Basic Math Examples

$\frac{1}{3} \cdot (3 w + 4) - \frac{2}{3} = - \frac{1}{3}$

Step 1

Simplify $\frac{1}{3} \cdot (3 w + 4) - \frac{2}{3}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{1}{3} (3 w) + \frac{1}{3} \cdot 4 - \frac{2}{3} = - \frac{1}{3}$

Step 1.1.2

Cancel the common factor of $3$ .

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Step 1.1.2.1

Factor $3$ out of $3 w$ .

$\frac{1}{3} (3 (w)) + \frac{1}{3} \cdot 4 - \frac{2}{3} = - \frac{1}{3}$

Step 1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 w) + \frac{1}{3} \cdot 4 - \frac{2}{3} = - \frac{1}{3}$

Step 1.1.2.3

Rewrite the expression.

$w + \frac{1}{3} \cdot 4 - \frac{2}{3} = - \frac{1}{3}$

Step 1.1.3

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

$w + \frac{4}{3} - \frac{2}{3} = - \frac{1}{3}$

Step 1.2

Combine fractions.

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Step 1.2.1

Combine the numerators over the common denominator.

$w + \frac{4 - 2}{3} = - \frac{1}{3}$

Step 1.2.2

Subtract $2$ from $4$ .

$w + \frac{2}{3} = - \frac{1}{3}$

Step 2

Move all terms not containing $w$ to the right side of the equation.

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Step 2.1

Subtract $\frac{2}{3}$ from both sides of the equation.

$w = - \frac{1}{3} - \frac{2}{3}$

Step 2.2

Combine the numerators over the common denominator.

$w = \frac{- 1 - 2}{3}$

Step 2.3

Subtract $2$ from $- 1$ .

$w = \frac{- 3}{3}$

Step 2.4

Divide $- 3$ by $3$ .

$w = - 1$