Basic Math Examples

$\frac{10}{39} \div 2 \frac{5}{13}$

Step 1

Convert

$2 \frac{5}{13}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{10}{39} \div (2 + \frac{5}{13})$

Step 1.2

Add

$2$ and

$\frac{5}{13}$ .

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Step 1.2.1

To write

$2$ as a fraction with a common denominator, multiply by

$\frac{13}{13}$ .

$\frac{10}{39} \div (2 \cdot \frac{13}{13} + \frac{5}{13})$

Step 1.2.2

Combine

$2$ and

$\frac{13}{13}$ .

$\frac{10}{39} \div (\frac{2 \cdot 13}{13} + \frac{5}{13})$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{10}{39} \div \frac{2 \cdot 13 + 5}{13}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$2$ by

$13$ .

$\frac{10}{39} \div \frac{26 + 5}{13}$

Step 1.2.4.2

Add

$26$ and

$5$ .

$\frac{10}{39} \div \frac{31}{13}$

Step 2

To divide by a fraction, multiply by its reciprocal.

$\frac{10}{39} \cdot \frac{13}{31}$

Step 3

Cancel the common factor of

$13$ .

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Step 3.1

Factor

$13$ out of

$39$ .

$\frac{10}{13 (3)} \cdot \frac{13}{31}$

Step 3.2

Cancel the common factor.

$\frac{10}{13 \cdot 3} \cdot \frac{13}{31}$

Step 3.3

Rewrite the expression.

$\frac{10}{3} \cdot \frac{1}{31}$

Step 4

Multiply

$\frac{10}{3}$ by

$\frac{1}{31}$ .

$\frac{10}{3 \cdot 31}$

Step 5

Multiply

$3$ by

$31$ .

$\frac{10}{93}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{10}{93}$

Decimal Form:

$0.10752688 \dots$