Find the Median 462 , 140/46

$462$ , $\frac{140}{46}$

Step 1

Arrange the terms in ascending order.

$\frac{140}{46}, 462$

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.

$\frac{\frac{140}{46} + 462}{2}$

Step 3

Remove parentheses.

$\frac{\frac{140}{46} + 462}{2}$

Step 4

Cancel the common factor of $140$ and $46$ .

Factor $2$ out of $140$ .

$\frac{\frac{2 (70)}{46} + 462}{2}$

Cancel the common factors.

Factor $2$ out of $46$ .

$\frac{\frac{2 \cdot 70}{2 \cdot 23} + 462}{2}$

Cancel the common factor.

$\frac{\frac{2 \cdot 70}{2 \cdot 23} + 462}{2}$

Rewrite the expression.

$\frac{\frac{70}{23} + 462}{2}$

Step 5

Cancel the common factor of $\frac{70}{23} + 462$ and $2$ .

Factor $2$ out of $\frac{70}{23}$ .

$\frac{2 (\frac{35}{23}) + 462}{2}$

Factor $2$ out of $462$ .

$\frac{2 (\frac{35}{23}) + 2 \cdot 231}{2}$

Factor $2$ out of $2 (\frac{35}{23}) + 2 \cdot 231$ .

$\frac{2 (\frac{35}{23} + 231)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{2 (\frac{35}{23} + 231)}{2 (1)}$

Cancel the common factor.

$\frac{2 (\frac{35}{23} + 231)}{2 \cdot 1}$

Rewrite the expression.

$\frac{\frac{35}{23} + 231}{1}$

Divide $\frac{35}{23} + 231$ by $1$ .

$\frac{35}{23} + 231$

Step 6

To write $231$ as a fraction with a common denominator, multiply by $\frac{23}{23}$ .

$\frac{35}{23} + 231 \cdot \frac{23}{23}$

Step 7

Combine $231$ and $\frac{23}{23}$ .

$\frac{35}{23} + \frac{231 \cdot 23}{23}$

Step 8

Combine the numerators over the common denominator.

$\frac{35 + 231 \cdot 23}{23}$

Step 9

Simplify the numerator.

Multiply $231$ by $23$ .

$\frac{35 + 5313}{23}$

Add $35$ and $5313$ .

$\frac{5348}{23}$

Step 10

Convert the median $\frac{5348}{23}$ to decimal.

$232.52173913$

Find the Median 462 , 140/46

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