# How do you simplify 10\div [ ( 1+ 5\div 6]?

Mar 26, 2017

#### Answer:

$\frac{60}{11} = 5 \frac{5}{11}$

#### Explanation:

To evaluate an expression with $\textcolor{b l u e}{\text{mixed operations}}$ there is a particular order that must be followed.

Follow the order as set out in the acronym PEMDAS

{Parenthesis (brackets), Exponents (powers), Multiplication, Division, Addition, Subtraction ]

$\Rightarrow 10 \div \left[\left(1 + 5 \div 6\right)\right]$

Evaluating the $\textcolor{b l u e}{\text{inner bracket first}}$

$5 \div 6 = \frac{5}{6} \leftarrow \textcolor{red}{\text{division in exact form}}$

$\Rightarrow 1 + \frac{5}{6} = 1 \frac{5}{6} = \frac{11}{6} \leftarrow \textcolor{red}{\text{ inner bracket}}$

The expression is now reduced to.

$10 \div \frac{11}{6}$

$= \frac{10}{1} \times \frac{6}{11}$

$= \frac{10 \times 6}{1 \times 11}$

$= \frac{60}{11} \leftarrow \textcolor{red}{\text{ improper fraction}}$

$= 5 \frac{5}{11} \leftarrow \textcolor{red}{\text{ mixed number}}$