Basic Math Examples

$\frac{1}{6} + \frac{5}{14}$

Step 1

To write

$\frac{1}{6}$ as a fraction with a common denominator, multiply by

$\frac{7}{7}$ .

$\frac{1}{6} \cdot \frac{7}{7} + \frac{5}{14}$

Step 2

To write

$\frac{5}{14}$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{1}{6} \cdot \frac{7}{7} + \frac{5}{14} \cdot \frac{3}{3}$

Step 3

Write each expression with a common denominator of

$42$ , by multiplying each by an appropriate factor of

$1$ .

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Step 3.1

Multiply

$\frac{1}{6}$ by

$\frac{7}{7}$ .

$\frac{7}{6 \cdot 7} + \frac{5}{14} \cdot \frac{3}{3}$

Step 3.2

Multiply

$6$ by

$7$ .

$\frac{7}{42} + \frac{5}{14} \cdot \frac{3}{3}$

Step 3.3

Multiply

$\frac{5}{14}$ by

$\frac{3}{3}$ .

$\frac{7}{42} + \frac{5 \cdot 3}{14 \cdot 3}$

Step 3.4

Multiply

$14$ by

$3$ .

$\frac{7}{42} + \frac{5 \cdot 3}{42}$

Step 4

Combine the numerators over the common denominator.

$\frac{7 + 5 \cdot 3}{42}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

$5$ by

$3$ .

$\frac{7 + 15}{42}$

Step 5.2

Add

$7$ and

$15$ .

$\frac{22}{42}$

Step 6

Cancel the common factor of

$22$ and

$42$ .

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Step 6.1

Factor

$2$ out of

$22$ .

$\frac{2 (11)}{42}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor

$2$ out of

$42$ .

$\frac{2 \cdot 11}{2 \cdot 21}$

Step 6.2.2

Cancel the common factor.

$\frac{2 \cdot 11}{2 \cdot 21}$

Step 6.2.3

Rewrite the expression.

$\frac{11}{21}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{21}$

Decimal Form:

$0.\overline{523809}$