# How do you simplify 1/2 - 1/3 times 1/4 + 1/5 1/6 ÷ 1/6?

Nov 1, 2017

See Process below;

#### Explanation:

Following the rule of PEDMAS

$\frac{1}{2} - \frac{1}{3} \times \frac{1}{4} + \frac{1}{5} \frac{1}{6} \div \frac{1}{6}$

$\frac{1}{5} \frac{1}{6} = \frac{1}{5} \cdot \frac{1}{6}$ since there is no symbol attached!

Hence;

$\frac{1}{2} - \frac{1}{3} \times \frac{1}{4} + \frac{1}{5} \cdot \frac{1}{6} \div \frac{1}{6}$

$\frac{1}{2} - \frac{1}{3} \times \frac{1}{4} + \frac{1}{5} \times \frac{1}{6} \div \frac{1}{6}$

So we'll take it step wise..

Since there are Parenthesis, Exponents.. we'll go to;

Division

$\frac{1}{2} - \frac{1}{3} \times \frac{1}{4} + \frac{1}{5} \times \textcolor{red}{\frac{1}{6} \div \frac{1}{6}}$

$\frac{1}{2} - \frac{1}{3} \times \frac{1}{4} + \frac{1}{5} \times \left(\textcolor{red}{\frac{1}{6} \times \frac{6}{1}}\right) \to \text{Transposed!}$

$\frac{1}{2} - \frac{1}{3} \times \frac{1}{4} + \frac{1}{5} \times \textcolor{red}{\frac{1}{\cancel{6}} \times \frac{\cancel{6}}{1}}$

$\frac{1}{2} - \frac{1}{3} \times \frac{1}{4} + \frac{1}{5} \times \frac{1}{1}$

Multiplication

$\frac{1}{2} - \textcolor{b l u e}{\frac{1}{3} \times \frac{1}{4}} + \textcolor{b l u e}{\frac{1}{5} \times \frac{1}{1}}$

$\frac{1}{2} - \frac{1}{12} + \frac{1}{5}$

$\frac{1}{2} - \textcolor{\mathmr{and} a n \ge}{\frac{1}{12} + \frac{1}{5}}$

Note, Addition and Subtraction deals with finding the LCM..

LCM of $12 \mathmr{and} 5 = 60$

$\frac{1}{2} - \textcolor{\mathmr{and} a n \ge}{\frac{5 + 12}{60}}$

$\frac{1}{2} - \frac{17}{60}$

Subtraction

$\textcolor{g r e e n}{\frac{1}{2} - \frac{17}{60}}$

LCM of $2 \mathmr{and} 60 = 60$

$\textcolor{g r e e n}{\frac{30 - 17}{60}}$

$\frac{13}{60}$