Basic Math Examples

$\frac{2}{13} - \frac{2}{3}$

Step 1

To write

$\frac{2}{13}$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{2}{13} \cdot \frac{3}{3} - \frac{2}{3}$

Step 2

To write

$- \frac{2}{3}$ as a fraction with a common denominator, multiply by

$\frac{13}{13}$ .

$\frac{2}{13} \cdot \frac{3}{3} - \frac{2}{3} \cdot \frac{13}{13}$

Step 3

Write each expression with a common denominator of

$39$ , by multiplying each by an appropriate factor of

$1$ .

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Step 3.1

Multiply

$\frac{2}{13}$ by

$\frac{3}{3}$ .

$\frac{2 \cdot 3}{13 \cdot 3} - \frac{2}{3} \cdot \frac{13}{13}$

Step 3.2

Multiply

$13$ by

$3$ .

$\frac{2 \cdot 3}{39} - \frac{2}{3} \cdot \frac{13}{13}$

Step 3.3

Multiply

$\frac{2}{3}$ by

$\frac{13}{13}$ .

$\frac{2 \cdot 3}{39} - \frac{2 \cdot 13}{3 \cdot 13}$

Step 3.4

Multiply

$3$ by

$13$ .

$\frac{2 \cdot 3}{39} - \frac{2 \cdot 13}{39}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 \cdot 3 - 2 \cdot 13}{39}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

$2$ by

$3$ .

$\frac{6 - 2 \cdot 13}{39}$

Step 5.2

Multiply

$- 2$ by

$13$ .

$\frac{6 - 26}{39}$

Step 5.3

Subtract

$26$ from

$6$ .

$\frac{- 20}{39}$

Step 6

Move the negative in front of the fraction.

$- \frac{20}{39}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{20}{39}$

Decimal Form:

$- 0.\overline{512820}$