Finite Math Examples

$30$ , $60$ , $60$ , $60$ , $60$ , $60$ , $60$ , $60$ , $60$ , $70$ , $100$ , $100$ , $100$ , $100$

Step 1

The mean of a set of numbers is the sum divided by the number of terms.

$\frac{30 + 60 + 60 + 60 + 60 + 60 + 60 + 60 + 60 + 70 + 100 + 100 + 100 + 100}{14}$

Step 2

Cancel the common factor of $30 + 60 + 60 + 60 + 60 + 60 + 60 + 60 + 60 + 70 + 100 + 100 + 100 + 100$ and $14$ .

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Step 2.1

Factor $2$ out of $30$ .

$\frac{2 (15) + 60 + 60 + 60 + 60 + 60 + 60 + 60 + 60 + 70 + 100 + 100 + 100 + 100}{14}$

Step 2.2

Factor $2$ out of $60$ .

$\frac{2 \cdot 15 + 2 \cdot 30 + 60 + 60 + 60 + 60 + 60 + 60 + 60 + 70 + 100 + 100 + 100 + 100}{14}$

Step 2.3

Factor $2$ out of $2 \cdot 15 + 2 \cdot 30$ .

$\frac{2 \cdot (15 + 30) + 60 + 60 + 60 + 60 + 60 + 60 + 60 + 70 + 100 + 100 + 100 + 100}{14}$

Step 2.4

Factor $2$ out of $60$ .

$\frac{2 \cdot (15 + 30) + 2 (30) + 60 + 60 + 60 + 60 + 60 + 60 + 70 + 100 + 100 + 100 + 100}{14}$

Step 2.5

Factor $2$ out of $2 \cdot (15 + 30) + 2 (30)$ .

$\frac{2 \cdot (15 + 30 + 30) + 60 + 60 + 60 + 60 + 60 + 60 + 70 + 100 + 100 + 100 + 100}{14}$

Step 2.6

Factor $2$ out of $60$ .

$\frac{2 \cdot (15 + 30 + 30) + 2 (30) + 60 + 60 + 60 + 60 + 60 + 70 + 100 + 100 + 100 + 100}{14}$

Step 2.7

Factor $2$ out of $2 \cdot (15 + 30 + 30) + 2 (30)$ .

$\frac{2 \cdot (15 + 30 + 30 + 30) + 60 + 60 + 60 + 60 + 60 + 70 + 100 + 100 + 100 + 100}{14}$

Step 2.8

Factor $2$ out of $60$ .

$\frac{2 \cdot (15 + 30 + 30 + 30) + 2 (30) + 60 + 60 + 60 + 60 + 70 + 100 + 100 + 100 + 100}{14}$

Step 2.9

Factor $2$ out of $2 \cdot (15 + 30 + 30 + 30) + 2 (30)$ .

$\frac{2 \cdot (15 + 30 + 30 + 30 + 30) + 60 + 60 + 60 + 60 + 70 + 100 + 100 + 100 + 100}{14}$

Step 2.10

Factor $2$ out of $60$ .

$\frac{2 \cdot (15 + 30 + 30 + 30 + 30) + 2 (30) + 60 + 60 + 60 + 70 + 100 + 100 + 100 + 100}{14}$

Step 2.11

Factor $2$ out of $2 \cdot (15 + 30 + 30 + 30 + 30) + 2 (30)$ .

$\frac{2 \cdot (15 + 30 + 30 + 30 + 30 + 30) + 60 + 60 + 60 + 70 + 100 + 100 + 100 + 100}{14}$

Step 2.12

Factor $2$ out of $60$ .

$\frac{2 \cdot (15 + 30 + 30 + 30 + 30 + 30) + 2 (30) + 60 + 60 + 70 + 100 + 100 + 100 + 100}{14}$

Step 2.13

Factor $2$ out of $2 \cdot (15 + 30 + 30 + 30 + 30 + 30) + 2 (30)$ .

$\frac{2 \cdot (15 + 30 + 30 + 30 + 30 + 30 + 30) + 60 + 60 + 70 + 100 + 100 + 100 + 100}{14}$

Step 2.14

Factor $2$ out of $60$ .

$\frac{2 \cdot (15 + 30 + 30 + 30 + 30 + 30 + 30) + 2 (30) + 60 + 70 + 100 + 100 + 100 + 100}{14}$

Step 2.15

Factor $2$ out of $2 \cdot (15 + 30 + 30 + 30 + 30 + 30 + 30) + 2 (30)$ .

$\frac{2 \cdot (15 + 30 + 30 + 30 + 30 + 30 + 30 + 30) + 60 + 70 + 100 + 100 + 100 + 100}{14}$

Step 2.16

Factor $2$ out of $60$ .

$\frac{2 \cdot (15 + 30 + 30 + 30 + 30 + 30 + 30 + 30) + 2 (30) + 70 + 100 + 100 + 100 + 100}{14}$

Step 2.17

Factor $2$ out of $2 \cdot (15 + 30 + 30 + 30 + 30 + 30 + 30 + 30) + 2 (30)$ .

$\frac{2 \cdot (15 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30) + 70 + 100 + 100 + 100 + 100}{14}$

Step 2.18

Factor $2$ out of $70$ .

$\frac{2 \cdot (15 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30) + 2 (35) + 100 + 100 + 100 + 100}{14}$

Step 2.19

Factor $2$ out of $2 \cdot (15 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30) + 2 (35)$ .

$\frac{2 \cdot (15 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 35) + 100 + 100 + 100 + 100}{14}$

Step 2.20

Factor $2$ out of $100$ .

$\frac{2 \cdot (15 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 35) + 2 (50) + 100 + 100 + 100}{14}$

Step 2.21

Factor $2$ out of $2 \cdot (15 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 35) + 2 (50)$ .

$\frac{2 \cdot (15 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 35 + 50) + 100 + 100 + 100}{14}$

Step 2.22

Factor $2$ out of $100$ .

$\frac{2 \cdot (15 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 35 + 50) + 2 (50) + 100 + 100}{14}$

Step 2.23

Factor $2$ out of $2 \cdot (15 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 35 + 50) + 2 (50)$ .

$\frac{2 \cdot (15 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 35 + 50 + 50) + 100 + 100}{14}$

Step 2.24

Factor $2$ out of $100$ .

$\frac{2 \cdot (15 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 35 + 50 + 50) + 2 (50) + 100}{14}$

Step 2.25

Factor $2$ out of $2 \cdot (15 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 35 + 50 + 50) + 2 (50)$ .

$\frac{2 \cdot (15 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 35 + 50 + 50 + 50) + 100}{14}$

Step 2.26

Factor $2$ out of $100$ .

$\frac{2 \cdot (15 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 35 + 50 + 50 + 50) + 2 (50)}{14}$

Step 2.27

Factor $2$ out of $2 \cdot (15 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 35 + 50 + 50 + 50) + 2 (50)$ .

$\frac{2 \cdot (15 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 35 + 50 + 50 + 50 + 50)}{14}$

Step 2.28

Cancel the common factors.

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Step 2.28.1

Factor $2$ out of $14$ .

$\frac{2 \cdot (15 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 35 + 50 + 50 + 50 + 50)}{2 (7)}$

Step 2.28.2

Cancel the common factor.

$\frac{2 \cdot (15 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 35 + 50 + 50 + 50 + 50)}{2 \cdot 7}$

Step 2.28.3

Rewrite the expression.

$\frac{15 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 35 + 50 + 50 + 50 + 50}{7}$

Step 3

Simplify the numerator.

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Step 3.1

Add $15$ and $30$ .

$\frac{45 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 35 + 50 + 50 + 50 + 50}{7}$

Step 3.2

Add $45$ and $30$ .

$\frac{75 + 30 + 30 + 30 + 30 + 30 + 30 + 35 + 50 + 50 + 50 + 50}{7}$

Step 3.3

Add $75$ and $30$ .

$\frac{105 + 30 + 30 + 30 + 30 + 30 + 35 + 50 + 50 + 50 + 50}{7}$

Step 3.4

Add $105$ and $30$ .

$\frac{135 + 30 + 30 + 30 + 30 + 35 + 50 + 50 + 50 + 50}{7}$

Step 3.5

Add $135$ and $30$ .

$\frac{165 + 30 + 30 + 30 + 35 + 50 + 50 + 50 + 50}{7}$

Step 3.6

Add $165$ and $30$ .

$\frac{195 + 30 + 30 + 35 + 50 + 50 + 50 + 50}{7}$

Step 3.7

Add $195$ and $30$ .

$\frac{225 + 30 + 35 + 50 + 50 + 50 + 50}{7}$

Step 3.8

Add $225$ and $30$ .

$\frac{255 + 35 + 50 + 50 + 50 + 50}{7}$

Step 3.9

Add $255$ and $35$ .

$\frac{290 + 50 + 50 + 50 + 50}{7}$

Step 3.10

Add $290$ and $50$ .

$\frac{340 + 50 + 50 + 50}{7}$

Step 3.11

Add $340$ and $50$ .

$\frac{390 + 50 + 50}{7}$

Step 3.12

Add $390$ and $50$ .

$\frac{440 + 50}{7}$

Step 3.13

Add $440$ and $50$ .

$\frac{490}{7}$

Step 4

Divide $490$ by $7$ .

$70$