Pre-Algebra Examples

$\frac{4}{\frac{5}{4}} = \frac{x}{12}$

Step 1

Rewrite the equation as $\frac{x}{12} = \frac{4}{\frac{5}{4}}$ .

$\frac{x}{12} = \frac{4}{\frac{5}{4}}$

Step 2

Multiply both sides of the equation by $12$ .

$12 \frac{x}{12} = 12 \frac{4}{\frac{5}{4}}$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $12$ .

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Step 3.1.1.1

Cancel the common factor.

$12 \frac{x}{12} = 12 \frac{4}{\frac{5}{4}}$

Step 3.1.1.2

Rewrite the expression.

$x = 12 \frac{4}{\frac{5}{4}}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $12 \frac{4}{\frac{5}{4}}$ .

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Step 3.2.1.1

Multiply the numerator by the reciprocal of the denominator.

$x = 12 (4 (\frac{4}{5}))$

Step 3.2.1.2

Multiply $4 (\frac{4}{5})$ .

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Step 3.2.1.2.1

Combine $4$ and $\frac{4}{5}$ .

$x = 12 \frac{4 \cdot 4}{5}$

Step 3.2.1.2.2

Multiply $4$ by $4$ .

$x = 12 (\frac{16}{5})$

Step 3.2.1.3

Multiply $12 (\frac{16}{5})$ .

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Step 3.2.1.3.1

Combine $12$ and $\frac{16}{5}$ .

$x = \frac{12 \cdot 16}{5}$

Step 3.2.1.3.2

Multiply $12$ by $16$ .

$x = \frac{192}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{192}{5}$

Decimal Form:

$x = 38.4$

Mixed Number Form:

$x = 38 \frac{2}{5}$