Finite Math Examples

$\frac{\frac{1}{2}}{\frac{5}{6}} = \frac{\frac{2}{3}}{n}$

Step 1

Rewrite the equation as $\frac{\frac{2}{3}}{n} = \frac{\frac{1}{2}}{\frac{5}{6}}$ .

$\frac{\frac{2}{3}}{n} = \frac{\frac{1}{2}}{\frac{5}{6}}$

Step 2

Simplify both sides.

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Step 2.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{2}{3} \cdot \frac{1}{n} = \frac{\frac{1}{2}}{\frac{5}{6}}$

Step 2.2

Multiply $\frac{2}{3}$ by $\frac{1}{n}$ .

$\frac{2}{3 n} = \frac{\frac{1}{2}}{\frac{5}{6}}$

Step 2.3

Multiply the numerator by the reciprocal of the denominator.

$\frac{2}{3 n} = \frac{1}{2} \cdot \frac{6}{5}$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Factor $2$ out of $6$ .

$\frac{2}{3 n} = \frac{1}{2} \cdot \frac{2 (3)}{5}$

Step 2.4.2

Cancel the common factor.

$\frac{2}{3 n} = \frac{1}{2} \cdot \frac{2 \cdot 3}{5}$

Step 2.4.3

Rewrite the expression.

$\frac{2}{3 n} = \frac{3}{5}$

Step 3

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$2 \cdot 5 = 3 n \cdot 3$

Step 4

Solve the equation for $n$ .

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Step 4.1

Rewrite the equation as $3 n \cdot 3 = 2 \cdot 5$ .

$3 n \cdot 3 = 2 \cdot 5$

Step 4.2

Simplify.

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Step 4.2.1

Multiply $3$ by $3$ .

$9 n = 2 \cdot 5$

Step 4.2.2

Multiply $2$ by $5$ .

$9 n = 10$

Step 4.3

Divide each term in $9 n = 10$ by $9$ and simplify.

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Step 4.3.1

Divide each term in $9 n = 10$ by $9$ .

$\frac{9 n}{9} = \frac{10}{9}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $9$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{9 n}{9} = \frac{10}{9}$

Step 4.3.2.1.2

Divide $n$ by $1$ .

$n = \frac{10}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$n = \frac{10}{9}$

Decimal Form:

$n = 1.\overline{1}$

Mixed Number Form:

$n = 1 \frac{1}{9}$