Basic Math Examples

$21$ , $600 - \frac{1}{4} - \frac{1}{5} - \frac{1}{10} - \frac{1}{9} - \frac{1}{4}$

Step 1

Arrange the terms in ascending order.

$21, 600 - \frac{1}{4} - \frac{1}{5} - \frac{1}{10} - \frac{1}{9} - \frac{1}{4}$

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.

$\frac{21 + 600 - \frac{1}{4} - \frac{1}{5} - \frac{1}{10} - \frac{1}{9} - \frac{1}{4}}{2}$

Step 3

Remove parentheses.

$\frac{21 + 600 - \frac{1}{4} - \frac{1}{5} - \frac{1}{10} - \frac{1}{9} - \frac{1}{4}}{2}$

Step 4

Simplify the numerator.

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Step 4.1

Add $21$ and $600$ .

$\frac{621 - \frac{1}{4} - \frac{1}{5} - \frac{1}{10} - \frac{1}{9} - \frac{1}{4}}{2}$

Step 4.2

To write $621$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{621 \cdot \frac{4}{4} - \frac{1}{4} - \frac{1}{5} - \frac{1}{10} - \frac{1}{9} - \frac{1}{4}}{2}$

Step 4.3

Combine $621$ and $\frac{4}{4}$ .

$\frac{\frac{621 \cdot 4}{4} - \frac{1}{4} - \frac{1}{5} - \frac{1}{10} - \frac{1}{9} - \frac{1}{4}}{2}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{\frac{621 \cdot 4 - 1}{4} - \frac{1}{5} - \frac{1}{10} - \frac{1}{9} - \frac{1}{4}}{2}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $621$ by $4$ .

$\frac{\frac{2484 - 1}{4} - \frac{1}{5} - \frac{1}{10} - \frac{1}{9} - \frac{1}{4}}{2}$

Step 4.5.2

Subtract $1$ from $2484$ .

$\frac{\frac{2483}{4} - \frac{1}{5} - \frac{1}{10} - \frac{1}{9} - \frac{1}{4}}{2}$

Step 4.6

To write $\frac{2483}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{\frac{2483}{4} \cdot \frac{5}{5} - \frac{1}{5} - \frac{1}{10} - \frac{1}{9} - \frac{1}{4}}{2}$

Step 4.7

To write $- \frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{\frac{2483}{4} \cdot \frac{5}{5} - \frac{1}{5} \cdot \frac{4}{4} - \frac{1}{10} - \frac{1}{9} - \frac{1}{4}}{2}$

Step 4.8

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.8.1

Multiply $\frac{2483}{4}$ by $\frac{5}{5}$ .

$\frac{\frac{2483 \cdot 5}{4 \cdot 5} - \frac{1}{5} \cdot \frac{4}{4} - \frac{1}{10} - \frac{1}{9} - \frac{1}{4}}{2}$

Step 4.8.2

Multiply $4$ by $5$ .

$\frac{\frac{2483 \cdot 5}{20} - \frac{1}{5} \cdot \frac{4}{4} - \frac{1}{10} - \frac{1}{9} - \frac{1}{4}}{2}$

Step 4.8.3

Multiply $\frac{1}{5}$ by $\frac{4}{4}$ .

$\frac{\frac{2483 \cdot 5}{20} - \frac{4}{5 \cdot 4} - \frac{1}{10} - \frac{1}{9} - \frac{1}{4}}{2}$

Step 4.8.4

Multiply $5$ by $4$ .

$\frac{\frac{2483 \cdot 5}{20} - \frac{4}{20} - \frac{1}{10} - \frac{1}{9} - \frac{1}{4}}{2}$

Step 4.9

Combine the numerators over the common denominator.

$\frac{\frac{2483 \cdot 5 - 4}{20} - \frac{1}{10} - \frac{1}{9} - \frac{1}{4}}{2}$

Step 4.10

Simplify the numerator.

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Step 4.10.1

Multiply $2483$ by $5$ .

$\frac{\frac{12415 - 4}{20} - \frac{1}{10} - \frac{1}{9} - \frac{1}{4}}{2}$

Step 4.10.2

Subtract $4$ from $12415$ .

$\frac{\frac{12411}{20} - \frac{1}{10} - \frac{1}{9} - \frac{1}{4}}{2}$

Step 4.11

To write $- \frac{1}{10}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{12411}{20} - \frac{1}{10} \cdot \frac{2}{2} - \frac{1}{9} - \frac{1}{4}}{2}$

Step 4.12

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.12.1

Multiply $\frac{1}{10}$ by $\frac{2}{2}$ .

$\frac{\frac{12411}{20} - \frac{2}{10 \cdot 2} - \frac{1}{9} - \frac{1}{4}}{2}$

Step 4.12.2

Multiply $10$ by $2$ .

$\frac{\frac{12411}{20} - \frac{2}{20} - \frac{1}{9} - \frac{1}{4}}{2}$

Step 4.13

Combine the numerators over the common denominator.

$\frac{\frac{12411 - 2}{20} - \frac{1}{9} - \frac{1}{4}}{2}$

Step 4.14

Subtract $2$ from $12411$ .

$\frac{\frac{12409}{20} - \frac{1}{9} - \frac{1}{4}}{2}$

Step 4.15

To write $\frac{12409}{20}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{\frac{12409}{20} \cdot \frac{9}{9} - \frac{1}{9} - \frac{1}{4}}{2}$

Step 4.16

To write $- \frac{1}{9}$ as a fraction with a common denominator, multiply by $\frac{20}{20}$ .

$\frac{\frac{12409}{20} \cdot \frac{9}{9} - \frac{1}{9} \cdot \frac{20}{20} - \frac{1}{4}}{2}$

Step 4.17

Write each expression with a common denominator of $180$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.17.1

Multiply $\frac{12409}{20}$ by $\frac{9}{9}$ .

$\frac{\frac{12409 \cdot 9}{20 \cdot 9} - \frac{1}{9} \cdot \frac{20}{20} - \frac{1}{4}}{2}$

Step 4.17.2

Multiply $20$ by $9$ .

$\frac{\frac{12409 \cdot 9}{180} - \frac{1}{9} \cdot \frac{20}{20} - \frac{1}{4}}{2}$

Step 4.17.3

Multiply $\frac{1}{9}$ by $\frac{20}{20}$ .

$\frac{\frac{12409 \cdot 9}{180} - \frac{20}{9 \cdot 20} - \frac{1}{4}}{2}$

Step 4.17.4

Multiply $9$ by $20$ .

$\frac{\frac{12409 \cdot 9}{180} - \frac{20}{180} - \frac{1}{4}}{2}$

Step 4.18

Combine the numerators over the common denominator.

$\frac{\frac{12409 \cdot 9 - 20}{180} - \frac{1}{4}}{2}$

Step 4.19

Simplify the numerator.

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Step 4.19.1

Multiply $12409$ by $9$ .

$\frac{\frac{111681 - 20}{180} - \frac{1}{4}}{2}$

Step 4.19.2

Subtract $20$ from $111681$ .

$\frac{\frac{111661}{180} - \frac{1}{4}}{2}$

Step 4.20

To write $- \frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{45}{45}$ .

$\frac{\frac{111661}{180} - \frac{1}{4} \cdot \frac{45}{45}}{2}$

Step 4.21

Write each expression with a common denominator of $180$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.21.1

Multiply $\frac{1}{4}$ by $\frac{45}{45}$ .

$\frac{\frac{111661}{180} - \frac{45}{4 \cdot 45}}{2}$

Step 4.21.2

Multiply $4$ by $45$ .

$\frac{\frac{111661}{180} - \frac{45}{180}}{2}$

Step 4.22

Combine the numerators over the common denominator.

$\frac{\frac{111661 - 45}{180}}{2}$

Step 4.23

Subtract $45$ from $111661$ .

$\frac{\frac{111616}{180}}{2}$

Step 4.24

Cancel the common factor of $111616$ and $180$ .

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Step 4.24.1

Factor $4$ out of $111616$ .

$\frac{\frac{4 (27904)}{180}}{2}$

Step 4.24.2

Cancel the common factors.

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Step 4.24.2.1

Factor $4$ out of $180$ .

$\frac{\frac{4 \cdot 27904}{4 \cdot 45}}{2}$

Step 4.24.2.2

Cancel the common factor.

$\frac{\frac{4 \cdot 27904}{4 \cdot 45}}{2}$

Step 4.24.2.3

Rewrite the expression.

$\frac{\frac{27904}{45}}{2}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{27904}{45} \cdot \frac{1}{2}$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Factor $2$ out of $27904$ .

$\frac{2 (13952)}{45} \cdot \frac{1}{2}$

Step 6.2

Cancel the common factor.

$\frac{2 \cdot 13952}{45} \cdot \frac{1}{2}$

Step 6.3

Rewrite the expression.

$\frac{13952}{45}$

Step 7

Convert the median $\frac{13952}{45}$ to decimal.

$310.0\overline{4}$