Algebra Examples

\frac{x}{5} = 2 \frac{1}{2}

$\frac{x}{5} = 2 \frac{1}{2}$

Step 1

Simplify the right side.

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Step 1.1

Convert

2 \frac{1}{2}

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

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Step 1.1.1

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

\frac{x}{5} = 2 + \frac{1}{2}

$\frac{x}{5} = 2 + \frac{1}{2}$

Step 1.1.2

Add

2

$2$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 1.1.2.1

To write

2

$2$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{x}{5} = 2 \cdot \frac{2}{2} + \frac{1}{2}

$\frac{x}{5} = 2 \cdot \frac{2}{2} + \frac{1}{2}$

Step 1.1.2.2

Combine

2

$2$ and

\frac{2}{2}

$\frac{2}{2}$ .

\frac{x}{5} = \frac{2 \cdot 2}{2} + \frac{1}{2}

$\frac{x}{5} = \frac{2 \cdot 2}{2} + \frac{1}{2}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$\frac{x}{5} = \frac{2 \cdot 2 + 1}{2}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply

$2$ by

$2$ .

$\frac{x}{5} = \frac{4 + 1}{2}$

Step 1.1.2.4.2

Add

$4$ and

$1$ .

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

Step 2

Multiply both sides of the equation by

$5$ .

$5 \frac{x}{5} = 5 (\frac{5}{2})$

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

$5$ .

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Step 3.1.1.1

Cancel the common factor.

$5 \frac{x}{5} = 5 (\frac{5}{2})$

Step 3.1.1.2

Rewrite the expression.

$x = 5 (\frac{5}{2})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply

$5 (\frac{5}{2})$ .

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Step 3.2.1.1

Combine

$5$ and

$\frac{5}{2}$ .

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

Step 3.2.1.2

Multiply

$5$ by

$5$ .

$x = \frac{25}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{25}{2}$

Decimal Form:

$x = 12.5$

Mixed Number Form:

$x = 12 \frac{1}{2}$