Basic Math Examples

$\frac{2 \cdot (\frac{5}{3})}{1 - (\frac{5}{3^{2}})}$

Step 1

Raise $3$ to the power of $2$ .

$\frac{2 \cdot \frac{5}{3}}{1 - \frac{5}{9}}$

Step 2

Combine $2$ and $\frac{5}{3}$ .

$\frac{\frac{2 \cdot 5}{3}}{1 - \frac{5}{9}}$

Step 3

Simplify the denominator.

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Step 3.1

Write $1$ as a fraction with a common denominator.

$\frac{\frac{2 \cdot 5}{3}}{\frac{9}{9} - \frac{5}{9}}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{\frac{2 \cdot 5}{3}}{\frac{9 - 5}{9}}$

Step 3.3

Subtract $5$ from $9$ .

$\frac{\frac{2 \cdot 5}{3}}{\frac{4}{9}}$

Step 4

Multiply $2$ by $5$ .

$\frac{\frac{10}{3}}{\frac{4}{9}}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{10}{3} \cdot \frac{9}{4}$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Factor $2$ out of $10$ .

$\frac{2 (5)}{3} \cdot \frac{9}{4}$

Step 6.2

Factor $2$ out of $4$ .

$\frac{2 \cdot 5}{3} \cdot \frac{9}{2 \cdot 2}$

Step 6.3

Cancel the common factor.

$\frac{2 \cdot 5}{3} \cdot \frac{9}{2 \cdot 2}$

Step 6.4

Rewrite the expression.

$\frac{5}{3} \cdot \frac{9}{2}$

Step 7

Cancel the common factor of $3$ .

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Step 7.1

Factor $3$ out of $9$ .

$\frac{5}{3} \cdot \frac{3 (3)}{2}$

Step 7.2

Cancel the common factor.

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

Step 7.3

Rewrite the expression.

$5 (\frac{3}{2})$

Step 8

Combine $5$ and $\frac{3}{2}$ .

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

Step 9

Multiply $5$ by $3$ .

$\frac{15}{2}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{15}{2}$

Decimal Form:

$7.5$

Mixed Number Form:

$7 \frac{1}{2}$