Basic Math Examples

$61$ , $750 (\frac{0.065}{12}) \div 1 - {(1 + \frac{0.065}{12})}^{- 12 \cdot 30}$

Step 1

Arrange the terms in ascending order.

$750 (\frac{0.065}{12}) \div 1 - {(1 + \frac{0.065}{12})}^{- 12 \cdot 30}, 61$

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.

$\frac{750 (\frac{0.065}{12}) \div 1 - {(1 + \frac{0.065}{12})}^{- 12 \cdot 30} + 61}{2}$

Step 3

Simplify the expression.

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Step 3.1

Remove parentheses.

$\frac{750 (\frac{0.065}{12}) \div 1 - {(1 + \frac{0.065}{12})}^{- 12 \cdot 30} + 61}{2}$

Step 3.2

Divide $750 (\frac{0.065}{12})$ by $1$ .

$\frac{750 (\frac{0.065}{12}) - {(1 + \frac{0.065}{12})}^{- 12 \cdot 30} + 61}{2}$

Step 4

Simplify the numerator.

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Step 4.1

Cancel the common factor of $6$ .

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Step 4.1.1

Factor $6$ out of $750$ .

$\frac{6 (125) \frac{0.065}{12} - {(1 + \frac{0.065}{12})}^{- 12 \cdot 30} + 61}{2}$

Step 4.1.2

Factor $6$ out of $12$ .

$\frac{6 \cdot 125 \frac{0.065}{6 \cdot 2} - {(1 + \frac{0.065}{12})}^{- 12 \cdot 30} + 61}{2}$

Step 4.1.3

Cancel the common factor.

$\frac{6 \cdot 125 \frac{0.065}{6 \cdot 2} - {(1 + \frac{0.065}{12})}^{- 12 \cdot 30} + 61}{2}$

Step 4.1.4

Rewrite the expression.

$\frac{125 (\frac{0.065}{2}) - {(1 + \frac{0.065}{12})}^{- 12 \cdot 30} + 61}{2}$

Step 4.2

Combine $125$ and $\frac{0.065}{2}$ .

$\frac{\frac{125 \cdot 0.065}{2} - {(1 + \frac{0.065}{12})}^{- 12 \cdot 30} + 61}{2}$

Step 4.3

Multiply $125$ by $0.065$ .

$\frac{\frac{8.125}{2} - {(1 + \frac{0.065}{12})}^{- 12 \cdot 30} + 61}{2}$

Step 4.4

Divide $8.125$ by $2$ .

$\frac{4.0625 - {(1 + \frac{0.065}{12})}^{- 12 \cdot 30} + 61}{2}$

Step 4.5

Divide $0.065$ by $12$ .

$\frac{4.0625 - {(1 + 0.00541\overline{6})}^{- 12 \cdot 30} + 61}{2}$

Step 4.6

Add $1$ and $0.00541\overline{6}$ .

$\frac{4.0625 - {1.00541\overline{6}}^{- 12 \cdot 30} + 61}{2}$

Step 4.7

Multiply $- 12$ by $30$ .

$\frac{4.0625 - {1.00541\overline{6}}^{- 360} + 61}{2}$

Step 4.8

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{4.0625 - \frac{1}{{1.00541\overline{6}}^{360}} + 61}{2}$

Step 4.9

Raise $1.00541\overline{6}$ to the power of $360$ .

$\frac{4.0625 - \frac{1}{6.99179797} + 61}{2}$

Step 4.10

Divide $1$ by $6.99179797$ .

$\frac{4.0625 - 1 \cdot 0.14302472 + 61}{2}$

Step 4.11

Multiply $- 1$ by $0.14302472$ .

$\frac{4.0625 - 0.14302472 + 61}{2}$

Step 4.12

Subtract $0.14302472$ from $4.0625$ .

$\frac{3.91947527 + 61}{2}$

Step 4.13

Add $3.91947527$ and $61$ .

$\frac{64.91947527}{2}$

Step 5

Divide $64.91947527$ by $2$ .

$32.45973763$

Step 6

Convert the median $32.45973763$ to decimal.

$32.45973763$