Evaluate 4/9(2n-3)

$\frac{4}{9} (2 n - 3)$

Step 1

Apply the distributive property.

$\frac{4}{9} (2 n) + \frac{4}{9} \cdot - 3$

Step 2

Multiply $\frac{4}{9} (2 n)$ .

Combine $2$ and $\frac{4}{9}$ .

$\frac{2 \cdot 4}{9} n + \frac{4}{9} \cdot - 3$

Multiply $2$ by $4$ .

$\frac{8}{9} n + \frac{4}{9} \cdot - 3$

Combine $\frac{8}{9}$ and $n$ .

$\frac{8 n}{9} + \frac{4}{9} \cdot - 3$

Step 3

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$\frac{8 n}{9} + \frac{4}{3 (3)} \cdot - 3$

Factor $3$ out of $- 3$ .

$\frac{8 n}{9} + \frac{4}{3 \cdot 3} \cdot (3 \cdot - 1)$

Cancel the common factor.

$\frac{8 n}{9} + \frac{4}{3 \cdot 3} \cdot (3 \cdot - 1)$

Rewrite the expression.

$\frac{8 n}{9} + \frac{4}{3} \cdot - 1$

Step 4

Combine $\frac{4}{3}$ and $- 1$ .

$\frac{8 n}{9} + \frac{4 \cdot - 1}{3}$

Step 5

Simplify the expression.

Multiply $4$ by $- 1$ .

$\frac{8 n}{9} + \frac{- 4}{3}$

Move the negative in front of the fraction.

$\frac{8 n}{9} - \frac{4}{3}$