Basic Math Examples

\frac{2}{11} + \frac{17}{19}

$\frac{2}{11} + \frac{17}{19}$

Step 1

To write

\frac{2}{11}

$\frac{2}{11}$ as a fraction with a common denominator, multiply by

\frac{19}{19}

$\frac{19}{19}$ .

\frac{2}{11} \cdot \frac{19}{19} + \frac{17}{19}

$\frac{2}{11} \cdot \frac{19}{19} + \frac{17}{19}$

Step 2

To write

\frac{17}{19}

$\frac{17}{19}$ as a fraction with a common denominator, multiply by

\frac{11}{11}

$\frac{11}{11}$ .

\frac{2}{11} \cdot \frac{19}{19} + \frac{17}{19} \cdot \frac{11}{11}

$\frac{2}{11} \cdot \frac{19}{19} + \frac{17}{19} \cdot \frac{11}{11}$

Step 3

Write each expression with a common denominator of

209

$209$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{2}{11}

$\frac{2}{11}$ by

\frac{19}{19}

$\frac{19}{19}$ .

\frac{2 \cdot 19}{11 \cdot 19} + \frac{17}{19} \cdot \frac{11}{11}

$\frac{2 \cdot 19}{11 \cdot 19} + \frac{17}{19} \cdot \frac{11}{11}$

Step 3.2

Multiply

11

$11$ by

19

$19$ .

\frac{2 \cdot 19}{209} + \frac{17}{19} \cdot \frac{11}{11}

$\frac{2 \cdot 19}{209} + \frac{17}{19} \cdot \frac{11}{11}$

Step 3.3

Multiply

\frac{17}{19}

$\frac{17}{19}$ by

\frac{11}{11}

$\frac{11}{11}$ .

\frac{2 \cdot 19}{209} + \frac{17 \cdot 11}{19 \cdot 11}

$\frac{2 \cdot 19}{209} + \frac{17 \cdot 11}{19 \cdot 11}$

Step 3.4

Multiply

19

$19$ by

11

$11$ .

\frac{2 \cdot 19}{209} + \frac{17 \cdot 11}{209}

$\frac{2 \cdot 19}{209} + \frac{17 \cdot 11}{209}$

\frac{2 \cdot 19}{209} + \frac{17 \cdot 11}{209}

$\frac{2 \cdot 19}{209} + \frac{17 \cdot 11}{209}$

Step 4

Combine the numerators over the common denominator.

\frac{2 \cdot 19 + 17 \cdot 11}{209}

$\frac{2 \cdot 19 + 17 \cdot 11}{209}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

2

$2$ by

19

$19$ .

\frac{38 + 17 \cdot 11}{209}

$\frac{38 + 17 \cdot 11}{209}$

Step 5.2

Multiply

17

$17$ by

11

$11$ .

\frac{38 + 187}{209}

$\frac{38 + 187}{209}$

Step 5.3

Add

38

$38$ and

187

$187$ .

\frac{225}{209}

$\frac{225}{209}$

\frac{225}{209}

$\frac{225}{209}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{225}{209}

$\frac{225}{209}$

Decimal Form:

1.07655502 \dots

$1.07655502 \dots$

Mixed Number Form:

1 \frac{16}{209}

$1 \frac{16}{209}$