Fractions

Reference data and engineering information about fractions for miscellaneous applications.

fractions

Overview

Engineering reference data for Fractions 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.

Proper fraction: A fraction where the numerator is smaller than the denominator, e.g., $\frac{3}{4}$ .
Improper fraction: A fraction where the numerator is larger than the denominator, e.g., $\frac{5}{3}$ .
Reducible fraction: A fraction that can be simplified to lower terms by dividing the numerator and denominator by a common factor.
Least common denominator (LCD): The smallest common multiple of the denominators of two or more fractions.
Mixed number: A combination of a whole number and a proper fraction, e.g., $2 \frac{1}{3}$ .

To add fractions, find a common denominator and add the numerators.

Example: Add $\frac{1}{4} + \frac{3}{16} + \frac{7}{8}$ .

Find the least common denominator (LCD) of 4, 16, and 8, which is 16.
Convert each fraction to have denominator 16:
- $\frac{1}{4} = \frac{4}{16}$
- $\frac{3}{16} = \frac{3}{16}$
- $\frac{7}{8} = \frac{14}{16}$
Add the numerators: $\frac{4}{16} + \frac{3}{16} + \frac{14}{16} = \frac{21}{16}$ .

To multiply fractions, multiply the numerators and multiply the denominators.

Example: Multiply $\frac{3}{4} \times \frac{9}{16}$ .

$\frac{3}{4} \times \frac{9}{16} = \frac{3 \times 9}{4 \times 16} = \frac{27}{64}$

To divide fractions, multiply by the reciprocal of the divisor.

Example: Divide $\frac{3}{4} \div \frac{9}{16}$ .

Multiply by the reciprocal: $\frac{3}{4} \times \frac{16}{9}$
Simplify: $\frac{3 \times 16}{4 \times 9} = \frac{48}{36} = \frac{4}{3}$ after dividing numerator and denominator by 12.