Basic Math Examples

\frac{1}{6} + \frac{1}{7} + \frac{2}{19}

$\frac{1}{6} + \frac{1}{7} + \frac{2}{19}$

Step 1

Find the common denominator.

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Step 1.1

Multiply

\frac{1}{6}

$\frac{1}{6}$ by

\frac{133}{133}

$\frac{133}{133}$ .

\frac{1}{6} \cdot \frac{133}{133} + \frac{1}{7} + \frac{2}{19}

$\frac{1}{6} \cdot \frac{133}{133} + \frac{1}{7} + \frac{2}{19}$

Step 1.2

Multiply

\frac{1}{6}

$\frac{1}{6}$ by

\frac{133}{133}

$\frac{133}{133}$ .

\frac{133}{6 \cdot 133} + \frac{1}{7} + \frac{2}{19}

$\frac{133}{6 \cdot 133} + \frac{1}{7} + \frac{2}{19}$

Step 1.3

Multiply

\frac{1}{7}

$\frac{1}{7}$ by

\frac{114}{114}

$\frac{114}{114}$ .

\frac{133}{6 \cdot 133} + \frac{1}{7} \cdot \frac{114}{114} + \frac{2}{19}

$\frac{133}{6 \cdot 133} + \frac{1}{7} \cdot \frac{114}{114} + \frac{2}{19}$

Step 1.4

Multiply

\frac{1}{7}

$\frac{1}{7}$ by

\frac{114}{114}

$\frac{114}{114}$ .

\frac{133}{6 \cdot 133} + \frac{114}{7 \cdot 114} + \frac{2}{19}

$\frac{133}{6 \cdot 133} + \frac{114}{7 \cdot 114} + \frac{2}{19}$

Step 1.5

Multiply

\frac{2}{19}

$\frac{2}{19}$ by

\frac{42}{42}

$\frac{42}{42}$ .

\frac{133}{6 \cdot 133} + \frac{114}{7 \cdot 114} + \frac{2}{19} \cdot \frac{42}{42}

$\frac{133}{6 \cdot 133} + \frac{114}{7 \cdot 114} + \frac{2}{19} \cdot \frac{42}{42}$

Step 1.6

Multiply

\frac{2}{19}

$\frac{2}{19}$ by

\frac{42}{42}

$\frac{42}{42}$ .

\frac{133}{6 \cdot 133} + \frac{114}{7 \cdot 114} + \frac{2 \cdot 42}{19 \cdot 42}

$\frac{133}{6 \cdot 133} + \frac{114}{7 \cdot 114} + \frac{2 \cdot 42}{19 \cdot 42}$

Step 1.7

Multiply

6

$6$ by

133

$133$ .

\frac{133}{798} + \frac{114}{7 \cdot 114} + \frac{2 \cdot 42}{19 \cdot 42}

$\frac{133}{798} + \frac{114}{7 \cdot 114} + \frac{2 \cdot 42}{19 \cdot 42}$

Step 1.8

Multiply

7

$7$ by

114

$114$ .

\frac{133}{798} + \frac{114}{798} + \frac{2 \cdot 42}{19 \cdot 42}

$\frac{133}{798} + \frac{114}{798} + \frac{2 \cdot 42}{19 \cdot 42}$

Step 1.9

Multiply

19

$19$ by

42

$42$ .

\frac{133}{798} + \frac{114}{798} + \frac{2 \cdot 42}{798}

$\frac{133}{798} + \frac{114}{798} + \frac{2 \cdot 42}{798}$

\frac{133}{798} + \frac{114}{798} + \frac{2 \cdot 42}{798}

$\frac{133}{798} + \frac{114}{798} + \frac{2 \cdot 42}{798}$

Step 2

Combine the numerators over the common denominator.

\frac{133 + 114 + 2 \cdot 42}{798}

$\frac{133 + 114 + 2 \cdot 42}{798}$

Step 3

Simplify the expression.

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Step 3.1

Multiply

2

$2$ by

42

$42$ .

\frac{133 + 114 + 84}{798}

$\frac{133 + 114 + 84}{798}$

Step 3.2

Add

133

$133$ and

114

$114$ .

\frac{247 + 84}{798}

$\frac{247 + 84}{798}$

Step 3.3

Add

247

$247$ and

84

$84$ .

\frac{331}{798}

$\frac{331}{798}$

\frac{331}{798}

$\frac{331}{798}$

Step 4

The result can be shown in multiple forms.

Exact Form:

\frac{331}{798}

$\frac{331}{798}$

Decimal Form:

0.41478696 \dots

$0.41478696 \dots$