Basic Math Examples

$f = \frac{1}{3} \cdot (g + h - k)$

Step 1

Rewrite the equation as $\frac{1}{3} \cdot (g + h - k) = f$ .

$\frac{1}{3} \cdot (g + h - k) = f$

Step 2

Multiply both sides of the equation by $3$ .

$3 (\frac{1}{3} \cdot (g + h - k)) = 3 f$

Step 3

Simplify the left side.

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Step 3.1

Simplify $3 (\frac{1}{3} \cdot (g + h - k))$ .

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Step 3.1.1

Apply the distributive property.

$3 (\frac{1}{3} g + \frac{1}{3} h + \frac{1}{3} (- k)) = 3 f$

Step 3.1.2

Simplify.

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Step 3.1.2.1

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

$3 (\frac{g}{3} + \frac{1}{3} h + \frac{1}{3} (- k)) = 3 f$

Step 3.1.2.2

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

$3 (\frac{g}{3} + \frac{h}{3} + \frac{1}{3} (- k)) = 3 f$

Step 3.1.2.3

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

$3 (\frac{g}{3} + \frac{h}{3} - \frac{k}{3}) = 3 f$

Step 3.1.3

Apply the distributive property.

$3 \frac{g}{3} + 3 \frac{h}{3} + 3 (- \frac{k}{3}) = 3 f$

Step 3.1.4

Simplify.

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Step 3.1.4.1

Cancel the common factor of $3$ .

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Step 3.1.4.1.1

Cancel the common factor.

$3 \frac{g}{3} + 3 \frac{h}{3} + 3 (- \frac{k}{3}) = 3 f$

Step 3.1.4.1.2

Rewrite the expression.

$g + 3 \frac{h}{3} + 3 (- \frac{k}{3}) = 3 f$

Step 3.1.4.2

Cancel the common factor of $3$ .

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Step 3.1.4.2.1

Cancel the common factor.

$g + 3 \frac{h}{3} + 3 (- \frac{k}{3}) = 3 f$

Step 3.1.4.2.2

Rewrite the expression.

$g + h + 3 (- \frac{k}{3}) = 3 f$

Step 3.1.4.3

Cancel the common factor of $3$ .

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Step 3.1.4.3.1

Move the leading negative in $- \frac{k}{3}$ into the numerator.

$g + h + 3 \frac{- k}{3} = 3 f$

Step 3.1.4.3.2

Cancel the common factor.

$g + h + 3 \frac{- k}{3} = 3 f$

Step 3.1.4.3.3

Rewrite the expression.

$g + h - k = 3 f$

Step 4

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

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Step 4.1

Subtract $h$ from both sides of the equation.

$g - k = 3 f - h$

Step 4.2

Add $k$ to both sides of the equation.

$g = 3 f - h + k$