Basic Math Examples

$18$ , $6 \div 2 \frac{7}{12}$

Step 1

Arrange the terms in ascending order.

$6 \div 2 \frac{7}{12}, 18$

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.

$\frac{6 \div 2 \frac{7}{12} + 18}{2}$

Step 3

Remove parentheses.

$\frac{6 \div 2 \frac{7}{12} + 18}{2}$

Step 4

Convert $2 \frac{7}{12}$ to an improper fraction.

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Step 4.1

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

$\frac{6 \div (2 + \frac{7}{12}) + 18}{2}$

Step 4.2

Add $2$ and $\frac{7}{12}$ .

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Step 4.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$\frac{6 \div (2 \cdot \frac{12}{12} + \frac{7}{12}) + 18}{2}$

Step 4.2.2

Combine $2$ and $\frac{12}{12}$ .

$\frac{6 \div (\frac{2 \cdot 12}{12} + \frac{7}{12}) + 18}{2}$

Step 4.2.3

Combine the numerators over the common denominator.

$\frac{6 \div \frac{2 \cdot 12 + 7}{12} + 18}{2}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $2$ by $12$ .

$\frac{6 \div \frac{24 + 7}{12} + 18}{2}$

Step 4.2.4.2

Add $24$ and $7$ .

$\frac{6 \div \frac{31}{12} + 18}{2}$

Step 5

Cancel the common factor of $6 \div \frac{31}{12} + 18$ and $2$ .

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Step 5.1

Factor $2$ out of $6 \div \frac{31}{12}$ .

$\frac{2 \frac{3}{\frac{31}{12}} + 18}{2}$

Step 5.2

Factor $2$ out of $18$ .

$\frac{2 \frac{3}{\frac{31}{12}} + 2 \cdot 9}{2}$

Step 5.3

Factor $2$ out of $2 \frac{3}{\frac{31}{12}} + 2 \cdot 9$ .

$\frac{2 (\frac{3}{\frac{31}{12}} + 9)}{2}$

Step 5.4

Cancel the common factors.

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Step 5.4.1

Factor $2$ out of $2$ .

$\frac{2 (\frac{3}{\frac{31}{12}} + 9)}{2 (1)}$

Step 5.4.2

Cancel the common factor.

$\frac{2 (\frac{3}{\frac{31}{12}} + 9)}{2 \cdot 1}$

Step 5.4.3

Rewrite the expression.

$\frac{\frac{3}{\frac{31}{12}} + 9}{1}$

Step 5.4.4

Divide $\frac{3}{\frac{31}{12}} + 9$ by $1$ .

$\frac{3}{\frac{31}{12}} + 9$

Step 6

Simplify each term.

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Step 6.1

Multiply the numerator by the reciprocal of the denominator.

$3 (\frac{12}{31}) + 9$

Step 6.2

Multiply $3 (\frac{12}{31})$ .

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Step 6.2.1

Combine $3$ and $\frac{12}{31}$ .

$\frac{3 \cdot 12}{31} + 9$

Step 6.2.2

Multiply $3$ by $12$ .

$\frac{36}{31} + 9$

Step 7

To write $9$ as a fraction with a common denominator, multiply by $\frac{31}{31}$ .

$\frac{36}{31} + 9 \cdot \frac{31}{31}$

Step 8

Combine $9$ and $\frac{31}{31}$ .

$\frac{36}{31} + \frac{9 \cdot 31}{31}$

Step 9

Combine the numerators over the common denominator.

$\frac{36 + 9 \cdot 31}{31}$

Step 10

Simplify the numerator.

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Step 10.1

Multiply $9$ by $31$ .

$\frac{36 + 279}{31}$

Step 10.2

Add $36$ and $279$ .

$\frac{315}{31}$

Step 11

Convert the median $\frac{315}{31}$ to decimal.

$10.16129032$