Pre-Algebra Examples

$\frac{1}{15} x = 4 \frac{1}{2}$

Step 1

Simplify the left side.

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Step 1.1

Combine $\frac{1}{15}$ and $x$ .

$\frac{x}{15} = 4 \frac{1}{2}$

Step 2

Simplify the right side.

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Step 2.1

Convert $4 \frac{1}{2}$ to an improper fraction.

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Step 2.1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{x}{15} = 4 + \frac{1}{2}$

Step 2.1.2

Add $4$ and $\frac{1}{2}$ .

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Step 2.1.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x}{15} = 4 \cdot \frac{2}{2} + \frac{1}{2}$

Step 2.1.2.2

Combine $4$ and $\frac{2}{2}$ .

$\frac{x}{15} = \frac{4 \cdot 2}{2} + \frac{1}{2}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$\frac{x}{15} = \frac{4 \cdot 2 + 1}{2}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $4$ by $2$ .

$\frac{x}{15} = \frac{8 + 1}{2}$

Step 2.1.2.4.2

Add $8$ and $1$ .

$\frac{x}{15} = \frac{9}{2}$

Step 3

Multiply both sides of the equation by $15$ .

$15 \frac{x}{15} = 15 (\frac{9}{2})$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $15$ .

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Step 4.1.1.1

Cancel the common factor.

$15 \frac{x}{15} = 15 (\frac{9}{2})$

Step 4.1.1.2

Rewrite the expression.

$x = 15 (\frac{9}{2})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $15 (\frac{9}{2})$ .

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Step 4.2.1.1

Combine $15$ and $\frac{9}{2}$ .

$x = \frac{15 \cdot 9}{2}$

Step 4.2.1.2

Multiply $15$ by $9$ .

$x = \frac{135}{2}$