SAT: Ratios, Rates & Proportions

A comparison of two quantities expressed as $a:b$ or $\frac{a}{b}$. Ratios can describe part-to-part or part-to-whole relationships and remain equivalent when both terms are multiplied or divided by the same nonzero number.

A rate in which the denominator is 1 unit. Unit rates make it easy to compare different rates and to scale quantities up or down proportionally.

An equation stating that two ratios are equal: $\frac{a}{b} = \frac{c}{d}$. Proportions can be solved by cross-multiplication, yielding $ad = bc$.

A relationship where $y = kx$ for some constant $k$. As one variable increases, the other increases proportionally. The graph passes through the origin and is a straight line with slope $k$.

A relationship where $xy = k$ or equivalently $y = \frac{k}{x}$. As one variable increases, the other decreases so that their product remains constant.

A method for converting units by multiplying by conversion factors written as fractions equal to 1. Units cancel algebraically, leaving the desired unit in the answer.

The constant multiplier that relates corresponding measurements in two similar figures or proportional situations. If the scale factor is $k$, then every length in the original is multiplied by $k$ in the scaled version.

The fixed ratio $k$ in a proportional relationship $y = kx$. It represents the unit rate and can be found by dividing any $y$-value by its corresponding $x$-value.

A part-to-part ratio compares two parts of a whole (e.g., boys to girls), while a part-to-whole ratio compares one part to the total. Converting between them requires knowing all the parts.

A technique for solving proportions. Given $\frac{a}{b} = \frac{c}{d}$, cross-multiplying gives $ad = bc$. This eliminates fractions and produces a solvable linear equation.