Pre-Algebra Examples

$\frac{12}{n} = \frac{\frac{2}{3}}{\frac{6}{9}}$

Step 1

Factor each term.

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Step 1.1

Cancel the common factor of $6$ and $9$ .

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Step 1.1.1

Factor $3$ out of $6$ .

$\frac{12}{n} = \frac{\frac{2}{3}}{\frac{3 (2)}{9}}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $3$ out of $9$ .

$\frac{12}{n} = \frac{\frac{2}{3}}{\frac{3 \cdot 2}{3 \cdot 3}}$

Step 1.1.2.2

Cancel the common factor.

$\frac{12}{n} = \frac{\frac{2}{3}}{\frac{3 \cdot 2}{3 \cdot 3}}$

Step 1.1.2.3

Rewrite the expression.

$\frac{12}{n} = \frac{\frac{2}{3}}{\frac{2}{3}}$

Step 1.2

Reduce the expression by cancelling the common factors.

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Step 1.2.1

Reduce the expression $\frac{\frac{2}{3}}{\frac{2}{3}}$ by cancelling the common factors.

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Step 1.2.1.1

Cancel the common factor.

$\frac{12}{n} = \frac{\frac{2}{3}}{\frac{2}{3}}$

Step 1.2.1.2

Rewrite the expression.

$\frac{12}{n} = \frac{1}{1}$

Step 1.2.2

Rewrite the expression.

$\frac{12}{n} = 1$

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.

$n, 1$

Step 2.2

The LCM of one and any expression is the expression.

$n$

Step 3

Multiply each term in $\frac{12}{n} = 1$ by $n$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{12}{n} = 1$ by $n$ .

$\frac{12}{n} n = 1 n$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $n$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{12}{n} n = 1 n$

Step 3.2.1.2

Rewrite the expression.

$12 = 1 n$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply $n$ by $1$ .

$12 = n$

Step 4

Rewrite the equation as $n = 12$ .

$n = 12$