Pre-Algebra Examples

$y = \frac{1}{3 x}$

Step 1

Rewrite the equation as $\frac{1}{3 x} = y$ .

$\frac{1}{3 x} = y$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$3 x, 1$

Step 2.2

The LCM of one and any expression is the expression.

$3 x$

Step 3

Multiply each term in $\frac{1}{3 x} = y$ by $3 x$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{1}{3 x} = y$ by $3 x$ .

$\frac{1}{3 x} (3 x) = y (3 x)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Rewrite using the commutative property of multiplication.

$3 \frac{1}{3 x} x = y (3 x)$

Step 3.2.2

Cancel the common factor of $3$ .

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Step 3.2.2.1

Factor $3$ out of $3 x$ .

$3 \frac{1}{3 (x)} x = y (3 x)$

Step 3.2.2.2

Cancel the common factor.

$3 \frac{1}{3 x} x = y (3 x)$

Step 3.2.2.3

Rewrite the expression.

$\frac{1}{x} x = y (3 x)$

Step 3.2.3

Cancel the common factor of $x$ .

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Step 3.2.3.1

Cancel the common factor.

$\frac{1}{x} x = y (3 x)$

Step 3.2.3.2

Rewrite the expression.

$1 = y (3 x)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Rewrite using the commutative property of multiplication.

$1 = 3 y x$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $3 y x = 1$ .

$3 y x = 1$

Step 4.2

Divide each term in $3 y x = 1$ by $3 y$ and simplify.

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Step 4.2.1

Divide each term in $3 y x = 1$ by $3 y$ .

$\frac{3 y x}{3 y} = \frac{1}{3 y}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $3$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{3 y x}{3 y} = \frac{1}{3 y}$

Step 4.2.2.1.2

Rewrite the expression.

$\frac{y x}{y} = \frac{1}{3 y}$

Step 4.2.2.2

Cancel the common factor of $y$ .

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Step 4.2.2.2.1

Cancel the common factor.

$\frac{y x}{y} = \frac{1}{3 y}$

Step 4.2.2.2.2

Divide $x$ by $1$ .

$x = \frac{1}{3 y}$