.
Double-check: (1) Did you match the values correctly? (2) Is it a direct proportion problem? (3) Did you calculate correctly? If the answer still seems wrong, review your setup.