Basic Math Examples

$\frac{z}{6} - \frac{z}{3} = \frac{z}{12}$

Step 1

Multiply both sides by $12$ .

$(\frac{z}{6} - \frac{z}{3}) \cdot 12 = \frac{z}{12} \cdot 12$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{z}{6} - \frac{z}{3}) \cdot 12$ .

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Step 2.1.1.1

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

$(\frac{z}{6} - \frac{z}{3} \cdot \frac{2}{2}) \cdot 12 = \frac{z}{12} \cdot 12$

Step 2.1.1.2

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1.1.2.1

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

$(\frac{z}{6} - \frac{z \cdot 2}{3 \cdot 2}) \cdot 12 = \frac{z}{12} \cdot 12$

Step 2.1.1.2.2

Multiply $3$ by $2$ .

$(\frac{z}{6} - \frac{z \cdot 2}{6}) \cdot 12 = \frac{z}{12} \cdot 12$

Step 2.1.1.3

Combine the numerators over the common denominator.

$\frac{z - z \cdot 2}{6} \cdot 12 = \frac{z}{12} \cdot 12$

Step 2.1.1.4

Simplify the numerator.

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Step 2.1.1.4.1

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

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Step 2.1.1.4.1.1

Raise $z$ to the power of $1$ .

$\frac{z^{1} - z \cdot 2}{6} \cdot 12 = \frac{z}{12} \cdot 12$

Step 2.1.1.4.1.2

Factor $z$ out of $z^{1}$ .

$\frac{z \cdot 1 - z \cdot 2}{6} \cdot 12 = \frac{z}{12} \cdot 12$

Step 2.1.1.4.1.3

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

$\frac{z \cdot 1 + z (- 1 \cdot 2)}{6} \cdot 12 = \frac{z}{12} \cdot 12$

Step 2.1.1.4.1.4

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

$\frac{z (1 - 1 \cdot 2)}{6} \cdot 12 = \frac{z}{12} \cdot 12$

Step 2.1.1.4.2

Multiply $- 1$ by $2$ .

$\frac{z (1 - 2)}{6} \cdot 12 = \frac{z}{12} \cdot 12$

Step 2.1.1.4.3

Subtract $2$ from $1$ .

$\frac{z \cdot - 1}{6} \cdot 12 = \frac{z}{12} \cdot 12$

Step 2.1.1.5

Reduce the expression by cancelling the common factors.

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Step 2.1.1.5.1

Cancel the common factor of $6$ .

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Step 2.1.1.5.1.1

Factor $6$ out of $12$ .

$\frac{z \cdot - 1}{6} \cdot (6 (2)) = \frac{z}{12} \cdot 12$

Step 2.1.1.5.1.2

Cancel the common factor.

$\frac{z \cdot - 1}{6} \cdot (6 \cdot 2) = \frac{z}{12} \cdot 12$

Step 2.1.1.5.1.3

Rewrite the expression.

$z \cdot - 1 \cdot 2 = \frac{z}{12} \cdot 12$

Step 2.1.1.5.2

Simplify the expression.

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Step 2.1.1.5.2.1

Multiply $2$ by $- 1$ .

$z \cdot - 2 = \frac{z}{12} \cdot 12$

Step 2.1.1.5.2.2

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

$- 2 z = \frac{z}{12} \cdot 12$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $12$ .

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Step 2.2.1.1

Cancel the common factor.

$- 2 z = \frac{z}{12} \cdot 12$

Step 2.2.1.2

Rewrite the expression.

$- 2 z = z$

Step 3

Solve for $z$ .

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Step 3.1

Move all terms containing $z$ to the left side of the equation.

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Step 3.1.1

Subtract $z$ from both sides of the equation.

$- 2 z - z = 0$

Step 3.1.2

Subtract $z$ from $- 2 z$ .

$- 3 z = 0$

Step 3.2

Divide each term in $- 3 z = 0$ by $- 3$ and simplify.

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Step 3.2.1

Divide each term in $- 3 z = 0$ by $- 3$ .

$\frac{- 3 z}{- 3} = \frac{0}{- 3}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 3$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 3 z}{- 3} = \frac{0}{- 3}$

Step 3.2.2.1.2

Divide $z$ by $1$ .

$z = \frac{0}{- 3}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $0$ by $- 3$ .

$z = 0$