Simplify 5/6(x+1/2+4)

$\frac{5}{6} (x + \frac{1}{2} + 4)$

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5}{6} \cdot (x + \frac{1}{2} + 4 \cdot \frac{2}{2})$

Combine $4$ and $\frac{2}{2}$ .

$\frac{5}{6} \cdot (x + \frac{1}{2} + \frac{4 \cdot 2}{2})$

Combine the numerators over the common denominator.

$\frac{5}{6} \cdot (x + \frac{1 + 4 \cdot 2}{2})$

Simplify the numerator.

Multiply $4$ by $2$ .

$\frac{5}{6} \cdot (x + \frac{1 + 8}{2})$

Add $1$ and $8$ .

$\frac{5}{6} \cdot (x + \frac{9}{2})$

Apply the distributive property.

$\frac{5}{6} x + \frac{5}{6} \cdot \frac{9}{2}$

Combine $\frac{5}{6}$ and $x$ .

$\frac{5 x}{6} + \frac{5}{6} \cdot \frac{9}{2}$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\frac{5 x}{6} + \frac{5}{3 (2)} \cdot \frac{9}{2}$

Factor $3$ out of $9$ .

$\frac{5 x}{6} + \frac{5}{3 \cdot 2} \cdot \frac{3 \cdot 3}{2}$

Cancel the common factor.

$\frac{5 x}{6} + \frac{5}{3 \cdot 2} \cdot \frac{3 \cdot 3}{2}$

Rewrite the expression.

$\frac{5 x}{6} + \frac{5}{2} \cdot \frac{3}{2}$

Multiply $\frac{5}{2}$ by $\frac{3}{2}$ .

$\frac{5 x}{6} + \frac{5 \cdot 3}{2 \cdot 2}$

Multiply.

Multiply $5$ by $3$ .

$\frac{5 x}{6} + \frac{15}{2 \cdot 2}$

Multiply $2$ by $2$ .

$\frac{5 x}{6} + \frac{15}{4}$