Simplify 4/9z-3/9z+5-5/9z-8

$\frac{4}{9} z - \frac{3}{9} z + 5 - \frac{5}{9} z - 8$

Simplify each term.

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

$\frac{4 z}{9} - \frac{3}{9} z + 5 - \frac{5}{9} z - 8$

Cancel the common factor of $3$ and $9$ .

Factor $3$ out of $3$ .

$\frac{4 z}{9} - \frac{3 (1)}{9} z + 5 - \frac{5}{9} z - 8$

Cancel the common factors.

Factor $3$ out of $9$ .

$\frac{4 z}{9} - \frac{3 \cdot 1}{3 \cdot 3} z + 5 - \frac{5}{9} z - 8$

Cancel the common factor.

$\frac{4 z}{9} - \frac{3 \cdot 1}{3 \cdot 3} z + 5 - \frac{5}{9} z - 8$

Rewrite the expression.

$\frac{4 z}{9} - \frac{1}{3} z + 5 - \frac{5}{9} z - 8$

Combine $z$ and $\frac{1}{3}$ .

$\frac{4 z}{9} - \frac{z}{3} + 5 - \frac{5}{9} z - 8$

Combine $z$ and $\frac{5}{9}$ .

$\frac{4 z}{9} - \frac{z}{3} + 5 - \frac{z \cdot 5}{9} - 8$

Move $5$ to the left of $z$ .

$\frac{4 z}{9} - \frac{z}{3} + 5 - \frac{5 z}{9} - 8$

Simplify terms.

Combine the numerators over the common denominator.

$5 - 8 + \frac{4 z - 5 z}{9} + \frac{- z}{3}$

Subtract $5 z$ from $4 z$ .

$5 - 8 + \frac{- z}{9} + \frac{- z}{3}$

Simplify each term.

Move the negative in front of the fraction.

$5 - 8 - \frac{z}{9} + \frac{- z}{3}$

Move the negative in front of the fraction.

$5 - 8 - \frac{z}{9} - \frac{z}{3}$

Subtract $8$ from $5$ .

$- 3 - \frac{z}{9} - \frac{z}{3}$

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

$- 3 - \frac{z}{9} - \frac{z}{3} \cdot \frac{3}{3}$

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

Multiply $\frac{z}{3}$ by $\frac{3}{3}$ .

$- 3 - \frac{z}{9} - \frac{z \cdot 3}{3 \cdot 3}$

Multiply $3$ by $3$ .

$- 3 - \frac{z}{9} - \frac{z \cdot 3}{9}$

Combine the numerators over the common denominator.

$- 3 + \frac{- z - z \cdot 3}{9}$

Simplify each term.

Simplify the numerator.

Factor $z$ out of $- z - z \cdot 3$ .

Factor $z$ out of $- z$ .

$- 3 + \frac{z \cdot - 1 - z \cdot 3}{9}$

Factor $z$ out of $- z \cdot 3$ .

$- 3 + \frac{z \cdot - 1 + z (- 1 \cdot 3)}{9}$

Factor $z$ out of $z \cdot - 1 + z (- 1 \cdot 3)$ .

$- 3 + \frac{z (- 1 - 1 \cdot 3)}{9}$

Multiply $- 1$ by $3$ .

$- 3 + \frac{z (- 1 - 3)}{9}$

Subtract $3$ from $- 1$ .

$- 3 + \frac{z \cdot - 4}{9}$

Move $- 4$ to the left of $z$ .

$- 3 + \frac{- 4 \cdot z}{9}$

Move the negative in front of the fraction.

$- 3 - \frac{4 z}{9}$

Simplify 4/9z-3/9z+5-5/9z-8

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