Basic Math Examples

$(\frac{15}{\frac{12}{\frac{3}{7}}}) = \frac{n}{\frac{4}{5}}$

Step 1

Rewrite the equation as $\frac{n}{\frac{4}{5}} = \frac{15}{\frac{12}{\frac{3}{7}}}$ .

$\frac{n}{\frac{4}{5}} = \frac{15}{\frac{12}{\frac{3}{7}}}$

Step 2

Multiply both sides of the equation by $\frac{4}{5}$ .

$\frac{4}{5} \cdot \frac{n}{\frac{4}{5}} = \frac{4}{5} \cdot \frac{15}{\frac{12}{\frac{3}{7}}}$

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 $\frac{4}{5} \cdot \frac{n}{\frac{4}{5}}$ .

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Step 3.1.1.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{4}{5} (n \frac{5}{4}) = \frac{4}{5} \cdot \frac{15}{\frac{12}{\frac{3}{7}}}$

Step 3.1.1.2

Combine $n$ and $\frac{5}{4}$ .

$\frac{4}{5} \cdot \frac{n \cdot 5}{4} = \frac{4}{5} \cdot \frac{15}{\frac{12}{\frac{3}{7}}}$

Step 3.1.1.3

Cancel the common factor of $4$ .

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Step 3.1.1.3.1

Cancel the common factor.

$\frac{4}{5} \cdot \frac{n \cdot 5}{4} = \frac{4}{5} \cdot \frac{15}{\frac{12}{\frac{3}{7}}}$

Step 3.1.1.3.2

Rewrite the expression.

$\frac{1}{5} (n \cdot 5) = \frac{4}{5} \cdot \frac{15}{\frac{12}{\frac{3}{7}}}$

Step 3.1.1.4

Cancel the common factor of $5$ .

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Step 3.1.1.4.1

Factor $5$ out of $n \cdot 5$ .

$\frac{1}{5} (5 \cdot n) = \frac{4}{5} \cdot \frac{15}{\frac{12}{\frac{3}{7}}}$

Step 3.1.1.4.2

Cancel the common factor.

$\frac{1}{5} (5 \cdot n) = \frac{4}{5} \cdot \frac{15}{\frac{12}{\frac{3}{7}}}$

Step 3.1.1.4.3

Rewrite the expression.

$n = \frac{4}{5} \cdot \frac{15}{\frac{12}{\frac{3}{7}}}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{4}{5} \cdot \frac{15}{\frac{12}{\frac{3}{7}}}$ .

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Step 3.2.1.1

Cancel the common factor of $5$ .

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Step 3.2.1.1.1

Factor $5$ out of $15$ .

$n = \frac{4}{5} \cdot \frac{5 (3)}{\frac{12}{\frac{3}{7}}}$

Step 3.2.1.1.2

Cancel the common factor.

$n = \frac{4}{5} \cdot \frac{5 \cdot 3}{\frac{12}{\frac{3}{7}}}$

Step 3.2.1.1.3

Rewrite the expression.

$n = 4 \frac{3}{\frac{12}{\frac{3}{7}}}$

Step 3.2.1.2

Combine $4$ and $\frac{3}{\frac{12}{\frac{3}{7}}}$ .

$n = \frac{4 \cdot 3}{\frac{12}{\frac{3}{7}}}$

Step 3.2.1.3

Multiply $4$ by $3$ .

$n = \frac{12}{\frac{12}{\frac{3}{7}}}$

Step 3.2.1.4

Multiply the numerator by the reciprocal of the denominator.

$n = 12 \frac{\frac{3}{7}}{12}$

Step 3.2.1.5

Cancel the common factor of $12$ .

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Step 3.2.1.5.1

Cancel the common factor.

$n = 12 \frac{\frac{3}{7}}{12}$

Step 3.2.1.5.2

Rewrite the expression.

$n = \frac{3}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$n = \frac{3}{7}$

Decimal Form:

$n = 0.\overline{428571}$