Finite Math Examples

$\frac{n}{3} - \frac{n - 11}{6} = \frac{9}{2}$

Step 1

Simplify $\frac{n}{3} - \frac{n - 11}{6}$ .

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Step 1.1

To write $\frac{n}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{n}{3} \cdot \frac{2}{2} - \frac{n - 11}{6} = \frac{9}{2}$

Step 1.2

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1

Multiply $\frac{n}{3}$ by $\frac{2}{2}$ .

$\frac{n \cdot 2}{3 \cdot 2} - \frac{n - 11}{6} = \frac{9}{2}$

Step 1.2.2

Multiply $3$ by $2$ .

$\frac{n \cdot 2}{6} - \frac{n - 11}{6} = \frac{9}{2}$

Step 1.3

Combine the numerators over the common denominator.

$\frac{n \cdot 2 - (n - 11)}{6} = \frac{9}{2}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Move $2$ to the left of $n$ .

$\frac{2 \cdot n - (n - 11)}{6} = \frac{9}{2}$

Step 1.4.2

Apply the distributive property.

$\frac{2 n - n - - 11}{6} = \frac{9}{2}$

Step 1.4.3

Multiply $- 1$ by $- 11$ .

$\frac{2 n - n + 11}{6} = \frac{9}{2}$

Step 1.4.4

Subtract $n$ from $2 n$ .

$\frac{n + 11}{6} = \frac{9}{2}$

Step 2

Multiply both sides of the equation by $6$ .

$6 \frac{n + 11}{6} = 6 (\frac{9}{2})$

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 $6$ .

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Step 3.1.1.1

Cancel the common factor.

$6 \frac{n + 11}{6} = 6 (\frac{9}{2})$

Step 3.1.1.2

Rewrite the expression.

$n + 11 = 6 (\frac{9}{2})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $6 (\frac{9}{2})$ .

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Step 3.2.1.1

Cancel the common factor of $2$ .

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Step 3.2.1.1.1

Factor $2$ out of $6$ .

$n + 11 = 2 (3) \frac{9}{2}$

Step 3.2.1.1.2

Cancel the common factor.

$n + 11 = 2 \cdot 3 \frac{9}{2}$

Step 3.2.1.1.3

Rewrite the expression.

$n + 11 = 3 \cdot 9$

Step 3.2.1.2

Multiply $3$ by $9$ .

$n + 11 = 27$

Step 4

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

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Step 4.1

Subtract $11$ from both sides of the equation.

$n = 27 - 11$

Step 4.2

Subtract $11$ from $27$ .

$n = 16$