Finite Math Examples

$\frac{1}{15} x + \frac{1}{12} x = 1$

Step 1

Simplify $\frac{1}{15} x + \frac{1}{12} x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$\frac{x}{15} + \frac{1}{12} x = 1$

Step 1.1.2

Combine $\frac{1}{12}$ and $x$ .

$\frac{x}{15} + \frac{x}{12} = 1$

Step 1.2

To write $\frac{x}{15}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x}{15} \cdot \frac{4}{4} + \frac{x}{12} = 1$

Step 1.3

To write $\frac{x}{12}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{x}{15} \cdot \frac{4}{4} + \frac{x}{12} \cdot \frac{5}{5} = 1$

Step 1.4

Write each expression with a common denominator of $60$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{x}{15}$ by $\frac{4}{4}$ .

$\frac{x \cdot 4}{15 \cdot 4} + \frac{x}{12} \cdot \frac{5}{5} = 1$

Step 1.4.2

Multiply $15$ by $4$ .

$\frac{x \cdot 4}{60} + \frac{x}{12} \cdot \frac{5}{5} = 1$

Step 1.4.3

Multiply $\frac{x}{12}$ by $\frac{5}{5}$ .

$\frac{x \cdot 4}{60} + \frac{x \cdot 5}{12 \cdot 5} = 1$

Step 1.4.4

Multiply $12$ by $5$ .

$\frac{x \cdot 4}{60} + \frac{x \cdot 5}{60} = 1$

Step 1.5

Combine the numerators over the common denominator.

$\frac{x \cdot 4 + x \cdot 5}{60} = 1$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Move $4$ to the left of $x$ .

$\frac{4 \cdot x + x \cdot 5}{60} = 1$

Step 1.6.2

Move $5$ to the left of $x$ .

$\frac{4 x + 5 \cdot x}{60} = 1$

Step 1.6.3

Add $4 x$ and $5 x$ .

$\frac{9 x}{60} = 1$

Step 1.7

Cancel the common factor of $9$ and $60$ .

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Step 1.7.1

Factor $3$ out of $9 x$ .

$\frac{3 (3 x)}{60} = 1$

Step 1.7.2

Cancel the common factors.

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Step 1.7.2.1

Factor $3$ out of $60$ .

$\frac{3 (3 x)}{3 (20)} = 1$

Step 1.7.2.2

Cancel the common factor.

$\frac{3 (3 x)}{3 \cdot 20} = 1$

Step 1.7.2.3

Rewrite the expression.

$\frac{3 x}{20} = 1$

Step 2

Multiply both sides of the equation by $\frac{20}{3}$ .

$\frac{20}{3} \cdot \frac{3 x}{20} = \frac{20}{3} \cdot 1$

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

Simplify $\frac{20}{3} \cdot \frac{3 x}{20}$ .

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Step 3.1.1.1

Cancel the common factor of $20$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{20}{3} \cdot \frac{3 x}{20} = \frac{20}{3} \cdot 1$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{20}{3} \cdot 1$

Step 3.1.1.2

Cancel the common factor of $3$ .

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Step 3.1.1.2.1

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{20}{3} \cdot 1$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{20}{3} \cdot 1$

Step 3.1.1.2.3

Rewrite the expression.

$x = \frac{20}{3} \cdot 1$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $\frac{20}{3}$ by $1$ .

$x = \frac{20}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{20}{3}$

Decimal Form:

$x = 6.\overline{6}$

Mixed Number Form:

$x = 6 \frac{2}{3}$