Algebra Examples

$1 \frac{1}{4}$ , $\frac{5}{8}$ , $\frac{3}{5}$ , $\frac{1}{2}$ , $1 \frac{1}{2}$ , $1 \frac{3}{4}$

Step 1

Arrange the terms in ascending order.

$\frac{1}{2}, \frac{3}{5}, \frac{5}{8}, 1 \frac{1}{4}, 1 \frac{1}{2}, 1 \frac{3}{4}$

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.

$\frac{\frac{5}{8} + 1 \frac{1}{4}}{2}$

Step 3

Remove parentheses.

$\frac{\frac{5}{8} + 1 \frac{1}{4}}{2}$

Step 4

Convert $1 \frac{1}{4}$ to an improper fraction.

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Step 4.1

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

$\frac{\frac{5}{8} + 1 + \frac{1}{4}}{2}$

Step 4.2

Add $1$ and $\frac{1}{4}$ .

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Step 4.2.1

Write $1$ as a fraction with a common denominator.

$\frac{\frac{5}{8} + \frac{4}{4} + \frac{1}{4}}{2}$

Step 4.2.2

Combine the numerators over the common denominator.

$\frac{\frac{5}{8} + \frac{4 + 1}{4}}{2}$

Step 4.2.3

Add $4$ and $1$ .

$\frac{\frac{5}{8} + \frac{5}{4}}{2}$

Step 5

Simplify the numerator.

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Step 5.1

To write $\frac{5}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{5}{8} + \frac{5}{4} \cdot \frac{2}{2}}{2}$

Step 5.2

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.2.1

Multiply $\frac{5}{4}$ by $\frac{2}{2}$ .

$\frac{\frac{5}{8} + \frac{5 \cdot 2}{4 \cdot 2}}{2}$

Step 5.2.2

Multiply $4$ by $2$ .

$\frac{\frac{5}{8} + \frac{5 \cdot 2}{8}}{2}$

Step 5.3

Combine the numerators over the common denominator.

$\frac{\frac{5 + 5 \cdot 2}{8}}{2}$

Step 5.4

Simplify the numerator.

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Step 5.4.1

Multiply $5$ by $2$ .

$\frac{\frac{5 + 10}{8}}{2}$

Step 5.4.2

Add $5$ and $10$ .

$\frac{\frac{15}{8}}{2}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$\frac{15}{8} \cdot \frac{1}{2}$

Step 7

Multiply $\frac{15}{8} \cdot \frac{1}{2}$ .

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Step 7.1

Multiply $\frac{15}{8}$ by $\frac{1}{2}$ .

$\frac{15}{8 \cdot 2}$

Step 7.2

Multiply $8$ by $2$ .

$\frac{15}{16}$

Step 8

Convert the median $\frac{15}{16}$ to decimal.

$0.9375$