Basic Math Examples

$\frac{1}{5} + \frac{1}{2} + \frac{5}{6} + \frac{1}{6}$

Step 1

Combine the numerators over the common denominator.

$\frac{1}{5} + \frac{1}{2} + \frac{5 + 1}{6}$

Step 2

Add $5$ and $1$ .

$\frac{1}{5} + \frac{1}{2} + \frac{6}{6}$

Step 3

Find the common denominator.

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Step 3.1

Multiply $\frac{1}{5}$ by $\frac{6}{6}$ .

$\frac{1}{5} \cdot \frac{6}{6} + \frac{1}{2} + \frac{6}{6}$

Step 3.2

Multiply $\frac{1}{5}$ by $\frac{6}{6}$ .

$\frac{6}{5 \cdot 6} + \frac{1}{2} + \frac{6}{6}$

Step 3.3

Multiply $\frac{1}{2}$ by $\frac{15}{15}$ .

$\frac{6}{5 \cdot 6} + \frac{1}{2} \cdot \frac{15}{15} + \frac{6}{6}$

Step 3.4

Multiply $\frac{1}{2}$ by $\frac{15}{15}$ .

$\frac{6}{5 \cdot 6} + \frac{15}{2 \cdot 15} + \frac{6}{6}$

Step 3.5

Multiply $\frac{6}{6}$ by $\frac{5}{5}$ .

$\frac{6}{5 \cdot 6} + \frac{15}{2 \cdot 15} + \frac{6}{6} \cdot \frac{5}{5}$

Step 3.6

Multiply $\frac{6}{6}$ by $\frac{5}{5}$ .

$\frac{6}{5 \cdot 6} + \frac{15}{2 \cdot 15} + \frac{6 \cdot 5}{6 \cdot 5}$

Step 3.7

Multiply $5$ by $6$ .

$\frac{6}{30} + \frac{15}{2 \cdot 15} + \frac{6 \cdot 5}{6 \cdot 5}$

Step 3.8

Multiply $2$ by $15$ .

$\frac{6}{30} + \frac{15}{30} + \frac{6 \cdot 5}{6 \cdot 5}$

Step 3.9

Reorder the factors of $6 \cdot 5$ .

$\frac{6}{30} + \frac{15}{30} + \frac{6 \cdot 5}{5 \cdot 6}$

Step 3.10

Multiply $5$ by $6$ .

$\frac{6}{30} + \frac{15}{30} + \frac{6 \cdot 5}{30}$

Step 4

Combine the numerators over the common denominator.

$\frac{6 + 15 + 6 \cdot 5}{30}$

Step 5

Simplify the expression.

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Step 5.1

Multiply $6$ by $5$ .

$\frac{6 + 15 + 30}{30}$

Step 5.2

Add $6$ and $15$ .

$\frac{21 + 30}{30}$

Step 5.3

Add $21$ and $30$ .

$\frac{51}{30}$

Step 6

Cancel the common factor of $51$ and $30$ .

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Step 6.1

Factor $3$ out of $51$ .

$\frac{3 (17)}{30}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $3$ out of $30$ .

$\frac{3 \cdot 17}{3 \cdot 10}$

Step 6.2.2

Cancel the common factor.

$\frac{3 \cdot 17}{3 \cdot 10}$

Step 6.2.3

Rewrite the expression.

$\frac{17}{10}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{17}{10}$

Decimal Form:

$1.7$

Mixed Number Form:

$1 \frac{7}{10}$