Lesson: Solving Proportions

In this lesson, we will learn how to solve proportions. A proportion is an equation that states that two ratios are equal. For example, if we have two ratios $\frac{a}{b}$and $\frac{c}{d}$, then we can write the proportion as:

$$\frac{a}{b} = \frac{c}{d}$$

Steps to Solve Proportions

1. Set up the proportion: Write the equation with the two ratios.
2. Cross-multiply: Multiply the numerator of one ratio by the denominator of the other ratio.
3. Solve for the unknown: Isolate the variable to find its value.

Example

Let's solve the proportion $\frac{x}{4} = \frac{3}{8}$.

1. Set up the proportion: $\frac{x}{4} = \frac{3}{8}$

2. Cross-multiply: $8x = 3 \cdot 4$ $8x = 12$

3. Solve for x: $x = \frac{12}{8}$ Simplifying gives us: $x = \frac{3}{2}$ or $1.5$

Key Questions

• What is a proportion?
• How do you cross-multiply?
• What steps do you take to isolate the variable?

Keywords

• Proportion
• Ratio
• Cross-multiply
• Isolate
• Variable