Basic Math Examples

\frac{5}{13} + \frac{6}{11}

$\frac{5}{13} + \frac{6}{11}$

Step 1

To write

\frac{5}{13}

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

\frac{11}{11}

$\frac{11}{11}$ .

\frac{5}{13} \cdot \frac{11}{11} + \frac{6}{11}

$\frac{5}{13} \cdot \frac{11}{11} + \frac{6}{11}$

Step 2

To write

\frac{6}{11}

$\frac{6}{11}$ as a fraction with a common denominator, multiply by

\frac{13}{13}

$\frac{13}{13}$ .

\frac{5}{13} \cdot \frac{11}{11} + \frac{6}{11} \cdot \frac{13}{13}

$\frac{5}{13} \cdot \frac{11}{11} + \frac{6}{11} \cdot \frac{13}{13}$

Step 3

Write each expression with a common denominator of

143

$143$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{5}{13}

$\frac{5}{13}$ by

\frac{11}{11}

$\frac{11}{11}$ .

\frac{5 \cdot 11}{13 \cdot 11} + \frac{6}{11} \cdot \frac{13}{13}

$\frac{5 \cdot 11}{13 \cdot 11} + \frac{6}{11} \cdot \frac{13}{13}$

Step 3.2

Multiply

13

$13$ by

11

$11$ .

\frac{5 \cdot 11}{143} + \frac{6}{11} \cdot \frac{13}{13}

$\frac{5 \cdot 11}{143} + \frac{6}{11} \cdot \frac{13}{13}$

Step 3.3

Multiply

\frac{6}{11}

$\frac{6}{11}$ by

\frac{13}{13}

$\frac{13}{13}$ .

\frac{5 \cdot 11}{143} + \frac{6 \cdot 13}{11 \cdot 13}

$\frac{5 \cdot 11}{143} + \frac{6 \cdot 13}{11 \cdot 13}$

Step 3.4

Multiply

11

$11$ by

13

$13$ .

\frac{5 \cdot 11}{143} + \frac{6 \cdot 13}{143}

$\frac{5 \cdot 11}{143} + \frac{6 \cdot 13}{143}$

\frac{5 \cdot 11}{143} + \frac{6 \cdot 13}{143}

$\frac{5 \cdot 11}{143} + \frac{6 \cdot 13}{143}$

Step 4

Combine the numerators over the common denominator.

\frac{5 \cdot 11 + 6 \cdot 13}{143}

$\frac{5 \cdot 11 + 6 \cdot 13}{143}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

5

$5$ by

11

$11$ .

\frac{55 + 6 \cdot 13}{143}

$\frac{55 + 6 \cdot 13}{143}$

Step 5.2

Multiply

6

$6$ by

13

$13$ .

\frac{55 + 78}{143}

$\frac{55 + 78}{143}$

Step 5.3

Add

55

$55$ and

78

$78$ .

\frac{133}{143}

$\frac{133}{143}$

\frac{133}{143}

$\frac{133}{143}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{133}{143}

$\frac{133}{143}$

Decimal Form:

0. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 930069

$0.\overline{930069}$