Pre-Algebra Examples

2

$2$ ,

4

$4$ ,

6

$6$ ,

8

$8$ ,

10

$10$ ,

12

$12$ ,

14

$14$ ,

16

$16$ ,

18

$18$ ,

20

$20$ ,

22

$22$ ,

24

$24$

Step 1

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

\frac{2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24}{12}

$\frac{2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24}{12}$

Step 2

Cancel the common factor of

2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24

$2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24$ and

12

$12$ .

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Step 2.1

Factor

2

$2$ out of

2

$2$ .

\frac{2 (1) + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24}{12}

$\frac{2 (1) + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24}{12}$

Step 2.2

Factor

2

$2$ out of

4

$4$ .

\frac{2 \cdot 1 + 2 \cdot 2 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24}{12}

$\frac{2 \cdot 1 + 2 \cdot 2 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24}{12}$

Step 2.3

Factor

2

$2$ out of

2 \cdot 1 + 2 \cdot 2

$2 \cdot 1 + 2 \cdot 2$ .

\frac{2 \cdot (1 + 2) + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24}{12}

$\frac{2 \cdot (1 + 2) + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24}{12}$

Step 2.4

Factor

2

$2$ out of

6

$6$ .

\frac{2 \cdot (1 + 2) + 2 (3) + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24}{12}

$\frac{2 \cdot (1 + 2) + 2 (3) + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24}{12}$

Step 2.5

Factor

2

$2$ out of

2 \cdot (1 + 2) + 2 (3)

$2 \cdot (1 + 2) + 2 (3)$ .

\frac{2 \cdot (1 + 2 + 3) + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24}{12}

$\frac{2 \cdot (1 + 2 + 3) + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24}{12}$

Step 2.6

Factor

2

$2$ out of

8

$8$ .

\frac{2 \cdot (1 + 2 + 3) + 2 (4) + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24}{12}

$\frac{2 \cdot (1 + 2 + 3) + 2 (4) + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24}{12}$

Step 2.7

Factor

2

$2$ out of

2 \cdot (1 + 2 + 3) + 2 (4)

$2 \cdot (1 + 2 + 3) + 2 (4)$ .

\frac{2 \cdot (1 + 2 + 3 + 4) + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24}{12}

$\frac{2 \cdot (1 + 2 + 3 + 4) + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24}{12}$

Step 2.8

Factor

2

$2$ out of

10

$10$ .

\frac{2 \cdot (1 + 2 + 3 + 4) + 2 (5) + 12 + 14 + 16 + 18 + 20 + 22 + 24}{12}

$\frac{2 \cdot (1 + 2 + 3 + 4) + 2 (5) + 12 + 14 + 16 + 18 + 20 + 22 + 24}{12}$

Step 2.9

Factor

2

$2$ out of

2 \cdot (1 + 2 + 3 + 4) + 2 (5)

$2 \cdot (1 + 2 + 3 + 4) + 2 (5)$ .

\frac{2 \cdot (1 + 2 + 3 + 4 + 5) + 12 + 14 + 16 + 18 + 20 + 22 + 24}{12}

$\frac{2 \cdot (1 + 2 + 3 + 4 + 5) + 12 + 14 + 16 + 18 + 20 + 22 + 24}{12}$

Step 2.10

Factor

2

$2$ out of

12

$12$ .

\frac{2 \cdot (1 + 2 + 3 + 4 + 5) + 2 (6) + 14 + 16 + 18 + 20 + 22 + 24}{12}

$\frac{2 \cdot (1 + 2 + 3 + 4 + 5) + 2 (6) + 14 + 16 + 18 + 20 + 22 + 24}{12}$

Step 2.11

Factor

2

$2$ out of

2 \cdot (1 + 2 + 3 + 4 + 5) + 2 (6)

$2 \cdot (1 + 2 + 3 + 4 + 5) + 2 (6)$ .

\frac{2 \cdot (1 + 2 + 3 + 4 + 5 + 6) + 14 + 16 + 18 + 20 + 22 + 24}{12}

$\frac{2 \cdot (1 + 2 + 3 + 4 + 5 + 6) + 14 + 16 + 18 + 20 + 22 + 24}{12}$

Step 2.12

Factor

2

$2$ out of

14

$14$ .

\frac{2 \cdot (1 + 2 + 3 + 4 + 5 + 6) + 2 (7) + 16 + 18 + 20 + 22 + 24}{12}

$\frac{2 \cdot (1 + 2 + 3 + 4 + 5 + 6) + 2 (7) + 16 + 18 + 20 + 22 + 24}{12}$

Step 2.13

Factor

2

$2$ out of

2 \cdot (1 + 2 + 3 + 4 + 5 + 6) + 2 (7)

$2 \cdot (1 + 2 + 3 + 4 + 5 + 6) + 2 (7)$ .

\frac{2 \cdot (1 + 2 + 3 + 4 + 5 + 6 + 7) + 16 + 18 + 20 + 22 + 24}{12}

$\frac{2 \cdot (1 + 2 + 3 + 4 + 5 + 6 + 7) + 16 + 18 + 20 + 22 + 24}{12}$

Step 2.14

Factor

2

$2$ out of

16

$16$ .

\frac{2 \cdot (1 + 2 + 3 + 4 + 5 + 6 + 7) + 2 (8) + 18 + 20 + 22 + 24}{12}

$\frac{2 \cdot (1 + 2 + 3 + 4 + 5 + 6 + 7) + 2 (8) + 18 + 20 + 22 + 24}{12}$

Step 2.15

Factor

2

$2$ out of

2 \cdot (1 + 2 + 3 + 4 + 5 + 6 + 7) + 2 (8)

$2 \cdot (1 + 2 + 3 + 4 + 5 + 6 + 7) + 2 (8)$ .

\frac{2 \cdot (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) + 18 + 20 + 22 + 24}{12}

$\frac{2 \cdot (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) + 18 + 20 + 22 + 24}{12}$

Step 2.16

Factor

2

$2$ out of

18

$18$ .

\frac{2 \cdot (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) + 2 (9) + 20 + 22 + 24}{12}

$\frac{2 \cdot (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) + 2 (9) + 20 + 22 + 24}{12}$

Step 2.17

Factor

2

$2$ out of

2 \cdot (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) + 2 (9)

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

\frac{2 \cdot (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) + 20 + 22 + 24}{12}

$\frac{2 \cdot (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) + 20 + 22 + 24}{12}$

Step 2.18

Factor

2

$2$ out of

20

$20$ .

\frac{2 \cdot (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) + 2 (10) + 22 + 24}{12}

$\frac{2 \cdot (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) + 2 (10) + 22 + 24}{12}$

Step 2.19

Factor

2

$2$ out of

2 \cdot (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) + 2 (10)

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

\frac{2 \cdot (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) + 22 + 24}{12}

$\frac{2 \cdot (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) + 22 + 24}{12}$

Step 2.20

Factor

2

$2$ out of

22

$22$ .

\frac{2 \cdot (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) + 2 (11) + 24}{12}

$\frac{2 \cdot (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) + 2 (11) + 24}{12}$

Step 2.21

Factor

2

$2$ out of

2 \cdot (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) + 2 (11)

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

\frac{2 \cdot (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11) + 24}{12}

$\frac{2 \cdot (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11) + 24}{12}$

Step 2.22

Factor

2

$2$ out of

24

$24$ .

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

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

Step 2.23

Factor

2

$2$ out of

2 \cdot (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11) + 2 (12)

$2 \cdot (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11) + 2 (12)$ .

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

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

Step 2.24

Cancel the common factors.

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Step 2.24.1

Factor

2

$2$ out of

12

$12$ .

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

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

Step 2.24.2

Cancel the common factor.

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

Step 2.24.3

Rewrite the expression.

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

Step 3

Simplify the numerator.

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Step 3.1

Add

$1$ and

$2$ .

$\frac{3 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12}{6}$

Step 3.2

Add

$3$ and

$3$ .

$\frac{6 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12}{6}$

Step 3.3

Add

$6$ and

$4$ .

$\frac{10 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12}{6}$

Step 3.4

Add

$10$ and

$5$ .

$\frac{15 + 6 + 7 + 8 + 9 + 10 + 11 + 12}{6}$

Step 3.5

Add

$15$ and

$6$ .

$\frac{21 + 7 + 8 + 9 + 10 + 11 + 12}{6}$

Step 3.6

Add

$21$ and

$7$ .

$\frac{28 + 8 + 9 + 10 + 11 + 12}{6}$

Step 3.7

Add

$28$ and

$8$ .

$\frac{36 + 9 + 10 + 11 + 12}{6}$

Step 3.8

Add

$36$ and

$9$ .

$\frac{45 + 10 + 11 + 12}{6}$

Step 3.9

Add

$45$ and

$10$ .

$\frac{55 + 11 + 12}{6}$

Step 3.10

Add

$55$ and

$11$ .

$\frac{66 + 12}{6}$

Step 3.11

Add

$66$ and

$12$ .

$\frac{78}{6}$

Step 4

Divide

$78$ by

$6$ .

$13$

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