# How do you subtract 9\frac { 1} { 12} - 5\frac { 3} { 8} - 1\frac { 3} { 4}?

Dec 20, 2016

$1 \frac{23}{24}$

#### Explanation:

Convert the mixed fractions to an improper fractions (numerator larger than the denominator)

$\textcolor{red}{9} \frac{\textcolor{g r e e n}{1}}{\textcolor{b l u e}{12}} - \textcolor{red}{5} \frac{\textcolor{g r e e n}{3}}{\textcolor{b l u e}{8}} - \textcolor{red}{1} \frac{\textcolor{g r e e n}{3}}{\textcolor{b l u e}{4}}$

$= \frac{\textcolor{red}{9} \left(\textcolor{b l u e}{12}\right) + \textcolor{g r e e n}{1}}{\textcolor{b l u e}{12}} - \frac{\textcolor{red}{5} \left(\textcolor{b l u e}{8}\right) + \textcolor{g r e e n}{3}}{\textcolor{b l u e}{8}} - \frac{\textcolor{red}{1} \left(\textcolor{b l u e}{4}\right) + \textcolor{g r e e n}{3}}{\textcolor{b l u e}{4}}$

$= \frac{109}{12} - \frac{43}{8} - \frac{7}{4}$

Unify the denominators

$= \frac{109 \textcolor{b r o w n}{\left(2\right)}}{12 \textcolor{b r o w n}{\left(2\right)}} - \frac{43 \textcolor{b r o w n}{\left(3\right)}}{8 \textcolor{b r o w n}{\left(3\right)}} - \frac{7 \textcolor{b r o w n}{\left(6\right)}}{4 \textcolor{b r o w n}{\left(6\right)}}$

$= \frac{218}{24} - \frac{129}{24} - \frac{42}{24}$

$= \frac{218 - 129 - 42}{24}$

$= \frac{47}{24}$

You can stop here or convert the solution to a mixed fraction

$= \frac{24 + 23}{24}$

$= \frac{24}{24} + \frac{23}{24}$

$= 1 + \frac{23}{24}$

$= 1 \frac{23}{24}$