Basic Math Examples

$\frac{18}{3000} = \frac{n}{\frac{1}{\frac{1000}{500000}}}$

Step 1

Rewrite the equation as $\frac{n}{\frac{1}{\frac{1000}{500000}}} = \frac{18}{3000}$ .

$\frac{n}{\frac{1}{\frac{1000}{500000}}} = \frac{18}{3000}$

Step 2

Multiply both sides of the equation by $\frac{1}{\frac{1000}{500000}}$ .

$\frac{1}{\frac{1000}{500000}} \cdot \frac{n}{\frac{1}{\frac{1000}{500000}}} = \frac{1}{\frac{1000}{500000}} \cdot \frac{18}{3000}$

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 $\frac{1}{\frac{1000}{500000}} \cdot \frac{n}{\frac{1}{\frac{1000}{500000}}}$ .

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Step 3.1.1.1

Cancel the common factor of $1000$ and $500000$ .

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Step 3.1.1.1.1

Factor $1000$ out of $1000$ .

$\frac{1}{\frac{1000 (1)}{500000}} \cdot \frac{n}{\frac{1}{\frac{1000}{500000}}} = \frac{1}{\frac{1000}{500000}} \cdot \frac{18}{3000}$

Step 3.1.1.1.2

Cancel the common factors.

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Step 3.1.1.1.2.1

Factor $1000$ out of $500000$ .

$\frac{1}{\frac{1000 \cdot 1}{1000 \cdot 500}} \cdot \frac{n}{\frac{1}{\frac{1000}{500000}}} = \frac{1}{\frac{1000}{500000}} \cdot \frac{18}{3000}$

Step 3.1.1.1.2.2

Cancel the common factor.

$\frac{1}{\frac{1000 \cdot 1}{1000 \cdot 500}} \cdot \frac{n}{\frac{1}{\frac{1000}{500000}}} = \frac{1}{\frac{1000}{500000}} \cdot \frac{18}{3000}$

Step 3.1.1.1.2.3

Rewrite the expression.

$\frac{1}{\frac{1}{500}} \cdot \frac{n}{\frac{1}{\frac{1000}{500000}}} = \frac{1}{\frac{1000}{500000}} \cdot \frac{18}{3000}$

Step 3.1.1.2

Multiply the numerator by the reciprocal of the denominator.

$1 \cdot 500 \frac{n}{\frac{1}{\frac{1000}{500000}}} = \frac{1}{\frac{1000}{500000}} \cdot \frac{18}{3000}$

Step 3.1.1.3

Multiply $500$ by $1$ .

$500 \frac{n}{\frac{1}{\frac{1000}{500000}}} = \frac{1}{\frac{1000}{500000}} \cdot \frac{18}{3000}$

Step 3.1.1.4

Cancel the common factor of $1000$ and $500000$ .

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Step 3.1.1.4.1

Factor $1000$ out of $1000$ .

$500 \frac{n}{\frac{1}{\frac{1000 (1)}{500000}}} = \frac{1}{\frac{1000}{500000}} \cdot \frac{18}{3000}$

Step 3.1.1.4.2

Cancel the common factors.

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Step 3.1.1.4.2.1

Factor $1000$ out of $500000$ .

$500 \frac{n}{\frac{1}{\frac{1000 \cdot 1}{1000 \cdot 500}}} = \frac{1}{\frac{1000}{500000}} \cdot \frac{18}{3000}$

Step 3.1.1.4.2.2

Cancel the common factor.

$500 \frac{n}{\frac{1}{\frac{1000 \cdot 1}{1000 \cdot 500}}} = \frac{1}{\frac{1000}{500000}} \cdot \frac{18}{3000}$

Step 3.1.1.4.2.3

Rewrite the expression.

$500 \frac{n}{\frac{1}{\frac{1}{500}}} = \frac{1}{\frac{1000}{500000}} \cdot \frac{18}{3000}$

Step 3.1.1.5

Multiply the numerator by the reciprocal of the denominator.

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Step 3.1.1.5.1

Factor $1000$ out of $1000$ .

$500 (n \frac{1000 (1)}{500000}) = \frac{1}{\frac{1000}{500000}} \cdot \frac{18}{3000}$

Step 3.1.1.5.2

Cancel the common factors.

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Step 3.1.1.5.2.1

Factor $1000$ out of $500000$ .

$500 (n \frac{1000 \cdot 1}{1000 \cdot 500}) = \frac{1}{\frac{1000}{500000}} \cdot \frac{18}{3000}$

Step 3.1.1.5.2.2

Cancel the common factor.

$500 (n \frac{1000 \cdot 1}{1000 \cdot 500}) = \frac{1}{\frac{1000}{500000}} \cdot \frac{18}{3000}$

Step 3.1.1.5.2.3

Rewrite the expression.

$500 (n \frac{1}{500}) = \frac{1}{\frac{1000}{500000}} \cdot \frac{18}{3000}$

Step 3.1.1.6

Combine $n$ and $\frac{1}{500}$ .

$500 \frac{n}{500} = \frac{1}{\frac{1000}{500000}} \cdot \frac{18}{3000}$

Step 3.1.1.7

Cancel the common factor of $500$ .

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Step 3.1.1.7.1

Cancel the common factor.

$500 \frac{n}{500} = \frac{1}{\frac{1000}{500000}} \cdot \frac{18}{3000}$

Step 3.1.1.7.2

Rewrite the expression.

$n = \frac{1}{\frac{1000}{500000}} \cdot \frac{18}{3000}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{1}{\frac{1000}{500000}} \cdot \frac{18}{3000}$ .

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Step 3.2.1.1

Cancel the common factor of $1000$ and $500000$ .

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Step 3.2.1.1.1

Factor $1000$ out of $1000$ .

$n = \frac{1}{\frac{1000 (1)}{500000}} \cdot \frac{18}{3000}$

Step 3.2.1.1.2

Cancel the common factors.

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Step 3.2.1.1.2.1

Factor $1000$ out of $500000$ .

$n = \frac{1}{\frac{1000 \cdot 1}{1000 \cdot 500}} \cdot \frac{18}{3000}$

Step 3.2.1.1.2.2

Cancel the common factor.

$n = \frac{1}{\frac{1000 \cdot 1}{1000 \cdot 500}} \cdot \frac{18}{3000}$

Step 3.2.1.1.2.3

Rewrite the expression.

$n = \frac{1}{\frac{1}{500}} \cdot \frac{18}{3000}$

Step 3.2.1.2

Multiply the numerator by the reciprocal of the denominator.

$n = 1 \cdot 500 \frac{18}{3000}$

Step 3.2.1.3

Cancel the common factor of $500$ .

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Step 3.2.1.3.1

Factor $500$ out of $1 \cdot 500$ .

$n = 500 \cdot 1 \frac{18}{3000}$

Step 3.2.1.3.2

Factor $500$ out of $3000$ .

$n = 500 \cdot 1 \frac{18}{500 (6)}$

Step 3.2.1.3.3

Cancel the common factor.

$n = 500 \cdot 1 \frac{18}{500 \cdot 6}$

Step 3.2.1.3.4

Rewrite the expression.

$n = \frac{18}{6}$

Step 3.2.1.4

Divide $18$ by $6$ .

$n = 3$