Basic Math Examples

$- \frac{1}{2}$ , $\frac{1}{3} - 1 + 3$

Step 1

Arrange the terms in ascending order.

$- \frac{1}{2}, \frac{1}{3} - 1 + 3$

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.

$\frac{- \frac{1}{2} + \frac{1}{3} - 1 + 3}{2}$

Step 3

Remove parentheses.

$\frac{- \frac{1}{2} + \frac{1}{3} - 1 + 3}{2}$

Step 4

Simplify the numerator.

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Step 4.1

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{- \frac{1}{2} \cdot \frac{3}{3} + \frac{1}{3} - 1 + 3}{2}$

Step 4.2

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{- \frac{1}{2} \cdot \frac{3}{3} + \frac{1}{3} \cdot \frac{2}{2} - 1 + 3}{2}$

Step 4.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.3.1

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$\frac{- \frac{3}{2 \cdot 3} + \frac{1}{3} \cdot \frac{2}{2} - 1 + 3}{2}$

Step 4.3.2

Multiply $2$ by $3$ .

$\frac{- \frac{3}{6} + \frac{1}{3} \cdot \frac{2}{2} - 1 + 3}{2}$

Step 4.3.3

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$\frac{- \frac{3}{6} + \frac{2}{3 \cdot 2} - 1 + 3}{2}$

Step 4.3.4

Multiply $3$ by $2$ .

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

Step 4.4

Combine the numerators over the common denominator.

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

Step 4.5

Add $- 3$ and $2$ .

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

Step 4.6

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

$\frac{\frac{- 1}{6} - 1 \cdot \frac{6}{6} + 3}{2}$

Step 4.7

Combine $- 1$ and $\frac{6}{6}$ .

$\frac{\frac{- 1}{6} + \frac{- 1 \cdot 6}{6} + 3}{2}$

Step 4.8

Combine the numerators over the common denominator.

$\frac{\frac{- 1 - 1 \cdot 6}{6} + 3}{2}$

Step 4.9

Simplify the numerator.

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Step 4.9.1

Multiply $- 1$ by $6$ .

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

Step 4.9.2

Subtract $6$ from $- 1$ .

$\frac{\frac{- 7}{6} + 3}{2}$

Step 4.10

To write $3$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

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

Step 4.11

Combine $3$ and $\frac{6}{6}$ .

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

Step 4.12

Combine the numerators over the common denominator.

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

Step 4.13

Simplify the numerator.

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Step 4.13.1

Multiply $3$ by $6$ .

$\frac{\frac{- 7 + 18}{6}}{2}$

Step 4.13.2

Add $- 7$ and $18$ .

$\frac{\frac{11}{6}}{2}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{11}{6} \cdot \frac{1}{2}$

Step 6

Multiply $\frac{11}{6} \cdot \frac{1}{2}$ .

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Step 6.1

Multiply $\frac{11}{6}$ by $\frac{1}{2}$ .

$\frac{11}{6 \cdot 2}$

Step 6.2

Multiply $6$ by $2$ .

$\frac{11}{12}$

Step 7

Convert the median $\frac{11}{12}$ to decimal.

$0.91\overline{6}$