Basic Math Examples

$0$ $2$ $4$ $6$ $8$ $10$ $12$ $14$ $16$ $18$ $20$ $22$

Step 1

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

$\frac{0 + 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22}{12}$

Step 2

Cancel the common factor of $0 + 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22$ and $12$ .

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Step 2.1

Factor $2$ out of $0$ .

$\frac{2 (0) + 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22}{12}$

Step 2.2

Factor $2$ out of $2$ .

$\frac{2 \cdot 0 + 2 \cdot 1 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22}{12}$

Step 2.3

Factor $2$ out of $2 \cdot 0 + 2 \cdot 1$ .

$\frac{2 \cdot (0 + 1) + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22}{12}$

Step 2.4

Factor $2$ out of $4$ .

$\frac{2 \cdot (0 + 1) + 2 (2) + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22}{12}$

Step 2.5

Factor $2$ out of $2 \cdot (0 + 1) + 2 (2)$ .

$\frac{2 \cdot (0 + 1 + 2) + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22}{12}$

Step 2.6

Factor $2$ out of $6$ .

$\frac{2 \cdot (0 + 1 + 2) + 2 (3) + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22}{12}$

Step 2.7

Factor $2$ out of $2 \cdot (0 + 1 + 2) + 2 (3)$ .

$\frac{2 \cdot (0 + 1 + 2 + 3) + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22}{12}$

Step 2.8

Factor $2$ out of $8$ .

$\frac{2 \cdot (0 + 1 + 2 + 3) + 2 (4) + 10 + 12 + 14 + 16 + 18 + 20 + 22}{12}$

Step 2.9

Factor $2$ out of $2 \cdot (0 + 1 + 2 + 3) + 2 (4)$ .

$\frac{2 \cdot (0 + 1 + 2 + 3 + 4) + 10 + 12 + 14 + 16 + 18 + 20 + 22}{12}$

Step 2.10

Factor $2$ out of $10$ .

$\frac{2 \cdot (0 + 1 + 2 + 3 + 4) + 2 (5) + 12 + 14 + 16 + 18 + 20 + 22}{12}$

Step 2.11

Factor $2$ out of $2 \cdot (0 + 1 + 2 + 3 + 4) + 2 (5)$ .

$\frac{2 \cdot (0 + 1 + 2 + 3 + 4 + 5) + 12 + 14 + 16 + 18 + 20 + 22}{12}$

Step 2.12

Factor $2$ out of $12$ .

$\frac{2 \cdot (0 + 1 + 2 + 3 + 4 + 5) + 2 (6) + 14 + 16 + 18 + 20 + 22}{12}$

Step 2.13

Factor $2$ out of $2 \cdot (0 + 1 + 2 + 3 + 4 + 5) + 2 (6)$ .

$\frac{2 \cdot (0 + 1 + 2 + 3 + 4 + 5 + 6) + 14 + 16 + 18 + 20 + 22}{12}$

Step 2.14

Factor $2$ out of $14$ .

$\frac{2 \cdot (0 + 1 + 2 + 3 + 4 + 5 + 6) + 2 (7) + 16 + 18 + 20 + 22}{12}$

Step 2.15

Factor $2$ out of $2 \cdot (0 + 1 + 2 + 3 + 4 + 5 + 6) + 2 (7)$ .

$\frac{2 \cdot (0 + 1 + 2 + 3 + 4 + 5 + 6 + 7) + 16 + 18 + 20 + 22}{12}$

Step 2.16

Factor $2$ out of $16$ .

$\frac{2 \cdot (0 + 1 + 2 + 3 + 4 + 5 + 6 + 7) + 2 (8) + 18 + 20 + 22}{12}$

Step 2.17

Factor $2$ out of $2 \cdot (0 + 1 + 2 + 3 + 4 + 5 + 6 + 7) + 2 (8)$ .

$\frac{2 \cdot (0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) + 18 + 20 + 22}{12}$

Step 2.18

Factor $2$ out of $18$ .

$\frac{2 \cdot (0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) + 2 (9) + 20 + 22}{12}$

Step 2.19

Factor $2$ out of $2 \cdot (0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) + 2 (9)$ .

$\frac{2 \cdot (0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) + 20 + 22}{12}$

Step 2.20

Factor $2$ out of $20$ .

$\frac{2 \cdot (0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) + 2 (10) + 22}{12}$

Step 2.21

Factor $2$ out of $2 \cdot (0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) + 2 (10)$ .

$\frac{2 \cdot (0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) + 22}{12}$

Step 2.22

Factor $2$ out of $22$ .

$\frac{2 \cdot (0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) + 2 (11)}{12}$

Step 2.23

Factor $2$ out of $2 \cdot (0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) + 2 (11)$ .

$\frac{2 \cdot (0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11)}{12}$

Step 2.24

Cancel the common factors.

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Step 2.24.1

Factor $2$ out of $12$ .

$\frac{2 \cdot (0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11)}{2 (6)}$

Step 2.24.2

Cancel the common factor.

$\frac{2 \cdot (0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11)}{2 \cdot 6}$

Step 2.24.3

Rewrite the expression.

$\frac{0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11}{6}$

Step 3

Simplify the numerator.

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Step 3.1

Add $0$ and $1$ .

$\frac{1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11}{6}$

Step 3.2

Add $1$ and $2$ .

$\frac{3 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11}{6}$

Step 3.3

Add $3$ and $3$ .

$\frac{6 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11}{6}$

Step 3.4

Add $6$ and $4$ .

$\frac{10 + 5 + 6 + 7 + 8 + 9 + 10 + 11}{6}$

Step 3.5

Add $10$ and $5$ .

$\frac{15 + 6 + 7 + 8 + 9 + 10 + 11}{6}$

Step 3.6

Add $15$ and $6$ .

$\frac{21 + 7 + 8 + 9 + 10 + 11}{6}$

Step 3.7

Add $21$ and $7$ .

$\frac{28 + 8 + 9 + 10 + 11}{6}$

Step 3.8

Add $28$ and $8$ .

$\frac{36 + 9 + 10 + 11}{6}$

Step 3.9

Add $36$ and $9$ .

$\frac{45 + 10 + 11}{6}$

Step 3.10

Add $45$ and $10$ .

$\frac{55 + 11}{6}$

Step 3.11

Add $55$ and $11$ .

$\frac{66}{6}$

Step 4

Divide $66$ by $6$ .

$11$