Key Concepts
- Ratios (e.g., 3:2) represent a comparison between two numbers and can be written as fractions or with a colon.
- Proportions (e.g., (\frac{a}{b} = \frac{c}{d})) are equations that show two ratios are equal.
- Cross-multiplication (e.g., (\frac{a}{b} = \frac{c}{d}) → (\a \cdot d = b \cdot c)) helps solve for unknown values in proportion problems.
Skills Covered
- Setting up and simplifying ratios.
- Using cross-multiplication to solve proportions.
- Applying proportional reasoning to real-world scenarios.
Example Problems
- The ratio of boys to girls in a class is 3:5. If there are 12 boys, how many girls are in the class?
- A recipe calls for 4 cups of flour to make 10 cookies. How much flour is needed for 25 cookies?