Basic Math Examples

$\frac{n}{\frac{2}{3}} = \frac{10}{15}$

Step 1

Multiply both sides of the equation by $\frac{2}{3}$ .

$\frac{2}{3} \cdot \frac{n}{\frac{2}{3}} = \frac{2}{3} \cdot \frac{10}{15}$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{2}{3} \cdot \frac{n}{\frac{2}{3}}$ .

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Step 2.1.1.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{2}{3} (n \frac{3}{2}) = \frac{2}{3} \cdot \frac{10}{15}$

Step 2.1.1.2

Combine $n$ and $\frac{3}{2}$ .

$\frac{2}{3} \cdot \frac{n \cdot 3}{2} = \frac{2}{3} \cdot \frac{10}{15}$

Step 2.1.1.3

Cancel the common factor of $2$ .

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Step 2.1.1.3.1

Cancel the common factor.

$\frac{2}{3} \cdot \frac{n \cdot 3}{2} = \frac{2}{3} \cdot \frac{10}{15}$

Step 2.1.1.3.2

Rewrite the expression.

$\frac{1}{3} (n \cdot 3) = \frac{2}{3} \cdot \frac{10}{15}$

Step 2.1.1.4

Cancel the common factor of $3$ .

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Step 2.1.1.4.1

Factor $3$ out of $n \cdot 3$ .

$\frac{1}{3} (3 \cdot n) = \frac{2}{3} \cdot \frac{10}{15}$

Step 2.1.1.4.2

Cancel the common factor.

$\frac{1}{3} (3 \cdot n) = \frac{2}{3} \cdot \frac{10}{15}$

Step 2.1.1.4.3

Rewrite the expression.

$n = \frac{2}{3} \cdot \frac{10}{15}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{2}{3} \cdot \frac{10}{15}$ .

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Step 2.2.1.1

Cancel the common factor of $10$ and $15$ .

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Step 2.2.1.1.1

Factor $5$ out of $10$ .

$n = \frac{2}{3} \cdot \frac{5 (2)}{15}$

Step 2.2.1.1.2

Cancel the common factors.

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Step 2.2.1.1.2.1

Factor $5$ out of $15$ .

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

Step 2.2.1.1.2.2

Cancel the common factor.

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

Step 2.2.1.1.2.3

Rewrite the expression.

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

Step 2.2.1.2

Multiply $\frac{2}{3} \cdot \frac{2}{3}$ .

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Step 2.2.1.2.1

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

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

Step 2.2.1.2.2

Multiply $2$ by $2$ .

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

Step 2.2.1.2.3

Multiply $3$ by $3$ .

$n = \frac{4}{9}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$n = \frac{4}{9}$

Decimal Form:

$n = 0.\overline{4}$