Simplify 2/3y+1/6y+y

$\frac{2}{3} y + \frac{1}{6} y + y$

Step 1

Simplify each term.

Combine $\frac{2}{3}$ and $y$ .

$\frac{2 y}{3} + \frac{1}{6} y + y$

Combine $\frac{1}{6}$ and $y$ .

$\frac{2 y}{3} + \frac{y}{6} + y$

Step 2

Find the common denominator.

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

$\frac{2 y}{3} \cdot \frac{2}{2} + \frac{y}{6} + y$

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

$\frac{2 y \cdot 2}{3 \cdot 2} + \frac{y}{6} + y$

Write $y$ as a fraction with denominator $1$ .

$\frac{2 y \cdot 2}{3 \cdot 2} + \frac{y}{6} + \frac{y}{1}$

Multiply $\frac{y}{1}$ by $\frac{6}{6}$ .

$\frac{2 y \cdot 2}{3 \cdot 2} + \frac{y}{6} + \frac{y}{1} \cdot \frac{6}{6}$

Multiply $\frac{y}{1}$ by $\frac{6}{6}$ .

$\frac{2 y \cdot 2}{3 \cdot 2} + \frac{y}{6} + \frac{y \cdot 6}{6}$

Reorder the factors of $3 \cdot 2$ .

$\frac{2 y \cdot 2}{2 \cdot 3} + \frac{y}{6} + \frac{y \cdot 6}{6}$

Multiply $2$ by $3$ .

$\frac{2 y \cdot 2}{6} + \frac{y}{6} + \frac{y \cdot 6}{6}$

Step 3

Combine the numerators over the common denominator.

$\frac{2 y \cdot 2 + y + y \cdot 6}{6}$

Step 4

Simplify each term.

Multiply $2$ by $2$ .

$\frac{4 y + y + y \cdot 6}{6}$

Move $6$ to the left of $y$ .

$\frac{4 y + y + 6 y}{6}$

Step 5

Simplify by adding terms.

Add $4 y$ and $y$ .

$\frac{5 y + 6 y}{6}$

Add $5 y$ and $6 y$ .

$\frac{11 y}{6}$