Algebra Examples

$\frac{2}{y} = \frac{x}{3 z}$

Step 1

Rewrite the equation as $\frac{x}{3 z} = \frac{2}{y}$ .

$\frac{x}{3 z} = \frac{2}{y}$

Step 2

Multiply both sides by $3 z$ .

$\frac{x}{3 z} (3 z) = \frac{2}{y} (3 z)$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{x}{3 z} (3 z)$ .

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Step 3.1.1.1

Rewrite using the commutative property of multiplication.

$3 \frac{x}{3 z} z = \frac{2}{y} (3 z)$

Step 3.1.1.2

Cancel the common factor of $3$ .

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Step 3.1.1.2.1

Factor $3$ out of $3 z$ .

$3 \frac{x}{3 (z)} z = \frac{2}{y} (3 z)$

Step 3.1.1.2.2

Cancel the common factor.

$3 \frac{x}{3 z} z = \frac{2}{y} (3 z)$

Step 3.1.1.2.3

Rewrite the expression.

$\frac{x}{z} z = \frac{2}{y} (3 z)$

Step 3.1.1.3

Cancel the common factor of $z$ .

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Step 3.1.1.3.1

Cancel the common factor.

$\frac{x}{z} z = \frac{2}{y} (3 z)$

Step 3.1.1.3.2

Rewrite the expression.

$x = \frac{2}{y} (3 z)$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{2}{y} (3 z)$ .

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Step 3.2.1.1

Rewrite using the commutative property of multiplication.

$x = 3 \frac{2}{y} z$

Step 3.2.1.2

Multiply $3 \frac{2}{y}$ .

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Step 3.2.1.2.1

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

$x = \frac{3 \cdot 2}{y} z$

Step 3.2.1.2.2

Multiply $3$ by $2$ .

$x = \frac{6}{y} z$

Step 3.2.1.3

Combine $\frac{6}{y}$ and $z$ .

$x = \frac{6 z}{y}$