Ratios & Proportions

Ratio: A comparison of two quantities using division. Can be written as $3:4$, $\frac{3}{4}$, or "3 to 4".

Example 1: If there are 12 boys and 8 girls, the ratio of boys to girls is $12:8$, which simplifies to $3:2$ by dividing both by 4.

Example 2: In a class of 30 students, 18 are girls. The ratio of girls to total students is $18:30 = 3:5$. This means 3 out of every 5 students are girls.

Order matters: The ratio $3:2$ is different from $2:3$. Always state what you're comparing! $3:2$ means 3 parts of the first quantity to 2 parts of the second.

Visual thinking: Imagine a ratio as parts of a whole. $3:2$ means if you have 5 total parts, 3 are one type and 2 are another type.

Three ways to write: $3:4$ (colon notation), $\frac{3}{4}$ (fraction form), or "3 to 4" (word form). All represent the same relationship!