Finite Math Examples

$\frac{{(38 - 23)}^{2} + {(19 - 23)}^{2} + {(17 - 23)}^{2} + {(27 - 23)}^{2} + {(24 - 23)}^{2} + {(13 - 23)}^{2}}{6}$

Step 1

Simplify the numerator.

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Step 1.1

Subtract $23$ from $38$ .

$\frac{15^{2} + {(19 - 23)}^{2} + {(17 - 23)}^{2} + {(27 - 23)}^{2} + {(24 - 23)}^{2} + {(13 - 23)}^{2}}{6}$

Step 1.2

Raise $15$ to the power of $2$ .

$\frac{225 + {(19 - 23)}^{2} + {(17 - 23)}^{2} + {(27 - 23)}^{2} + {(24 - 23)}^{2} + {(13 - 23)}^{2}}{6}$

Step 1.3

Subtract $23$ from $19$ .

$\frac{225 + {(- 4)}^{2} + {(17 - 23)}^{2} + {(27 - 23)}^{2} + {(24 - 23)}^{2} + {(13 - 23)}^{2}}{6}$

Step 1.4

Raise $- 4$ to the power of $2$ .

$\frac{225 + 16 + {(17 - 23)}^{2} + {(27 - 23)}^{2} + {(24 - 23)}^{2} + {(13 - 23)}^{2}}{6}$

Step 1.5

Subtract $23$ from $17$ .

$\frac{225 + 16 + {(- 6)}^{2} + {(27 - 23)}^{2} + {(24 - 23)}^{2} + {(13 - 23)}^{2}}{6}$

Step 1.6

Raise $- 6$ to the power of $2$ .

$\frac{225 + 16 + 36 + {(27 - 23)}^{2} + {(24 - 23)}^{2} + {(13 - 23)}^{2}}{6}$

Step 1.7

Subtract $23$ from $27$ .

$\frac{225 + 16 + 36 + 4^{2} + {(24 - 23)}^{2} + {(13 - 23)}^{2}}{6}$

Step 1.8

Raise $4$ to the power of $2$ .

$\frac{225 + 16 + 36 + 16 + {(24 - 23)}^{2} + {(13 - 23)}^{2}}{6}$

Step 1.9

Subtract $23$ from $24$ .

$\frac{225 + 16 + 36 + 16 + 1^{2} + {(13 - 23)}^{2}}{6}$

Step 1.10

One to any power is one.

$\frac{225 + 16 + 36 + 16 + 1 + {(13 - 23)}^{2}}{6}$

Step 1.11

Subtract $23$ from $13$ .

$\frac{225 + 16 + 36 + 16 + 1 + {(- 10)}^{2}}{6}$

Step 1.12

Raise $- 10$ to the power of $2$ .

$\frac{225 + 16 + 36 + 16 + 1 + 100}{6}$

Step 1.13

Add $225$ and $16$ .

$\frac{241 + 36 + 16 + 1 + 100}{6}$

Step 1.14

Add $241$ and $36$ .

$\frac{277 + 16 + 1 + 100}{6}$

Step 1.15

Add $277$ and $16$ .

$\frac{293 + 1 + 100}{6}$

Step 1.16

Add $293$ and $1$ .

$\frac{294 + 100}{6}$

Step 1.17

Add $294$ and $100$ .

$\frac{394}{6}$

Step 2

Cancel the common factor of $394$ and $6$ .

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Step 2.1

Factor $2$ out of $394$ .

$\frac{2 (197)}{6}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $6$ .

$\frac{2 \cdot 197}{2 \cdot 3}$

Step 2.2.2

Cancel the common factor.

$\frac{2 \cdot 197}{2 \cdot 3}$

Step 2.2.3

Rewrite the expression.

$\frac{197}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{197}{3}$

Decimal Form:

$65.\overline{6}$

Mixed Number Form:

$65 \frac{2}{3}$