Math - Fraction Arithmetic

Addition & Subtraction

Like denominators

To add or subtract fractions with like denominators, combine the numerators and keep the denominator the same.

$\frac{a}{b} + \frac{c}{b} = \frac{a+c}{b}$
$\frac{a}{b} - \frac{c}{b} = \frac{a-c}{b}$

Unlike denominators

How to Add and Subtract Fractions (youtube)

$\frac{a}{b} + \frac{c}{d} = \frac{(a * d)+(c * b)}{b * d}$
$\frac{a}{b} - \frac{c}{d} = \frac{(a * d)-(c * b)}{b * d}$

Examples

$\frac{1}{2} + \frac{1}{2} = \frac{2}{2}\\ \frac{8}{8} - \frac{3}{8} = \frac{5}{8}\\ \frac{4}{10} + \frac{7}{12} = \frac{(4*12)+(7*10)}{10*12} = \frac{118}{120}\\ \frac{-5}{4} - \frac{3}{8} = \frac{(-5*8)-(3*4)}{4*8} = \frac{-52}{32}$

Multiplication

To multiply fractions, multiply the numerators and the denominators.

$\frac{a}{b} * \frac{c}{b} = \frac{a * c}{b * b}$
$\frac{a}{b} * \frac{c}{d} = \frac{a * c}{b * d}$

Examples

$\frac{7}{1} * \frac{5}{2} = \frac{35}{2}\\ \frac{2}{8} * \frac{11}{4} = \frac{22}{32}$

Division

To divide fractions, flip the second fraction then multiply.

$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} * \frac{d}{c}$

Examples

$\frac{8}{8} \div \frac{9}{3} = \frac{8}{8} * \frac{3}{9} = \frac{24}{72}\\ \frac{3}{9} \div \frac{12}{3} = \frac{3}{9} * \frac{3}{12} = \frac{9}{108}$