Basic Math Examples

$15 \frac{1}{5} \cdot 20$ , $500$

Step 1

Arrange the terms in ascending order.

$15 \frac{1}{5} \cdot 20, 500$

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.

$\frac{15 \frac{1}{5} \cdot 20 + 500}{2}$

Step 3

Remove parentheses.

$\frac{15 \frac{1}{5} \cdot 20 + 500}{2}$

Step 4

Convert $15 \frac{1}{5}$ to an improper fraction.

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Step 4.1

A mixed number is an addition of its whole and fractional parts.

$\frac{(15 + \frac{1}{5}) \cdot 20 + 500}{2}$

Step 4.2

Add $15$ and $\frac{1}{5}$ .

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Step 4.2.1

To write $15$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{(15 \cdot \frac{5}{5} + \frac{1}{5}) \cdot 20 + 500}{2}$

Step 4.2.2

Combine $15$ and $\frac{5}{5}$ .

$\frac{(\frac{15 \cdot 5}{5} + \frac{1}{5}) \cdot 20 + 500}{2}$

Step 4.2.3

Combine the numerators over the common denominator.

$\frac{\frac{15 \cdot 5 + 1}{5} \cdot 20 + 500}{2}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $15$ by $5$ .

$\frac{\frac{75 + 1}{5} \cdot 20 + 500}{2}$

Step 4.2.4.2

Add $75$ and $1$ .

$\frac{\frac{76}{5} \cdot 20 + 500}{2}$

Step 5

Cancel the common factor of $\frac{76}{5} \cdot 20 + 500$ and $2$ .

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Step 5.1

Factor $2$ out of $\frac{76}{5} \cdot 20$ .

$\frac{2 (\frac{38}{5} \cdot 20) + 500}{2}$

Step 5.2

Factor $2$ out of $500$ .

$\frac{2 (\frac{38}{5} \cdot 20) + 2 \cdot 250}{2}$

Step 5.3

Factor $2$ out of $2 (\frac{38}{5} \cdot 20) + 2 (250)$ .

$\frac{2 (\frac{38}{5} \cdot 20 + 250)}{2}$

Step 5.4

Cancel the common factors.

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Step 5.4.1

Factor $2$ out of $2$ .

$\frac{2 (\frac{38}{5} \cdot 20 + 250)}{2 (1)}$

Step 5.4.2

Cancel the common factor.

$\frac{2 (\frac{38}{5} \cdot 20 + 250)}{2 \cdot 1}$

Step 5.4.3

Rewrite the expression.

$\frac{\frac{38}{5} \cdot 20 + 250}{1}$

Step 5.4.4

Divide $\frac{38}{5} \cdot 20 + 250$ by $1$ .

$\frac{38}{5} \cdot 20 + 250$

Step 6

Simplify each term.

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Step 6.1

Cancel the common factor of $5$ .

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Step 6.1.1

Factor $5$ out of $20$ .

$\frac{38}{5} \cdot (5 (4)) + 250$

Step 6.1.2

Cancel the common factor.

$\frac{38}{5} \cdot (5 \cdot 4) + 250$

Step 6.1.3

Rewrite the expression.

$38 \cdot 4 + 250$

Step 6.2

Multiply $38$ by $4$ .

$152 + 250$

Step 7

Add $152$ and $250$ .

$402$

Step 8

Convert the median $402$ to decimal.

$402$