Finite Math Examples

$\frac{x}{6} + \frac{x}{5} = \frac{11}{30}$

Step 1

Simplify $\frac{x}{6} + \frac{x}{5}$ .

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Step 1.1

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

$\frac{x}{6} \cdot \frac{5}{5} + \frac{x}{5} = \frac{11}{30}$

Step 1.2

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

$\frac{x}{6} \cdot \frac{5}{5} + \frac{x}{5} \cdot \frac{6}{6} = \frac{11}{30}$

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 $\frac{x}{6}$ by $\frac{5}{5}$ .

$\frac{x \cdot 5}{6 \cdot 5} + \frac{x}{5} \cdot \frac{6}{6} = \frac{11}{30}$

Step 1.3.2

Multiply $6$ by $5$ .

$\frac{x \cdot 5}{30} + \frac{x}{5} \cdot \frac{6}{6} = \frac{11}{30}$

Step 1.3.3

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

$\frac{x \cdot 5}{30} + \frac{x \cdot 6}{5 \cdot 6} = \frac{11}{30}$

Step 1.3.4

Multiply $5$ by $6$ .

$\frac{x \cdot 5}{30} + \frac{x \cdot 6}{30} = \frac{11}{30}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x \cdot 5 + x \cdot 6}{30} = \frac{11}{30}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

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

$\frac{5 \cdot x + x \cdot 6}{30} = \frac{11}{30}$

Step 1.5.2

Move $6$ to the left of $x$ .

$\frac{5 x + 6 \cdot x}{30} = \frac{11}{30}$

Step 1.5.3

Add $5 x$ and $6 x$ .

$\frac{11 x}{30} = \frac{11}{30}$

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$11 x = 11$

Step 3

Divide each term in $11 x = 11$ by $11$ and simplify.

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Step 3.1

Divide each term in $11 x = 11$ by $11$ .

$\frac{11 x}{11} = \frac{11}{11}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $11$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{11 x}{11} = \frac{11}{11}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{11}{11}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $11$ by $11$ .

$x = 1$