Understanding Ratios
A ratio is a comparison of two or more quantities. It shows how much of one thing there is compared to another. Ratios are written using a colon (A:B) or as a fraction (A/B). They are used extensively in mathematics, cooking, mixing, finance, and many other fields.
Key Concepts
Simplifying Ratios
Divide all terms by their Greatest Common Divisor (GCD) to find the simplest form.
Equivalent Ratios
Multiply or divide all terms by the same number to get equivalent ratios.
Scaling Ratios
Scale a ratio so that one term equals a specific target value.
How to Find the GCD
The Greatest Common Divisor (GCD) is the largest number that divides evenly into all terms of the ratio. You can find it using the Euclidean algorithm: repeatedly divide the larger number by the smaller and take the remainder, until the remainder is zero. The last non-zero remainder is the GCD.
Real-World Applications
- Cooking: scaling recipes up or down (2:3 cups of flour to sugar)
- Maps: scale ratios like 1:50,000
- Finance: debt-to-income ratios, price-to-earnings ratios
- Mixing: paint colors, concrete, chemicals
- Science: stoichiometric ratios in chemical equations