Ratios and proportions are important ideas in math that help us solve problems.

What They Mean

• Ratio: This is when we compare two amounts. We can write it as $a:b$ or $\frac{a}{b}$.

• Proportion: This is an equation that shows two ratios are the same. We write it as $\frac{a}{b} = \frac{c}{d}$.

Types of Proportions

1. Direct Proportion: This happens when one amount increases, and the other amount also increases at the same rate. We can write it as $y = kx$, where $k$ is a constant (a fixed number). For example, if $x = 2$ and $y = 6$, then $k$ is found by dividing $y$ by $x$. So, $k = \frac{y}{x} = 3$.

2. Inverse Proportion: In this situation, when one amount goes up, the other one goes down. We can write this as $y = \frac{k}{x}$. For example, if $x = 4$ and $y = 3$, then we find $k$ by multiplying $x$ and $y$. So, $k = xy = 12$.

Example in a Class

Let’s say a class has 30 students. If we look at their test scores in the ratio of 2:3:5, the total parts add up to 30. This helps us figure out how many students scored in each part.