Fractions

Multiple operations

Remember the rules for order of operations:

1. First perform any calculations inside square brackets.
2. Next perform any calculations inside parentheses.
3. Next perform all multiplications and divisions, working from left to right.
4. Lastly, perform all additions and subtractions, working from left to right

$\frac{1}{3}\[\frac{2}{4}-$\frac{5}{6}+\frac{1}{3}-\frac{3}{4}$+\frac{2}{5}:\frac{3}{10}\]=\frac{1}{3}\[\frac{2}{4}-$\frac{10}{12}+\frac{4}{12}-\frac{9}{12}$+\frac{2}{5}:\frac{3}{10}\]=\frac{1}{3}\[\frac{2}{4}-\frac{10+4-9}{12}+\frac{2}{5}:\frac{3}{10}\]=$

$\frac{1}{3}\[\frac{2}{4}-\frac{5}{12}+\frac{2}{5}:\frac{3}{10}\]=\frac{1}{3}\[\frac{2}{4}-\frac{5}{12}+\frac{2\cdot10}{5\cdot3}\]=\frac{1}{3}\[\frac{2}{4}-\frac{5}{12}+\frac{20}{15}\]=\frac{1}{3}\[\frac{2}{4}-\frac{5}{12}+\frac{4}{3}\]=$

$\frac{1}{3}\[\frac{6}{12}-\frac{5}{12}+\frac{16}{12}\]=\frac{1}{3}\[\frac{6-5+16}{12}\]=\frac{1}{3}\cdot\frac{17}{12}=\frac{17}{36}$

Calculate:

$\frac{6}{9}\[\frac{-5}{2}-$\frac{9}{5}+\frac{1}{8}+\frac{4}{4}$+\frac{2}{7}:\frac{-8}{7}\]$

Solution (reduce the result)