Algebra Examples

$\frac{7}{9} z - \frac{6}{9} z + 2 - \frac{5}{9} z - 9$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{7}{9}$ and $z$ .

$\frac{7 z}{9} - \frac{6}{9} z + 2 - \frac{5}{9} z - 9$

Step 1.2

Cancel the common factor of $6$ and $9$ .

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Step 1.2.1

Factor $3$ out of $6$ .

$\frac{7 z}{9} - \frac{3 (2)}{9} z + 2 - \frac{5}{9} z - 9$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $3$ out of $9$ .

$\frac{7 z}{9} - \frac{3 \cdot 2}{3 \cdot 3} z + 2 - \frac{5}{9} z - 9$

Step 1.2.2.2

Cancel the common factor.

$\frac{7 z}{9} - \frac{3 \cdot 2}{3 \cdot 3} z + 2 - \frac{5}{9} z - 9$

Step 1.2.2.3

Rewrite the expression.

$\frac{7 z}{9} - \frac{2}{3} z + 2 - \frac{5}{9} z - 9$

Step 1.3

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

$\frac{7 z}{9} - \frac{z \cdot 2}{3} + 2 - \frac{5}{9} z - 9$

Step 1.4

Move $2$ to the left of $z$ .

$\frac{7 z}{9} - \frac{2 \cdot z}{3} + 2 - \frac{5}{9} z - 9$

Step 1.5

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

$\frac{7 z}{9} - \frac{2 z}{3} + 2 - \frac{z \cdot 5}{9} - 9$

Step 1.6

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

$\frac{7 z}{9} - \frac{2 z}{3} + 2 - \frac{5 z}{9} - 9$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$2 - 9 + \frac{7 z - 5 z}{9} + \frac{- 2 z}{3}$

Step 2.2

Subtract $5 z$ from $7 z$ .

$2 - 9 + \frac{2 z}{9} + \frac{- 2 z}{3}$

Step 2.3

Simplify the expression.

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Step 2.3.1

Move the negative in front of the fraction.

$2 - 9 + \frac{2 z}{9} - \frac{2 z}{3}$

Step 2.3.2

Subtract $9$ from $2$ .

$- 7 + \frac{2 z}{9} - \frac{2 z}{3}$

Step 3

To write $- \frac{2 z}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- 7 + \frac{2 z}{9} - \frac{2 z}{3} \cdot \frac{3}{3}$

Step 4

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

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Step 4.1

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

$- 7 + \frac{2 z}{9} - \frac{2 z \cdot 3}{3 \cdot 3}$

Step 4.2

Multiply $3$ by $3$ .

$- 7 + \frac{2 z}{9} - \frac{2 z \cdot 3}{9}$

Step 5

Combine the numerators over the common denominator.

$- 7 + \frac{2 z - 2 z \cdot 3}{9}$

Step 6

Simplify each term.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Factor $2 z$ out of $2 z - 2 z \cdot 3$ .

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Step 6.1.1.1

Factor $2 z$ out of $2 z$ .

$- 7 + \frac{2 z (1) - 2 z \cdot 3}{9}$

Step 6.1.1.2

Factor $2 z$ out of $- 2 z \cdot 3$ .

$- 7 + \frac{2 z (1) + 2 z (- 1 \cdot 3)}{9}$

Step 6.1.1.3

Factor $2 z$ out of $2 z (1) + 2 z (- 1 \cdot 3)$ .

$- 7 + \frac{2 z (1 - 1 \cdot 3)}{9}$

Step 6.1.2

Multiply $- 1$ by $3$ .

$- 7 + \frac{2 z (1 - 3)}{9}$

Step 6.1.3

Subtract $3$ from $1$ .

$- 7 + \frac{2 z \cdot - 2}{9}$

Step 6.1.4

Multiply $- 2$ by $2$ .

$- 7 + \frac{- 4 z}{9}$

Step 6.2

Move the negative in front of the fraction.

$- 7 - \frac{4 z}{9}$