Algebra Examples

$- \frac{1}{9} (5 G - 3) + \frac{2}{9} G$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- \frac{1}{9} (5 G) - \frac{1}{9} \cdot - 3 + \frac{2}{9} G$

Step 1.2

Multiply $- \frac{1}{9} (5 G)$ .

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Step 1.2.1

Multiply $5$ by $- 1$ .

$- 5 (\frac{1}{9}) G - \frac{1}{9} \cdot - 3 + \frac{2}{9} G$

Step 1.2.2

Combine $- 5$ and $\frac{1}{9}$ .

$\frac{- 5}{9} G - \frac{1}{9} \cdot - 3 + \frac{2}{9} G$

Step 1.2.3

Combine $\frac{- 5}{9}$ and $G$ .

$\frac{- 5 G}{9} - \frac{1}{9} \cdot - 3 + \frac{2}{9} G$

Step 1.3

Cancel the common factor of $3$ .

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Step 1.3.1

Move the leading negative in $- \frac{1}{9}$ into the numerator.

$\frac{- 5 G}{9} + \frac{- 1}{9} \cdot - 3 + \frac{2}{9} G$

Step 1.3.2

Factor $3$ out of $9$ .

$\frac{- 5 G}{9} + \frac{- 1}{3 (3)} \cdot - 3 + \frac{2}{9} G$

Step 1.3.3

Factor $3$ out of $- 3$ .

$\frac{- 5 G}{9} + \frac{- 1}{3 \cdot 3} \cdot (3 \cdot - 1) + \frac{2}{9} G$

Step 1.3.4

Cancel the common factor.

$\frac{- 5 G}{9} + \frac{- 1}{3 \cdot 3} \cdot (3 \cdot - 1) + \frac{2}{9} G$

Step 1.3.5

Rewrite the expression.

$\frac{- 5 G}{9} + \frac{- 1}{3} \cdot - 1 + \frac{2}{9} G$

Step 1.4

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

$\frac{- 5 G}{9} + \frac{- - 1}{3} + \frac{2}{9} G$

Step 1.5

Multiply $- 1$ by $- 1$ .

$\frac{- 5 G}{9} + \frac{1}{3} + \frac{2}{9} G$

Step 1.6

Move the negative in front of the fraction.

$- \frac{5 G}{9} + \frac{1}{3} + \frac{2}{9} G$

Step 1.7

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

$- \frac{5 G}{9} + \frac{1}{3} + \frac{2 G}{9}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{- 5 G + 2 G}{9} + \frac{1}{3}$

Step 2.2

Add $- 5 G$ and $2 G$ .

$\frac{- 3 G}{9} + \frac{1}{3}$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Factor $3$ out of $- 3 G$ .

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

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $3$ out of $9$ .

$\frac{3 (- G)}{3 (3)} + \frac{1}{3}$

Step 3.1.2.2

Cancel the common factor.

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

Step 3.1.2.3

Rewrite the expression.

$\frac{- G}{3} + \frac{1}{3}$

Step 3.2

Move the negative in front of the fraction.

$- \frac{G}{3} + \frac{1}{3}$