Basic Math Examples

$\frac{5}{11} \cdot \frac{1}{5} + \frac{6}{11} \cdot \frac{5}{12}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $5$ .

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Step 1.1.1

Cancel the common factor.

$\frac{5}{11} \cdot \frac{1}{5} + \frac{6}{11} \cdot \frac{5}{12}$

Step 1.1.2

Rewrite the expression.

$\frac{1}{11} + \frac{6}{11} \cdot \frac{5}{12}$

Step 1.2

Cancel the common factor of $6$ .

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Step 1.2.1

Factor $6$ out of $12$ .

$\frac{1}{11} + \frac{6}{11} \cdot \frac{5}{6 (2)}$

Step 1.2.2

Cancel the common factor.

$\frac{1}{11} + \frac{6}{11} \cdot \frac{5}{6 \cdot 2}$

Step 1.2.3

Rewrite the expression.

$\frac{1}{11} + \frac{1}{11} \cdot \frac{5}{2}$

Step 1.3

Multiply $\frac{1}{11}$ by $\frac{5}{2}$ .

$\frac{1}{11} + \frac{5}{11 \cdot 2}$

Step 1.4

Multiply $11$ by $2$ .

$\frac{1}{11} + \frac{5}{22}$

Step 2

To write $\frac{1}{11}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{11} \cdot \frac{2}{2} + \frac{5}{22}$

Step 3

Write each expression with a common denominator of $22$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{11}$ by $\frac{2}{2}$ .

$\frac{2}{11 \cdot 2} + \frac{5}{22}$

Step 3.2

Multiply $11$ by $2$ .

$\frac{2}{22} + \frac{5}{22}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 + 5}{22}$

Step 5

Add $2$ and $5$ .

$\frac{7}{22}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{22}$

Decimal Form:

$0.3\overline{18}$