Ratio and Proportion Calculator

Understanding Ratios and Proportions

A ratio is a way to compare two or more quantities of the same kind. It shows their relative sizes. For example, if a recipe calls for 2 cups of flour and 1 cup of sugar, the ratio of flour to sugar is $2:1$. Ratios can be simplified by dividing all parts by their greatest common divisor (GCD).

A proportion is an equation stating that two ratios are equivalent. For example, $1:2 = 3:6$. Proportions are often used to solve for an unknown quantity when a known relationship exists.

• Direct Proportion: Two quantities increase or decrease together at the same rate. If $y$ is directly proportional to $x$, then $y = kx$ or $\frac{y}{x} = k$, where $k$ is the constant of proportionality. This means $\frac{a}{b} = \frac{c}{d}$.
• Inverse Proportion: When one quantity increases, the other decreases proportionally, and vice-versa. If $y$ is inversely proportional to $x$, then $y = \frac{k}{x}$ or $xy = k$. This means $a \times b = c \times d$ if the product is constant for corresponding pairs.

This calculator will help you simplify ratios, find missing terms in equivalent ratios, divide quantities according to a given ratio, and solve problems involving direct and inverse proportions, including common applied laws.