Overview
This lecture explains how to solve proportions using cross multiplication, demonstrating each step with detailed examples.
Steps for Solving Proportions with Cross Multiplication
- A proportion is an equation stating that two ratios are equal.
- To solve, use cross multiplication: multiply diagonally across the equal sign.
- Set the results (cross products) equal to each other to form an equation.
- Solve for the unknown variable by isolating it, usually via division.
Example 1: Solving 3/12 = 5/x
- Cross multiply: 3 × x and 12 × 5.
- Form equation: 3x = 60.
- Divide both sides by 3: x = 20.
Example 2: Solving 33/x = 6/2
- Cross multiply: 33 × 2 and x × 6.
- Form equation: 66 = 6x.
- Divide both sides by 6: x = 11.
Tips for Cross Multiplication
- Order of multiplication (which diagonal first) does not affect the solution.
- Always multiply diagonally and set products equal to each other.
Key Terms & Definitions
- Proportion — An equation that states two ratios are equal.
- Cross Multiplication — A method where the numerator of one ratio is multiplied by the denominator of the other.
Action Items / Next Steps
- Practice solving proportions using cross multiplication with additional problems.
- Review definitions and steps to reinforce the method.