# How do you simplify (\frac { 3} { 4} \div \frac { 3} { 100} - 23 \frac { 1} { 2} ) \div 1\frac { 1} { 2} \cdot \frac { 2} { 3} + 1\frac { 1} { 6?

Sep 21, 2017

$1 \frac{5}{6}$

#### Explanation:

$\left(\frac{3}{4} \div i \mathrm{de} \frac{3}{100} - 23 \frac{1}{2}\right) \div i \mathrm{de} 1 \frac{1}{2} \cdot \frac{2}{3} + 1 \frac{1}{6}$

We need to follow Order of Operations.

First, deal with the division inside the bracket and flip the second fraction and change the operation to multiplication:

$= \left(\frac{3}{4} \setminus \textcolor{red}{\cdot} \frac{\textcolor{red}{100}}{\textcolor{red}{3}} - 23 \frac{1}{2}\right) \div i \mathrm{de} 1 \frac{1}{2} \cdot \frac{2}{3} + 1 \frac{1}{6}$

Cancel the 3's:

$= \left(\frac{\textcolor{red}{1}}{4} \cdot \frac{100}{\textcolor{red}{1}} - 23 \frac{1}{2}\right) \div i \mathrm{de} 1 \frac{1}{2} \cdot \frac{2}{3} + 1 \frac{1}{6}$

Cancel the 100 and 4:

$= \left(\frac{1}{\textcolor{red}{1}} \cdot \frac{\textcolor{red}{25}}{1} - 23 \frac{1}{\setminus} 2\right) \div i \mathrm{de} 1 \frac{1}{2} \cdot \frac{2}{3} + 1 \frac{1}{6}$

Simplifying we now have:

$= \left(\textcolor{red}{25} - 23 \frac{1}{\setminus} 2\right) \div i \mathrm{de} 1 \frac{1}{2} \cdot \frac{2}{3} + 1 \frac{1}{6}$

Dealing with the subtraction inside the brackets:

$= \left(\textcolor{red}{1} \frac{\textcolor{red}{1}}{\textcolor{red}{2}}\right) \div i \mathrm{de} 1 \frac{1}{2} \cdot \frac{2}{3} + 1 \frac{1}{6}$

We must work left to right when dealing with multiplication and division:

$= \textcolor{red}{1} \frac{\textcolor{red}{1}}{\textcolor{red}{2}} \textcolor{red}{\div} i \mathrm{de} \textcolor{red}{1} \frac{\textcolor{red}{1}}{\textcolor{red}{2}} \cdot \frac{2}{3} + 1 \frac{1}{6}$

$= \textcolor{red}{1} \cdot \frac{2}{3} + 1 \frac{1}{6}$

Multiplying:

$= \frac{\textcolor{red}{2}}{\textcolor{red}{3}} + 1 \frac{1}{6}$

Change the first fraction to obtain a common denominator:

$= \frac{4}{6} + 1 \frac{1}{6}$

$= 1 \frac{5}{6}$