Pre-Algebra Examples

$\frac{2}{5}$ , $\frac{5}{12}$

Step 1

There are $2$ observations, so the median is the mean of the two middle numbers of the arranged set of data. Splitting the observations either side of the median gives two groups of observations. The median of the lower half of data is the lower or first quartile. The median of the upper half of data is the upper or third quartile.

The median of the lower half of data is the lower or first quartile

The median of the upper half of data is the upper or third quartile

Step 2

Arrange the terms in ascending order.

$\frac{2}{5}, \frac{5}{12}$

Step 3

Find the median of $\frac{2}{5}, \frac{5}{12}$ .

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Step 3.1

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.

$\frac{\frac{2}{5} + \frac{5}{12}}{2}$

Step 3.2

Remove parentheses.

$\frac{\frac{2}{5} + \frac{5}{12}}{2}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

To write $\frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$\frac{\frac{2}{5} \cdot \frac{12}{12} + \frac{5}{12}}{2}$

Step 3.3.2

To write $\frac{5}{12}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{\frac{2}{5} \cdot \frac{12}{12} + \frac{5}{12} \cdot \frac{5}{5}}{2}$

Step 3.3.3

Write each expression with a common denominator of $60$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.3.1

Multiply $\frac{2}{5}$ by $\frac{12}{12}$ .

$\frac{\frac{2 \cdot 12}{5 \cdot 12} + \frac{5}{12} \cdot \frac{5}{5}}{2}$

Step 3.3.3.2

Multiply $5$ by $12$ .

$\frac{\frac{2 \cdot 12}{60} + \frac{5}{12} \cdot \frac{5}{5}}{2}$

Step 3.3.3.3

Multiply $\frac{5}{12}$ by $\frac{5}{5}$ .

$\frac{\frac{2 \cdot 12}{60} + \frac{5 \cdot 5}{12 \cdot 5}}{2}$

Step 3.3.3.4

Multiply $12$ by $5$ .

$\frac{\frac{2 \cdot 12}{60} + \frac{5 \cdot 5}{60}}{2}$

Step 3.3.4

Combine the numerators over the common denominator.

$\frac{\frac{2 \cdot 12 + 5 \cdot 5}{60}}{2}$

Step 3.3.5

Simplify the numerator.

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Step 3.3.5.1

Multiply $2$ by $12$ .

$\frac{\frac{24 + 5 \cdot 5}{60}}{2}$

Step 3.3.5.2

Multiply $5$ by $5$ .

$\frac{\frac{24 + 25}{60}}{2}$

Step 3.3.5.3

Add $24$ and $25$ .

$\frac{\frac{49}{60}}{2}$

Step 3.4

Multiply the numerator by the reciprocal of the denominator.

$\frac{49}{60} \cdot \frac{1}{2}$

Step 3.5

Multiply $\frac{49}{60} \cdot \frac{1}{2}$ .

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Step 3.5.1

Multiply $\frac{49}{60}$ by $\frac{1}{2}$ .

$\frac{49}{60 \cdot 2}$

Step 3.5.2

Multiply $60$ by $2$ .

$\frac{49}{120}$

Step 3.6

Convert the median $\frac{49}{120}$ to decimal.

$0.408\overline{3}$

Step 4

The lower half of data is the set below the median.

$\frac{2}{5}$