How do you simplify 34n+3m−13n+14?

Question

How do you simplify  34n+3m−13n+14?

Jaden Petersen · Accepted Answer

Step 1  Collecting like terms.  34n−13n+3m+14m  Converting fractions to fractions with common denominators  =(3×33×4n−4×14×3n)+(3×41×4m+14m)  =(912n−412n)+(124m+14m)  =512n+134m=5n12+13m4

Pierce Carey · Accepted Answer

Step 1
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 = (\frac{3}{4} - \frac{1}{3}) \times n + (3 + \frac{1}{4}) \times 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 = (\frac{3}{4} - \frac{1}{3}) \times n + (3 + \frac{1}{4}) \times m =

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

How do you simplify \frac{3}{4}n+3m-\frac{1}{3}n+\frac{1}{4}?

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