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

$\frac{1}{4} x + \frac{5 x}{2}$

Step 1

Combine $\frac{1}{4}$ and $x$ .

$\frac{x}{4} + \frac{5 x}{2}$

Step 2

To write $\frac{5 x}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x}{4} + \frac{5 x}{2} \cdot \frac{2}{2}$

Step 3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{x}{4} + \frac{5 x \cdot 2}{2 \cdot 2}$

Multiply $2$ by $2$ .

$\frac{x}{4} + \frac{5 x \cdot 2}{4}$

Step 4

Combine the numerators over the common denominator.

$\frac{x + 5 x \cdot 2}{4}$

Step 5

Simplify the numerator.

Factor $x$ out of $x + 5 x \cdot 2$ .

Raise $x$ to the power of $1$ .

$\frac{x^{1} + 5 x \cdot 2}{4}$

Factor $x$ out of $x^{1}$ .

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

Factor $x$ out of $5 x \cdot 2$ .

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

Factor $x$ out of $x \cdot 1 + x (5 \cdot 2)$ .

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

Multiply $5$ by $2$ .

$\frac{x (1 + 10)}{4}$

Add $1$ and $10$ .

$\frac{x \cdot 11}{4}$

Step 6

Move $11$ to the left of $x$ .

$\frac{11 x}{4}$