Find the Mean 1/6 , 3/14

$\frac{1}{6}$ , $\frac{3}{14}$

Step 1

The mean of a set of numbers is the sum divided by the number of terms.

$\frac{\frac{1}{6} + \frac{3}{14}}{2}$

Step 2

Simplify the numerator.

To write $\frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{\frac{1}{6} \cdot \frac{7}{7} + \frac{3}{14}}{2}$

To write $\frac{3}{14}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{\frac{1}{6} \cdot \frac{7}{7} + \frac{3}{14} \cdot \frac{3}{3}}{2}$

Write each expression with a common denominator of $42$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{6}$ by $\frac{7}{7}$ .

$\frac{\frac{7}{6 \cdot 7} + \frac{3}{14} \cdot \frac{3}{3}}{2}$

Multiply $6$ by $7$ .

$\frac{\frac{7}{42} + \frac{3}{14} \cdot \frac{3}{3}}{2}$

Multiply $\frac{3}{14}$ by $\frac{3}{3}$ .

$\frac{\frac{7}{42} + \frac{3 \cdot 3}{14 \cdot 3}}{2}$

Multiply $14$ by $3$ .

$\frac{\frac{7}{42} + \frac{3 \cdot 3}{42}}{2}$

Combine the numerators over the common denominator.

$\frac{\frac{7 + 3 \cdot 3}{42}}{2}$

Simplify the numerator.

Multiply $3$ by $3$ .

$\frac{\frac{7 + 9}{42}}{2}$

Add $7$ and $9$ .

$\frac{\frac{16}{42}}{2}$

Cancel the common factor of $16$ and $42$ .

Factor $2$ out of $16$ .

$\frac{\frac{2 (8)}{42}}{2}$

Cancel the common factors.

Factor $2$ out of $42$ .

$\frac{\frac{2 \cdot 8}{2 \cdot 21}}{2}$

Cancel the common factor.

$\frac{\frac{2 \cdot 8}{2 \cdot 21}}{2}$

Rewrite the expression.

$\frac{\frac{8}{21}}{2}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{8}{21} \cdot \frac{1}{2}$

Step 4

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$\frac{2 (4)}{21} \cdot \frac{1}{2}$

Cancel the common factor.

$\frac{2 \cdot 4}{21} \cdot \frac{1}{2}$

Rewrite the expression.

$\frac{4}{21}$

Step 5

Divide.

$0.\overline{190476}$

Step 6

The mean should be rounded to one more decimal place than the original data. If the original data were mixed, round to one decimal place more than the least precise.

$0.2$

Find the Mean 1/6 , 3/14

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