Question

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`?

Answer 1

`1(5)/6`

Explanation:

`(3/4divide3/100-23(1)/2)divide1(1)/2cdot2/3+1(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:

`=(3/4\color{red}cdot color{red}100/color{red}3-23(1)/2)divide1(1)/2cdot2/3+1(1)/6`

Cancel the 3's:

`=(color{red}1/4cdot100/color{red}1-23(1)/2)divide1(1)/2cdot2/3+1(1)/6`

Cancel the 100 and 4:

`=(1/color{red}1cdotcolor{red}25/1-23(1)/\2)divide1(1)/2cdot2/3+1(1)/6`

Simplifying we now have:

`=(color{red}25-23(1)/\2)divide1(1)/2cdot2/3+1(1)/6`

Dealing with the subtraction inside the brackets:

`=(color{red}1(color{red}1)/color{red}2)divide1(1)/2cdot2/3+1(1)/6`

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

`=color{red}1(color{red}1)/color{red}2color{red}dividecolor{red}1(color{red}1)/color{red}2cdot2/3+1(1)/6`

`=color{red}1cdot2/3+1(1)/6`

Multiplying:

`=color{red}2/color{red}3+1(1)/6`

Change the first fraction to obtain a common denominator:

`=4/6+1(1)/6`

Adding:

`=1(5)/6`