# How do you simplify 3/4n+3m-1/3n+1/4m?

Dec 27, 2016

$\frac{5}{12} n + \frac{13}{4} m$

#### Explanation:

Collecting like terms.

$\frac{3}{4} n - \frac{1}{3} n + 3 m + \frac{1}{4} m$

Converting fractions to fractions with $\textcolor{b l u e}{\text{common denominators}}$

$= \left(\frac{3 \times 3}{3 \times 4} n - \frac{4 \times 1}{4 \times 3} n\right) + \left(\frac{3 \times 4}{1 \times 4} m + \frac{1}{4} m\right)$

$= \left(\frac{9}{12} n - \frac{4}{12} n\right) + \left(\frac{12}{4} m + \frac{1}{4} m\right)$

$= \frac{5}{12} n + \frac{13}{4} m = \frac{5 n}{12} + \frac{13 m}{4}$

Dec 27, 2016

$\frac{3}{4} n + 3 m - \frac{1}{3} n + \frac{1}{4} m = \frac{5}{12} n + \frac{13}{4} m$

#### Explanation:

We can simplify expressions of this type, drawing common factor each of the variables or literal parts of those terms that contain them. In this case we do the following:

$\frac{3}{4} n + 3 m - \frac{1}{3} n + \frac{1}{4} m = \left(\frac{3}{4} - \frac{1}{3}\right) \cdot n + \left(3 + \frac{1}{4}\right) \cdot m$.

Then, we perform the operations with the numbers in parentheses and, if possible, simplify the fractions obtained. In this case, it is necessary to add or subtract by placing previously common denominator and the resulting fractions are already reduced to their canonical representatives:

$\frac{3}{4} - \frac{1}{3} = \frac{9}{12} - \frac{4}{12} = \frac{5}{12}$,

and

$3 + \frac{1}{4} = \frac{12}{4} + \frac{1}{4} = \frac{13}{4}$.

Therefore, the original expression, once simplified is as follows:

$\frac{3}{4} n + 3 m - \frac{1}{3} n + \frac{1}{4} m = \left(\frac{3}{4} - \frac{1}{3}\right) \cdot n + \left(3 + \frac{1}{4}\right) \cdot m =$

$= \frac{5}{12} n + \frac{13}{4} m$.