Finite Math Examples

$\frac{x}{15} + \frac{1}{5} = \frac{1}{30}$

Step 1

Move all terms not containing $x$ to the right side of the equation.

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Step 1.1

Subtract $\frac{1}{5}$ from both sides of the equation.

$\frac{x}{15} = \frac{1}{30} - \frac{1}{5}$

Step 1.2

To write $- \frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{x}{15} = \frac{1}{30} - \frac{1}{5} \cdot \frac{6}{6}$

Step 1.3

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{1}{5}$ by $\frac{6}{6}$ .

$\frac{x}{15} = \frac{1}{30} - \frac{6}{5 \cdot 6}$

Step 1.3.2

Multiply $5$ by $6$ .

$\frac{x}{15} = \frac{1}{30} - \frac{6}{30}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x}{15} = \frac{1 - 6}{30}$

Step 1.5

Subtract $6$ from $1$ .

$\frac{x}{15} = \frac{- 5}{30}$

Step 1.6

Cancel the common factor of $- 5$ and $30$ .

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Step 1.6.1

Factor $5$ out of $- 5$ .

$\frac{x}{15} = \frac{5 (- 1)}{30}$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $5$ out of $30$ .

$\frac{x}{15} = \frac{5 \cdot - 1}{5 \cdot 6}$

Step 1.6.2.2

Cancel the common factor.

$\frac{x}{15} = \frac{5 \cdot - 1}{5 \cdot 6}$

Step 1.6.2.3

Rewrite the expression.

$\frac{x}{15} = \frac{- 1}{6}$

Step 1.7

Move the negative in front of the fraction.

$\frac{x}{15} = - \frac{1}{6}$

Step 2

Multiply both sides of the equation by $15$ .

$15 \frac{x}{15} = 15 (- \frac{1}{6})$

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 $15$ .

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Step 3.1.1.1

Cancel the common factor.

$15 \frac{x}{15} = 15 (- \frac{1}{6})$

Step 3.1.1.2

Rewrite the expression.

$x = 15 (- \frac{1}{6})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $15 (- \frac{1}{6})$ .

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Step 3.2.1.1

Cancel the common factor of $3$ .

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Step 3.2.1.1.1

Move the leading negative in $- \frac{1}{6}$ into the numerator.

$x = 15 (\frac{- 1}{6})$

Step 3.2.1.1.2

Factor $3$ out of $15$ .

$x = 3 (5) \frac{- 1}{6}$

Step 3.2.1.1.3

Factor $3$ out of $6$ .

$x = 3 \cdot 5 \frac{- 1}{3 \cdot 2}$

Step 3.2.1.1.4

Cancel the common factor.

$x = 3 \cdot 5 \frac{- 1}{3 \cdot 2}$

Step 3.2.1.1.5

Rewrite the expression.

$x = 5 (\frac{- 1}{2})$

Step 3.2.1.2

Combine $5$ and $\frac{- 1}{2}$ .

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

Step 3.2.1.3

Simplify the expression.

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Step 3.2.1.3.1

Multiply $5$ by $- 1$ .

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

Step 3.2.1.3.2

Move the negative in front of the fraction.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 2.5$

Mixed Number Form:

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