Simplify 1/2(2n+4+6m)

$\frac{1}{2} (2 n + 4 + 6 m)$

Apply the distributive property.

$\frac{1}{2} (2 n) + \frac{1}{2} \cdot 4 + \frac{1}{2} (6 m)$

Simplify.

Cancel the common factor of $2$ .

Factor $2$ out of $2 n$ .

$\frac{1}{2} (2 (n)) + \frac{1}{2} \cdot 4 + \frac{1}{2} (6 m)$

Cancel the common factor.

$\frac{1}{2} (2 n) + \frac{1}{2} \cdot 4 + \frac{1}{2} (6 m)$

Rewrite the expression.

$n + \frac{1}{2} \cdot 4 + \frac{1}{2} (6 m)$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$n + \frac{1}{2} \cdot (2 (2)) + \frac{1}{2} (6 m)$

Cancel the common factor.

$n + \frac{1}{2} \cdot (2 \cdot 2) + \frac{1}{2} (6 m)$

Rewrite the expression.

$n + 2 + \frac{1}{2} (6 m)$

Cancel the common factor of $2$ .

Factor $2$ out of $6 m$ .

$n + 2 + \frac{1}{2} (2 (3 m))$

Cancel the common factor.

$n + 2 + \frac{1}{2} (2 (3 m))$

Rewrite the expression.

$n + 2 + 3 m$

Move $2$ .

$n + 3 m + 2$

Reorder $n$ and $3 m$ .

$3 m + n + 2$