Pre-Algebra Examples

$\frac{n - 11}{4} + \frac{n + 2}{9} = \frac{13}{18}$

Step 1

Simplify $\frac{n - 11}{4} + \frac{n + 2}{9}$ .

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Step 1.1

To write $\frac{n - 11}{4}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{n - 11}{4} \cdot \frac{9}{9} + \frac{n + 2}{9} = \frac{13}{18}$

Step 1.2

To write $\frac{n + 2}{9}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{n - 11}{4} \cdot \frac{9}{9} + \frac{n + 2}{9} \cdot \frac{4}{4} = \frac{13}{18}$

Step 1.3

Write each expression with a common denominator of $36$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{n - 11}{4}$ by $\frac{9}{9}$ .

$\frac{(n - 11) \cdot 9}{4 \cdot 9} + \frac{n + 2}{9} \cdot \frac{4}{4} = \frac{13}{18}$

Step 1.3.2

Multiply $4$ by $9$ .

$\frac{(n - 11) \cdot 9}{36} + \frac{n + 2}{9} \cdot \frac{4}{4} = \frac{13}{18}$

Step 1.3.3

Multiply $\frac{n + 2}{9}$ by $\frac{4}{4}$ .

$\frac{(n - 11) \cdot 9}{36} + \frac{(n + 2) \cdot 4}{9 \cdot 4} = \frac{13}{18}$

Step 1.3.4

Multiply $9$ by $4$ .

$\frac{(n - 11) \cdot 9}{36} + \frac{(n + 2) \cdot 4}{36} = \frac{13}{18}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{(n - 11) \cdot 9 + (n + 2) \cdot 4}{36} = \frac{13}{18}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Apply the distributive property.

$\frac{n \cdot 9 - 11 \cdot 9 + (n + 2) \cdot 4}{36} = \frac{13}{18}$

Step 1.5.2

Move $9$ to the left of $n$ .

$\frac{9 \cdot n - 11 \cdot 9 + (n + 2) \cdot 4}{36} = \frac{13}{18}$

Step 1.5.3

Multiply $- 11$ by $9$ .

$\frac{9 \cdot n - 99 + (n + 2) \cdot 4}{36} = \frac{13}{18}$

Step 1.5.4

Apply the distributive property.

$\frac{9 n - 99 + n \cdot 4 + 2 \cdot 4}{36} = \frac{13}{18}$

Step 1.5.5

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

$\frac{9 n - 99 + 4 \cdot n + 2 \cdot 4}{36} = \frac{13}{18}$

Step 1.5.6

Multiply $2$ by $4$ .

$\frac{9 n - 99 + 4 \cdot n + 8}{36} = \frac{13}{18}$

Step 1.5.7

Add $9 n$ and $4 n$ .

$\frac{13 n - 99 + 8}{36} = \frac{13}{18}$

Step 1.5.8

Add $- 99$ and $8$ .

$\frac{13 n - 91}{36} = \frac{13}{18}$

Step 1.5.9

Factor $13$ out of $13 n - 91$ .

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Step 1.5.9.1

Factor $13$ out of $13 n$ .

$\frac{13 (n) - 91}{36} = \frac{13}{18}$

Step 1.5.9.2

Factor $13$ out of $- 91$ .

$\frac{13 n + 13 \cdot - 7}{36} = \frac{13}{18}$

Step 1.5.9.3

Factor $13$ out of $13 n + 13 \cdot - 7$ .

$\frac{13 (n - 7)}{36} = \frac{13}{18}$

Step 2

Multiply both sides of the equation by $\frac{36}{13}$ .

$\frac{36}{13} \cdot \frac{13 (n - 7)}{36} = \frac{36}{13} \cdot \frac{13}{18}$

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 $\frac{36}{13} \cdot \frac{13 (n - 7)}{36}$ .

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Step 3.1.1.1

Cancel the common factor of $36$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{36}{13} \cdot \frac{13 (n - 7)}{36} = \frac{36}{13} \cdot \frac{13}{18}$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{13} (13 (n - 7)) = \frac{36}{13} \cdot \frac{13}{18}$

Step 3.1.1.2

Cancel the common factor of $13$ .

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Step 3.1.1.2.1

Cancel the common factor.

$\frac{1}{13} (13 (n - 7)) = \frac{36}{13} \cdot \frac{13}{18}$

Step 3.1.1.2.2

Rewrite the expression.

$n - 7 = \frac{36}{13} \cdot \frac{13}{18}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{36}{13} \cdot \frac{13}{18}$ .

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Step 3.2.1.1

Cancel the common factor of $18$ .

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Step 3.2.1.1.1

Factor $18$ out of $36$ .

$n - 7 = \frac{18 (2)}{13} \cdot \frac{13}{18}$

Step 3.2.1.1.2

Cancel the common factor.

$n - 7 = \frac{18 \cdot 2}{13} \cdot \frac{13}{18}$

Step 3.2.1.1.3

Rewrite the expression.

$n - 7 = \frac{2}{13} \cdot 13$

Step 3.2.1.2

Cancel the common factor of $13$ .

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Step 3.2.1.2.1

Cancel the common factor.

$n - 7 = \frac{2}{13} \cdot 13$

Step 3.2.1.2.2

Rewrite the expression.

$n - 7 = 2$

Step 4

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

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Step 4.1

Add $7$ to both sides of the equation.

$n = 2 + 7$

Step 4.2

Add $2$ and $7$ .

$n = 9$