Basic Math Examples

$\frac{(n - 2) \cdot 180}{n} = 72$

Step 1

Factor each term.

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Step 1.1

Move $180$ to the left of $n - 2$ .

$\frac{180 \cdot (n - 2)}{n} = 72$

Step 1.2

Multiply $180$ by $n - 2$ .

$\frac{180 (n - 2)}{n} = 72$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$n, 1$

Step 2.2

The LCM of one and any expression is the expression.

$n$

Step 3

Multiply each term in $\frac{180 (n - 2)}{n} = 72$ by $n$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{180 (n - 2)}{n} = 72$ by $n$ .

$\frac{180 (n - 2)}{n} n = 72 n$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $n$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{180 (n - 2)}{n} n = 72 n$

Step 3.2.1.2

Rewrite the expression.

$180 (n - 2) = 72 n$

Step 3.2.2

Apply the distributive property.

$180 n + 180 \cdot - 2 = 72 n$

Step 3.2.3

Multiply $180$ by $- 2$ .

$180 n - 360 = 72 n$

Step 4

Solve the equation.

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Step 4.1

Move all terms containing $n$ to the left side of the equation.

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Step 4.1.1

Subtract $72 n$ from both sides of the equation.

$180 n - 360 - 72 n = 0$

Step 4.1.2

Subtract $72 n$ from $180 n$ .

$108 n - 360 = 0$

Step 4.2

Add $360$ to both sides of the equation.

$108 n = 360$

Step 4.3

Divide each term in $108 n = 360$ by $108$ and simplify.

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Step 4.3.1

Divide each term in $108 n = 360$ by $108$ .

$\frac{108 n}{108} = \frac{360}{108}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $108$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{108 n}{108} = \frac{360}{108}$

Step 4.3.2.1.2

Divide $n$ by $1$ .

$n = \frac{360}{108}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Cancel the common factor of $360$ and $108$ .

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Step 4.3.3.1.1

Factor $36$ out of $360$ .

$n = \frac{36 (10)}{108}$

Step 4.3.3.1.2

Cancel the common factors.

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Step 4.3.3.1.2.1

Factor $36$ out of $108$ .

$n = \frac{36 \cdot 10}{36 \cdot 3}$

Step 4.3.3.1.2.2

Cancel the common factor.

$n = \frac{36 \cdot 10}{36 \cdot 3}$

Step 4.3.3.1.2.3

Rewrite the expression.

$n = \frac{10}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$n = \frac{10}{3}$

Decimal Form:

$n = 3.\overline{3}$

Mixed Number Form:

$n = 3 \frac{1}{3}$