Fundamental Property of Proportion
The Fundamental Property of Proportion is the most important rule for working with proportions. It gives us a powerful tool to check if proportions are true and to find unknown values.
📜 The Property Statement
In any true proportion a : b = c : d
a × d = b × c
The product of the extreme terms equals the product of the middle terms
This property is the foundation for ALL proportion work:
- ✅ Checking if proportions are true
- ✅ Finding unknown values
- ✅ Solving word problems
- ✅ Rearranging proportions
👁️ Visual Understanding
Extremes = Outer terms (first and last): a and d
Middles = Inner terms (second and third): b and c
Cross-multiply: Multiply diagonally and the products are equal!
🔬 Why Does This Property Work? (Proof)
Step-by-Step Proof:
| Step 1: | Start with proportion: a : b = c : d |
| Step 2: | Write as fractions: a/b = c/d |
| Step 3: | Multiply both sides by b × d |
| Step 4: | (a/b) × bd = (c/d) × bd |
| Step 5: | a × d = b × c ✓ |
Interactive visualization — available in the full lesson