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#?
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#(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#
