Math - Fraction Operation

Addition & Subtraction

Like Denominators

When adding or subtracting fractions with like denominators, simply keep the denominator unchanged and add or subtract the numerators.

ab+cb=a+cb\frac{a}{b} + \frac{c}{b} = \frac{a+c}{b}
ab−cb=a−cb\frac{a}{b} - \frac{c}{b} = \frac{a-c}{b}


Unlike Denominators

How to Add and Subtract Fractions (youtube)

ab+cd=(a×d)+(c×b)b×d\frac{a}{b} + \frac{c}{d} = \frac{(a \times d)+(c \times b)}{b \times d}
ab−cd=(a×d)−(c×b)b×d\frac{a}{b} - \frac{c}{d} = \frac{(a \times d)-(c \times b)}{b \times d}


Examples
12+12=2288−38=58410+712=(4×12)+(7×10)10×12=118120−54−38=(−5×8)−(3×4)4×8=−5232\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\times12)+(7\times10)}{10\times12} = \frac{118}{120}\\ \frac{-5}{4} - \frac{3}{8} = \frac{(-5\times8)-(3\times4)}{4\times8} = \frac{-52}{32}

Multiplication

When multiplying fractions, multiply the numerators together and the denominators together.

ab×cb=a×cb×b\frac{a}{b} \times \frac{c}{b} = \frac{a \times c}{b \times b}
ab×cd=a×cb×d\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}


Examples
71×52=35228×114=2232\frac{7}{1} \times \frac{5}{2} = \frac{35}{2}\\ \frac{2}{8} \times \frac{11}{4} = \frac{22}{32}

Division

When dividing fractions, flip the second fraction and multiply.

ab÷cd=ab×dc\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}


Examples
88÷93=88×39=247239÷123=39×312=9108\frac{8}{8} \div \frac{9}{3} = \frac{8}{8} \times \frac{3}{9} = \frac{24}{72}\\ \frac{3}{9} \div \frac{12}{3} = \frac{3}{9} \times \frac{3}{12} = \frac{9}{108}