Simplify (3(a-b))/9+4/9b

$\frac{3 (a - b)}{9} + \frac{4}{9} b$

Simplify each term.

Cancel the common factors.

Factor $3$ out of $9$ .

$\frac{3 (a - b)}{3 \cdot 3} + \frac{4}{9} b$

Cancel the common factor.

$\frac{3 (a - b)}{3 \cdot 3} + \frac{4}{9} b$

Rewrite the expression.

$\frac{a - b}{3} + \frac{4}{9} b$

Combine $\frac{4}{9}$ and $b$ .

$\frac{a - b}{3} + \frac{4 b}{9}$

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

$\frac{a - b}{3} \cdot \frac{3}{3} + \frac{4 b}{9}$

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{a - b}{3}$ by $\frac{3}{3}$ .

$\frac{(a - b) \cdot 3}{3 \cdot 3} + \frac{4 b}{9}$

Multiply $3$ by $3$ .

$\frac{(a - b) \cdot 3}{9} + \frac{4 b}{9}$

Combine the numerators over the common denominator.

$\frac{(a - b) \cdot 3 + 4 b}{9}$

Simplify the numerator.

Apply the distributive property.

$\frac{a \cdot 3 - b \cdot 3 + 4 b}{9}$

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

$\frac{3 \cdot a - b \cdot 3 + 4 b}{9}$

Multiply $3$ by $- 1$ .

$\frac{3 \cdot a - 3 b + 4 b}{9}$

Add $- 3 b$ and $4 b$ .

$\frac{3 a + b}{9}$