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Summary of the operations on fractions

Here is a summary of the operations on fractions.

Operation Formula Example
Addition $$\displaystyle \frac{\Tblue{a}}{\Tviolet{b}} + \frac{\Tgreen{c}}{\Torange{d}} = \frac{\Tblue{a}\Torange{d}+\Tviolet {b}\Tgreen{c}}{\Tviolet{b}\Torange{d}}$$ $$\displaystyle\frac{1}{5} + \frac{2}{3} = \frac{13}{15} $$
Subtraction $$\displaystyle \frac{\Tblue{a}}{\Tviolet {b}} - \frac{\Tgreen{c}}{\Torange{d}} = \frac{\Tblue{a}\Torange{d}-\Tviolet {b}\Tgreen{c}}{\Tviolet{b}\Torange{d}}$$ $$\displaystyle\frac{2}{5} - \frac{1}{6} = \frac{7}{30} $$
Multiplication $$\displaystyle \frac{\Tblue{a}}{\Tviolet {b}}\times \frac{\Tgreen{c}}{\Torange{d}} = \frac{\Tblue{a}\Tgreen{c}}{\Tviolet {b}\Torange{d}}$$ $$\displaystyle\frac{2}{7} \times \frac{3}{5} = \frac{6}{35} $$
Division $$\displaystyle \frac{\Tblue{a}}{\Tviolet {b}} \div \frac{\Tgreen{c}}{\Torange{d}}= \frac{\Tblue{a}\Torange{d}}{\Tviolet {b} \Tgreen{c}}$$ $$\displaystyle\frac{2}{7} \div \frac{3}{5} = \frac{10}{21} $$