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?

1 Answer
Sep 21, 2017

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