Basic Math Examples

\frac{13}{3} + \frac{13}{5}

$\frac{13}{3} + \frac{13}{5}$

Step 1

To write

\frac{13}{3}

$\frac{13}{3}$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{13}{3} \cdot \frac{5}{5} + \frac{13}{5}

$\frac{13}{3} \cdot \frac{5}{5} + \frac{13}{5}$

Step 2

To write

\frac{13}{5}

$\frac{13}{5}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{13}{3} \cdot \frac{5}{5} + \frac{13}{5} \cdot \frac{3}{3}

$\frac{13}{3} \cdot \frac{5}{5} + \frac{13}{5} \cdot \frac{3}{3}$

Step 3

Write each expression with a common denominator of

15

$15$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{13}{3}

$\frac{13}{3}$ by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{13 \cdot 5}{3 \cdot 5} + \frac{13}{5} \cdot \frac{3}{3}

$\frac{13 \cdot 5}{3 \cdot 5} + \frac{13}{5} \cdot \frac{3}{3}$

Step 3.2

Multiply

3

$3$ by

5

$5$ .

\frac{13 \cdot 5}{15} + \frac{13}{5} \cdot \frac{3}{3}

$\frac{13 \cdot 5}{15} + \frac{13}{5} \cdot \frac{3}{3}$

Step 3.3

Multiply

\frac{13}{5}

$\frac{13}{5}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{13 \cdot 5}{15} + \frac{13 \cdot 3}{5 \cdot 3}

$\frac{13 \cdot 5}{15} + \frac{13 \cdot 3}{5 \cdot 3}$

Step 3.4

Multiply

5

$5$ by

3

$3$ .

\frac{13 \cdot 5}{15} + \frac{13 \cdot 3}{15}

$\frac{13 \cdot 5}{15} + \frac{13 \cdot 3}{15}$

\frac{13 \cdot 5}{15} + \frac{13 \cdot 3}{15}

$\frac{13 \cdot 5}{15} + \frac{13 \cdot 3}{15}$

Step 4

Combine the numerators over the common denominator.

\frac{13 \cdot 5 + 13 \cdot 3}{15}

$\frac{13 \cdot 5 + 13 \cdot 3}{15}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

13

$13$ by

5

$5$ .

\frac{65 + 13 \cdot 3}{15}

$\frac{65 + 13 \cdot 3}{15}$

Step 5.2

Multiply

13

$13$ by

3

$3$ .

\frac{65 + 39}{15}

$\frac{65 + 39}{15}$

Step 5.3

Add

65

$65$ and

39

$39$ .

\frac{104}{15}

$\frac{104}{15}$

\frac{104}{15}

$\frac{104}{15}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{104}{15}

$\frac{104}{15}$

Decimal Form:

6.9 ¯ 3

$6.9\overline{3}$

Mixed Number Form:

6 \frac{14}{15}

$6 \frac{14}{15}$