Basic Concepts
In a nutshell: Ratios compare two or more quantities and can be simplified.
## What Are Ratios?
Ratios help us compare two or more quantities. Imagine you have 4 apples and 6 oranges. The ratio of apples to oranges is 4 to 6, or written as \(4:6\) or \(\frac{4}{6}\).
## How Do We Use Ratios?
Ratios can show relationships in many ways:
- \(2:3\)
- \(\frac{2}{3}\)
- "2 to 3"
You can simplify ratios just like fractions. For example, \(4:6\) simplifies to \(2:3\).
## Why Are Ratios Important?
Ratios are everywhere! They help us with recipes, maps, mixing paint, or comparing scores.
### How to Simplify Ratios
Find the greatest common factor (GCF) of both numbers and divide each by that number.
## Real-World Uses
If a recipe needs 2 cups of flour for every 3 cups of sugar, the ratio is \(2:3\).
Examples
- A classroom has 10 boys and 15 girls. The ratio of boys to girls is 10:15 or 2:3.
- If a map shows 1 inch represents 5 miles, the ratio is 1:5.
Key terms
- Ratio
- A comparison of two quantities by division.
- Simplify
- To reduce a ratio to its smallest whole numbers.