What is a Ratio?
A ratio is a comparison between two or more quantities. It shows how many times one value contains another. Ratios are written as A:B or A/B and can be used to compare sizes, amounts, or other measurable quantities.
What is a Proportion?
A proportion is an equation stating that two ratios are equal. If A:B = C:D, then A×D = B×C (cross multiplication). This property is used to solve for unknown values.
A : B = C : D → A × D = B × C
How to Simplify Ratios
To simplify a ratio, divide both parts by their Greatest Common Divisor (GCD). For example:
- 12 : 18 → GCD is 6 → 2 : 3
- 24 : 36 → GCD is 12 → 2 : 3
- 100 : 25 → GCD is 25 → 4 : 1
How to Solve Proportions
When you have three of four values in a proportion A:B = C:D, you can find the missing value:
- Missing A: A = (B × C) ÷ D
- Missing B: B = (A × D) ÷ C
- Missing C: C = (A × D) ÷ B
- Missing D: D = (B × C) ÷ A
Common Uses of Ratios
- Cooking: Scaling recipes up or down
- Maps: Converting between map scale and real distances
- Mixing: Paint colors, concrete, drinks
- Finance: Price-to-earnings ratio, debt ratios
- Photography: Aspect ratios (16:9, 4:3)
Golden Ratio
The golden ratio (φ ≈ 1.618) is a special ratio found in nature, art, and architecture. A rectangle with sides in the golden ratio is considered aesthetically pleasing.