Finite Math Examples

${(1 - 2.7)}^{2} (\frac{1}{6}) + {(2 - 2.7)}^{2} (\frac{1}{6}) + {(3 - 2.7)}^{2} (\frac{1}{6}) + {(4 - 2.7)}^{2} (\frac{1}{6}) + {(5 - 2.7)}^{2} (\frac{1}{6}) + {(6 - 2.7)}^{2} (\frac{1}{6})$

Step 1

Simplify each term.

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Step 1.1

Subtract $2.7$ from $1$ .

${(- 1.7)}^{2} \frac{1}{6} + {(2 - 2.7)}^{2} (\frac{1}{6}) + {(3 - 2.7)}^{2} (\frac{1}{6}) + {(4 - 2.7)}^{2} (\frac{1}{6}) + {(5 - 2.7)}^{2} (\frac{1}{6}) + {(6 - 2.7)}^{2} (\frac{1}{6})$

Step 1.2

Raise $- 1.7$ to the power of $2$ .

$2.89 (\frac{1}{6}) + {(2 - 2.7)}^{2} (\frac{1}{6}) + {(3 - 2.7)}^{2} (\frac{1}{6}) + {(4 - 2.7)}^{2} (\frac{1}{6}) + {(5 - 2.7)}^{2} (\frac{1}{6}) + {(6 - 2.7)}^{2} (\frac{1}{6})$

Step 1.3

Combine $2.89$ and $\frac{1}{6}$ .

$\frac{2.89}{6} + {(2 - 2.7)}^{2} (\frac{1}{6}) + {(3 - 2.7)}^{2} (\frac{1}{6}) + {(4 - 2.7)}^{2} (\frac{1}{6}) + {(5 - 2.7)}^{2} (\frac{1}{6}) + {(6 - 2.7)}^{2} (\frac{1}{6})$

Step 1.4

Divide $2.89$ by $6$ .

$0.481\overline{6} + {(2 - 2.7)}^{2} (\frac{1}{6}) + {(3 - 2.7)}^{2} (\frac{1}{6}) + {(4 - 2.7)}^{2} (\frac{1}{6}) + {(5 - 2.7)}^{2} (\frac{1}{6}) + {(6 - 2.7)}^{2} (\frac{1}{6})$

Step 1.5

Subtract $2.7$ from $2$ .

$0.481\overline{6} + {(- 0.7)}^{2} \frac{1}{6} + {(3 - 2.7)}^{2} (\frac{1}{6}) + {(4 - 2.7)}^{2} (\frac{1}{6}) + {(5 - 2.7)}^{2} (\frac{1}{6}) + {(6 - 2.7)}^{2} (\frac{1}{6})$

Step 1.6

Raise $- 0.7$ to the power of $2$ .

$0.481\overline{6} + 0.49 (\frac{1}{6}) + {(3 - 2.7)}^{2} (\frac{1}{6}) + {(4 - 2.7)}^{2} (\frac{1}{6}) + {(5 - 2.7)}^{2} (\frac{1}{6}) + {(6 - 2.7)}^{2} (\frac{1}{6})$

Step 1.7

Combine $0.49$ and $\frac{1}{6}$ .

$0.481\overline{6} + \frac{0.49}{6} + {(3 - 2.7)}^{2} (\frac{1}{6}) + {(4 - 2.7)}^{2} (\frac{1}{6}) + {(5 - 2.7)}^{2} (\frac{1}{6}) + {(6 - 2.7)}^{2} (\frac{1}{6})$

Step 1.8

Divide $0.49$ by $6$ .

$0.481\overline{6} + 0.081\overline{6} + {(3 - 2.7)}^{2} (\frac{1}{6}) + {(4 - 2.7)}^{2} (\frac{1}{6}) + {(5 - 2.7)}^{2} (\frac{1}{6}) + {(6 - 2.7)}^{2} (\frac{1}{6})$

Step 1.9

Subtract $2.7$ from $3$ .

$0.481\overline{6} + 0.081\overline{6} + {0.3}^{2} \frac{1}{6} + {(4 - 2.7)}^{2} (\frac{1}{6}) + {(5 - 2.7)}^{2} (\frac{1}{6}) + {(6 - 2.7)}^{2} (\frac{1}{6})$

Step 1.10

Raise $0.3$ to the power of $2$ .

$0.481\overline{6} + 0.081\overline{6} + 0.09 (\frac{1}{6}) + {(4 - 2.7)}^{2} (\frac{1}{6}) + {(5 - 2.7)}^{2} (\frac{1}{6}) + {(6 - 2.7)}^{2} (\frac{1}{6})$

Step 1.11

Cancel the common factor of $0.03$ .

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Step 1.11.1

Factor $0.03$ out of $0.09$ .

$0.481\overline{6} + 0.081\overline{6} + 0.03 (3) \frac{1}{6} + {(4 - 2.7)}^{2} (\frac{1}{6}) + {(5 - 2.7)}^{2} (\frac{1}{6}) + {(6 - 2.7)}^{2} (\frac{1}{6})$

Step 1.11.2

Factor $0.03$ out of $6$ .

$0.481\overline{6} + 0.081\overline{6} + 0.03 \cdot 3 \frac{1}{0.03 \cdot 200} + {(4 - 2.7)}^{2} (\frac{1}{6}) + {(5 - 2.7)}^{2} (\frac{1}{6}) + {(6 - 2.7)}^{2} (\frac{1}{6})$

Step 1.11.3

Cancel the common factor.

$0.481\overline{6} + 0.081\overline{6} + 0.03 \cdot 3 \frac{1}{0.03 \cdot 200} + {(4 - 2.7)}^{2} (\frac{1}{6}) + {(5 - 2.7)}^{2} (\frac{1}{6}) + {(6 - 2.7)}^{2} (\frac{1}{6})$

Step 1.11.4

Rewrite the expression.

$0.481\overline{6} + 0.081\overline{6} + 3 (\frac{1}{200}) + {(4 - 2.7)}^{2} (\frac{1}{6}) + {(5 - 2.7)}^{2} (\frac{1}{6}) + {(6 - 2.7)}^{2} (\frac{1}{6})$

Step 1.12

Combine $3$ and $\frac{1}{200}$ .

$0.481\overline{6} + 0.081\overline{6} + \frac{3}{200} + {(4 - 2.7)}^{2} (\frac{1}{6}) + {(5 - 2.7)}^{2} (\frac{1}{6}) + {(6 - 2.7)}^{2} (\frac{1}{6})$

Step 1.13

Subtract $2.7$ from $4$ .

$0.481\overline{6} + 0.081\overline{6} + \frac{3}{200} + {1.3}^{2} \frac{1}{6} + {(5 - 2.7)}^{2} (\frac{1}{6}) + {(6 - 2.7)}^{2} (\frac{1}{6})$

Step 1.14

Raise $1.3$ to the power of $2$ .

$0.481\overline{6} + 0.081\overline{6} + \frac{3}{200} + 1.69 (\frac{1}{6}) + {(5 - 2.7)}^{2} (\frac{1}{6}) + {(6 - 2.7)}^{2} (\frac{1}{6})$

Step 1.15

Combine $1.69$ and $\frac{1}{6}$ .

$0.481\overline{6} + 0.081\overline{6} + \frac{3}{200} + \frac{1.69}{6} + {(5 - 2.7)}^{2} (\frac{1}{6}) + {(6 - 2.7)}^{2} (\frac{1}{6})$

Step 1.16

Divide $1.69$ by $6$ .

$0.481\overline{6} + 0.081\overline{6} + \frac{3}{200} + 0.281\overline{6} + {(5 - 2.7)}^{2} (\frac{1}{6}) + {(6 - 2.7)}^{2} (\frac{1}{6})$

Step 1.17

Subtract $2.7$ from $5$ .

$0.481\overline{6} + 0.081\overline{6} + \frac{3}{200} + 0.281\overline{6} + {2.3}^{2} \frac{1}{6} + {(6 - 2.7)}^{2} (\frac{1}{6})$

Step 1.18

Raise $2.3$ to the power of $2$ .

$0.481\overline{6} + 0.081\overline{6} + \frac{3}{200} + 0.281\overline{6} + 5.29 (\frac{1}{6}) + {(6 - 2.7)}^{2} (\frac{1}{6})$

Step 1.19

Combine $5.29$ and $\frac{1}{6}$ .

$0.481\overline{6} + 0.081\overline{6} + \frac{3}{200} + 0.281\overline{6} + \frac{5.29}{6} + {(6 - 2.7)}^{2} (\frac{1}{6})$

Step 1.20

Divide $5.29$ by $6$ .

$0.481\overline{6} + 0.081\overline{6} + \frac{3}{200} + 0.281\overline{6} + 0.881\overline{6} + {(6 - 2.7)}^{2} (\frac{1}{6})$

Step 1.21

Subtract $2.7$ from $6$ .

$0.481\overline{6} + 0.081\overline{6} + \frac{3}{200} + 0.281\overline{6} + 0.881\overline{6} + {3.3}^{2} \frac{1}{6}$

Step 1.22

Raise $3.3$ to the power of $2$ .

$0.481\overline{6} + 0.081\overline{6} + \frac{3}{200} + 0.281\overline{6} + 0.881\overline{6} + 10.89 (\frac{1}{6})$

Step 1.23

Combine $10.89$ and $\frac{1}{6}$ .

$0.481\overline{6} + 0.081\overline{6} + \frac{3}{200} + 0.281\overline{6} + 0.881\overline{6} + \frac{10.89}{6}$

Step 1.24

Divide $10.89$ by $6$ .

$0.481\overline{6} + 0.081\overline{6} + \frac{3}{200} + 0.281\overline{6} + 0.881\overline{6} + 1.815$

Step 2

Find the common denominator.

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Step 2.1

Write $0.481\overline{6}$ as a fraction with denominator $1$ .

$\frac{0.481\overline{6}}{1} + 0.081\overline{6} + \frac{3}{200} + 0.281\overline{6} + 0.881\overline{6} + 1.815$

Step 2.2

Multiply $\frac{0.481\overline{6}}{1}$ by $\frac{200}{200}$ .

$\frac{0.481\overline{6}}{1} \cdot \frac{200}{200} + 0.081\overline{6} + \frac{3}{200} + 0.281\overline{6} + 0.881\overline{6} + 1.815$

Step 2.3

Multiply $\frac{0.481\overline{6}}{1}$ by $\frac{200}{200}$ .

$\frac{0.481\overline{6} \cdot 200}{200} + 0.081\overline{6} + \frac{3}{200} + 0.281\overline{6} + 0.881\overline{6} + 1.815$

Step 2.4

Write $0.081\overline{6}$ as a fraction with denominator $1$ .

$\frac{0.481\overline{6} \cdot 200}{200} + \frac{0.081\overline{6}}{1} + \frac{3}{200} + 0.281\overline{6} + 0.881\overline{6} + 1.815$

Step 2.5

Multiply $\frac{0.081\overline{6}}{1}$ by $\frac{200}{200}$ .

$\frac{0.481\overline{6} \cdot 200}{200} + \frac{0.081\overline{6}}{1} \cdot \frac{200}{200} + \frac{3}{200} + 0.281\overline{6} + 0.881\overline{6} + 1.815$

Step 2.6

Multiply $\frac{0.081\overline{6}}{1}$ by $\frac{200}{200}$ .

$\frac{0.481\overline{6} \cdot 200}{200} + \frac{0.081\overline{6} \cdot 200}{200} + \frac{3}{200} + 0.281\overline{6} + 0.881\overline{6} + 1.815$

Step 2.7

Write $0.281\overline{6}$ as a fraction with denominator $1$ .

$\frac{0.481\overline{6} \cdot 200}{200} + \frac{0.081\overline{6} \cdot 200}{200} + \frac{3}{200} + \frac{0.281\overline{6}}{1} + 0.881\overline{6} + 1.815$

Step 2.8

Multiply $\frac{0.281\overline{6}}{1}$ by $\frac{200}{200}$ .

$\frac{0.481\overline{6} \cdot 200}{200} + \frac{0.081\overline{6} \cdot 200}{200} + \frac{3}{200} + \frac{0.281\overline{6}}{1} \cdot \frac{200}{200} + 0.881\overline{6} + 1.815$

Step 2.9

Multiply $\frac{0.281\overline{6}}{1}$ by $\frac{200}{200}$ .

$\frac{0.481\overline{6} \cdot 200}{200} + \frac{0.081\overline{6} \cdot 200}{200} + \frac{3}{200} + \frac{0.281\overline{6} \cdot 200}{200} + 0.881\overline{6} + 1.815$

Step 2.10

Write $0.881\overline{6}$ as a fraction with denominator $1$ .

$\frac{0.481\overline{6} \cdot 200}{200} + \frac{0.081\overline{6} \cdot 200}{200} + \frac{3}{200} + \frac{0.281\overline{6} \cdot 200}{200} + \frac{0.881\overline{6}}{1} + 1.815$

Step 2.11

Multiply $\frac{0.881\overline{6}}{1}$ by $\frac{200}{200}$ .

$\frac{0.481\overline{6} \cdot 200}{200} + \frac{0.081\overline{6} \cdot 200}{200} + \frac{3}{200} + \frac{0.281\overline{6} \cdot 200}{200} + \frac{0.881\overline{6}}{1} \cdot \frac{200}{200} + 1.815$

Step 2.12

Multiply $\frac{0.881\overline{6}}{1}$ by $\frac{200}{200}$ .

$\frac{0.481\overline{6} \cdot 200}{200} + \frac{0.081\overline{6} \cdot 200}{200} + \frac{3}{200} + \frac{0.281\overline{6} \cdot 200}{200} + \frac{0.881\overline{6} \cdot 200}{200} + 1.815$

Step 2.13

Write $1.815$ as a fraction with denominator $1$ .

Step 2.14

Multiply $\frac{1.815}{1}$ by $\frac{200}{200}$ .

Step 2.15

Multiply $\frac{1.815}{1}$ by $\frac{200}{200}$ .

Step 3

Combine the numerators over the common denominator.

$\frac{0.481\overline{6} \cdot 200 + 0.081\overline{6} \cdot 200 + 3 + 0.281\overline{6} \cdot 200 + 0.881\overline{6} \cdot 200 + 1.815 \cdot 200}{200}$

Step 4

Simplify each term.

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Step 4.1

Multiply $0.481\overline{6}$ by $200$ .

$\frac{96.\overline{3} + 0.081\overline{6} \cdot 200 + 3 + 0.281\overline{6} \cdot 200 + 0.881\overline{6} \cdot 200 + 1.815 \cdot 200}{200}$

Step 4.2

Multiply $0.081\overline{6}$ by $200$ .

$\frac{96.\overline{3} + 16.\overline{3} + 3 + 0.281\overline{6} \cdot 200 + 0.881\overline{6} \cdot 200 + 1.815 \cdot 200}{200}$

Step 4.3

Multiply $0.281\overline{6}$ by $200$ .

$\frac{96.\overline{3} + 16.\overline{3} + 3 + 56.\overline{3} + 0.881\overline{6} \cdot 200 + 1.815 \cdot 200}{200}$

Step 4.4

Multiply $0.881\overline{6}$ by $200$ .

$\frac{96.\overline{3} + 16.\overline{3} + 3 + 56.\overline{3} + 176.\overline{3} + 1.815 \cdot 200}{200}$

Step 4.5

Multiply $1.815$ by $200$ .

$\frac{96.\overline{3} + 16.\overline{3} + 3 + 56.\overline{3} + 176.\overline{3} + 363}{200}$

Step 5

Simplify the expression.

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Step 5.1

Add $96.\overline{3}$ and $16.\overline{3}$ .

$\frac{112.\overline{6} + 3 + 56.\overline{3} + 176.\overline{3} + 363}{200}$

Step 5.2

Add $112.\overline{6}$ and $3$ .

$\frac{115.\overline{6} + 56.\overline{3} + 176.\overline{3} + 363}{200}$

Step 5.3

Add $115.\overline{6}$ and $56.\overline{3}$ .

$\frac{172 + 176.\overline{3} + 363}{200}$

Step 5.4

Add $172$ and $176.\overline{3}$ .

$\frac{348.\overline{3} + 363}{200}$

Step 5.5

Add $348.\overline{3}$ and $363$ .

$\frac{711.\overline{3}}{200}$

Step 5.6

Divide $711.\overline{3}$ by $200$ .

$3.55\overline{6}$