Find the Median 4/6 , 2/9

$\frac{4}{6}$ , $\frac{2}{9}$

Step 1

Arrange the terms in ascending order.

$\frac{2}{9}, \frac{4}{6}$

Step 2

The median is the middle term in the arranged data set. In the case of an even number of terms, the median is the average of the two middle terms.

$\frac{\frac{2}{9} + \frac{4}{6}}{2}$

Step 3

Reduce the expression by cancelling the common factors.

Remove parentheses.

$\frac{\frac{2}{9} + \frac{4}{6}}{2}$

Cancel the common factor of $4$ and $6$ .

Factor $2$ out of $4$ .

$\frac{\frac{2}{9} + \frac{2 (2)}{6}}{2}$

Cancel the common factors.

Factor $2$ out of $6$ .

$\frac{\frac{2}{9} + \frac{2 \cdot 2}{2 \cdot 3}}{2}$

Cancel the common factor.

$\frac{\frac{2}{9} + \frac{2 \cdot 2}{2 \cdot 3}}{2}$

Rewrite the expression.

$\frac{\frac{2}{9} + \frac{2}{3}}{2}$

Step 4

Simplify the numerator.

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{\frac{2}{9} + \frac{2}{3} \cdot \frac{3}{3}}{2}$

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{3}$ by $\frac{3}{3}$ .

$\frac{\frac{2}{9} + \frac{2 \cdot 3}{3 \cdot 3}}{2}$

Multiply $3$ by $3$ .

$\frac{\frac{2}{9} + \frac{2 \cdot 3}{9}}{2}$

Combine the numerators over the common denominator.

$\frac{\frac{2 + 2 \cdot 3}{9}}{2}$

Simplify the numerator.

Multiply $2$ by $3$ .

$\frac{\frac{2 + 6}{9}}{2}$

Add $2$ and $6$ .

$\frac{\frac{8}{9}}{2}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{8}{9} \cdot \frac{1}{2}$

Step 6

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$\frac{2 (4)}{9} \cdot \frac{1}{2}$

Cancel the common factor.

$\frac{2 \cdot 4}{9} \cdot \frac{1}{2}$

Rewrite the expression.

$\frac{4}{9}$

Step 7

Convert the median $\frac{4}{9}$ to decimal.

$0.\overline{4}$

Find the Median 4/6 , 2/9

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