Ratio Proportion

Reference data and engineering information about ratio proportion for miscellaneous applications.

Overview

Engineering reference data for Ratio Proportion in miscellaneous.

$y = x \cdot k$

Multiply by conversion factor.

$y = y_1 + \frac{(x - x_1)(y_2 - y_1)}{x_2 - x_1}$

Estimate between two known points.

$p = \frac{\text{part}}{\text{whole}} \times 100\%$

Part as fraction of whole.

A ratio compares two quantities of the same kind. It expresses how many times one quantity contains another.

Notation: The ratio of a to b can be written as a : b or as the fraction $\frac{a}{b}$ .
Example: The ratio of 3 to 6 is 3 : 6, which simplifies to $\frac{1}{2}$ or 0.5.

A proportion is an equation that states two ratios are equal.

Notation: If the ratio of a to b equals the ratio of c to d, it is written as: $a : b = c : d \quad \text{or} \quad \frac{a}{b} = \frac{c}{d}$
Example: 1 : 2 = 3 : 6 is a proportion because $\frac{1}{2} = \frac{3}{6}$ .

Cross-Multiplication: In a proportion $\frac{a}{b} = \frac{c}{d}$ , the cross-products are equal: $a \cdot d = b \cdot c$ .
Inverse (Reciprocal) Ratio: The inverse ratio of a : b is b : a. It is also expressed as $\frac{b}{a}$ .

Ratio: $\text{Ratio of } a \text{ to } b = \frac{a}{b}$

Proportion (Cross-Multiplication): $\text{If } \frac{a}{b} = \frac{c}{d}, \text{ then } a \cdot d = b \cdot c$

Symbol	Description
$a, c$	First terms (antecedents) of the ratios
$b, d$	Second terms (consequents) of the ratios