# How do you solve 2 5/12 = -3 1/4 + k?

Aug 28, 2017

See a solution process below:

#### Explanation:

First, convert each mixed number into an improper fraction:

$2 \frac{5}{12} = - 3 \frac{1}{4} + k$

$2 + \frac{5}{12} = - \left(3 + \frac{1}{4}\right) + k$

$\left(\frac{12}{12} \times 2\right) + \frac{5}{12} = - \left(\left[\frac{4}{4} \times 3\right] + \frac{1}{4}\right) + k$

$\frac{24}{12} + \frac{5}{12} = - \left(\frac{12}{4} + \frac{1}{4}\right) + k$

$\frac{29}{12} = - \frac{13}{4} + k$

Next, add $\textcolor{red}{\frac{13}{4}}$ to each side of the equation to isolate $k$ while keeping the equation balanced:

$\textcolor{red}{\frac{13}{4}} + \frac{29}{12} = \textcolor{red}{\frac{13}{4}} - \frac{13}{4} + k$

$\frac{13}{4} + \frac{29}{12} = 0 + k$

$\frac{13}{4} + \frac{29}{12} = k$

Then, we need to put $\frac{13}{4}$ over a common denominator so we can add the two fractions by multiplying it by an appropriate form of $1$:

$\left(\frac{3}{3} \times \frac{13}{4}\right) + \frac{29}{12} = k$

$\frac{39}{12} + \frac{29}{12} = k$

$\frac{68}{12} = k$

Now, if necessary we can convert the improper fraction back into a mixed number:

$\frac{60}{12} + \frac{8}{12} = k$

$5 + \frac{4 \times 2}{4 \times 3} = k$

$5 + \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} \times 2}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} \times 3} = k$

$5 + \frac{2}{3} = k$

$5 \frac{2}{3} = k$

$k = 5 \frac{2}{3}$