Solve for y y+y/3=12

$y + \frac{y}{3} = 12$

Step 1

Simplify $y + \frac{y}{3}$ .

To write $y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y \cdot \frac{3}{3} + \frac{y}{3} = 12$

Simplify terms.

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

$\frac{y \cdot 3}{3} + \frac{y}{3} = 12$

Combine the numerators over the common denominator.

$\frac{y \cdot 3 + y}{3} = 12$

Simplify the numerator.

Move $3$ to the left of $y$ .

$\frac{3 \cdot y + y}{3} = 12$

Add $3 y$ and $y$ .

$\frac{4 y}{3} = 12$

Step 2

Multiply both sides of the equation by $\frac{3}{4}$ .

$\frac{3}{4} \cdot \frac{4 y}{3} = \frac{3}{4} \cdot 12$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{4} \cdot \frac{4 y}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{4} \cdot \frac{4 y}{3} = \frac{3}{4} \cdot 12$

Rewrite the expression.

$\frac{1}{4} (4 y) = \frac{3}{4} \cdot 12$

Cancel the common factor of $4$ .

Factor $4$ out of $4 y$ .

$\frac{1}{4} (4 (y)) = \frac{3}{4} \cdot 12$

Cancel the common factor.

$\frac{1}{4} (4 y) = \frac{3}{4} \cdot 12$

Rewrite the expression.

$y = \frac{3}{4} \cdot 12$

Simplify the right side.

Simplify $\frac{3}{4} \cdot 12$ .

Cancel the common factor of $4$ .

Factor $4$ out of $12$ .

$y = \frac{3}{4} \cdot (4 (3))$

Cancel the common factor.

$y = \frac{3}{4} \cdot (4 \cdot 3)$

Rewrite the expression.

$y = 3 \cdot 3$

Multiply $3$ by $3$ .

$y = 9$