Basic Math Examples

$(n + 2) + (n - 2) + (n \cdot 2) + (\frac{n}{2}) = 45$

Step 1

Simplify $n + 2 + n - 2 + n \cdot 2 + \frac{n}{2}$ .

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Step 1.1

Combine the opposite terms in $n + 2 + n - 2 + n \cdot 2 + \frac{n}{2}$ .

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Step 1.1.1

Subtract $2$ from $2$ .

$n + n + 0 + n \cdot 2 + \frac{n}{2} = 45$

Step 1.1.2

Add $n + n$ and $0$ .

$n + n + n \cdot 2 + \frac{n}{2} = 45$

Step 1.2

Find the common denominator.

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Step 1.2.1

Write $n$ as a fraction with denominator $1$ .

$\frac{n}{1} + n + n \cdot 2 + \frac{n}{2} = 45$

Step 1.2.2

Multiply $\frac{n}{1}$ by $\frac{2}{2}$ .

$\frac{n}{1} \cdot \frac{2}{2} + n + n \cdot 2 + \frac{n}{2} = 45$

Step 1.2.3

Multiply $\frac{n}{1}$ by $\frac{2}{2}$ .

$\frac{n \cdot 2}{2} + n + n \cdot 2 + \frac{n}{2} = 45$

Step 1.2.4

Write $n$ as a fraction with denominator $1$ .

$\frac{n \cdot 2}{2} + \frac{n}{1} + n \cdot 2 + \frac{n}{2} = 45$

Step 1.2.5

Multiply $\frac{n}{1}$ by $\frac{2}{2}$ .

$\frac{n \cdot 2}{2} + \frac{n}{1} \cdot \frac{2}{2} + n \cdot 2 + \frac{n}{2} = 45$

Step 1.2.6

Multiply $\frac{n}{1}$ by $\frac{2}{2}$ .

$\frac{n \cdot 2}{2} + \frac{n \cdot 2}{2} + n \cdot 2 + \frac{n}{2} = 45$

Step 1.2.7

Write $n \cdot 2$ as a fraction with denominator $1$ .

$\frac{n \cdot 2}{2} + \frac{n \cdot 2}{2} + \frac{n \cdot 2}{1} + \frac{n}{2} = 45$

Step 1.2.8

Multiply $\frac{n \cdot 2}{1}$ by $\frac{2}{2}$ .

$\frac{n \cdot 2}{2} + \frac{n \cdot 2}{2} + \frac{n \cdot 2}{1} \cdot \frac{2}{2} + \frac{n}{2} = 45$

Step 1.2.9

Multiply $\frac{n \cdot 2}{1}$ by $\frac{2}{2}$ .

$\frac{n \cdot 2}{2} + \frac{n \cdot 2}{2} + \frac{n \cdot 2 \cdot 2}{2} + \frac{n}{2} = 45$

Step 1.3

Combine the numerators over the common denominator.

$\frac{n \cdot 2 + n \cdot 2 + n \cdot 2 \cdot 2 + n}{2} = 45$

Step 1.4

Simplify each term.

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Step 1.4.1

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

$\frac{2 \cdot n + n \cdot 2 + n \cdot 2 \cdot 2 + n}{2} = 45$

Step 1.4.2

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

$\frac{2 n + 2 \cdot n + n \cdot 2 \cdot 2 + n}{2} = 45$

Step 1.4.3

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

$\frac{2 n + 2 n + 2 \cdot n \cdot 2 + n}{2} = 45$

Step 1.4.4

Multiply $2$ by $2$ .

$\frac{2 n + 2 n + 4 n + n}{2} = 45$

Step 1.5

Simplify by adding terms.

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Step 1.5.1

Add $2 n$ and $2 n$ .

$\frac{4 n + 4 n + n}{2} = 45$

Step 1.5.2

Add $4 n$ and $4 n$ .

$\frac{8 n + n}{2} = 45$

Step 1.5.3

Add $8 n$ and $n$ .

$\frac{9 n}{2} = 45$

Step 2

Multiply both sides of the equation by $\frac{2}{9}$ .

$\frac{2}{9} \cdot \frac{9 n}{2} = \frac{2}{9} \cdot 45$

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 $\frac{2}{9} \cdot \frac{9 n}{2}$ .

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Step 3.1.1.1

Cancel the common factor of $2$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{2}{9} \cdot \frac{9 n}{2} = \frac{2}{9} \cdot 45$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{9} (9 n) = \frac{2}{9} \cdot 45$

Step 3.1.1.2

Cancel the common factor of $9$ .

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Step 3.1.1.2.1

Factor $9$ out of $9 n$ .

$\frac{1}{9} (9 (n)) = \frac{2}{9} \cdot 45$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{9} (9 n) = \frac{2}{9} \cdot 45$

Step 3.1.1.2.3

Rewrite the expression.

$n = \frac{2}{9} \cdot 45$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{2}{9} \cdot 45$ .

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Step 3.2.1.1

Cancel the common factor of $9$ .

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Step 3.2.1.1.1

Factor $9$ out of $45$ .

$n = \frac{2}{9} \cdot (9 (5))$

Step 3.2.1.1.2

Cancel the common factor.

$n = \frac{2}{9} \cdot (9 \cdot 5)$

Step 3.2.1.1.3

Rewrite the expression.

$n = 2 \cdot 5$

Step 3.2.1.2

Multiply $2$ by $5$ .

$n = 10$