Algebra Examples

101

$101$ ,

102

$102$ ,

103

$103$ ,

104

$104$ ,

105

$105$ ,

106

$106$ ,

107

$107$ ,

108

$108$ ,

109

$109$ ,

110

$110$ ,

111

$111$ ,

112

$112$

Step 1

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

\frac{101 + 102 + 103 + 104 + 105 + 106 + 107 + 108 + 109 + 110 + 111 + 112}{12}

$\frac{101 + 102 + 103 + 104 + 105 + 106 + 107 + 108 + 109 + 110 + 111 + 112}{12}$

Step 2

Simplify the numerator.

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Step 2.1

Add

101

$101$ and

102

$102$ .

\frac{203 + 103 + 104 + 105 + 106 + 107 + 108 + 109 + 110 + 111 + 112}{12}

$\frac{203 + 103 + 104 + 105 + 106 + 107 + 108 + 109 + 110 + 111 + 112}{12}$

Step 2.2

Add

203

$203$ and

103

$103$ .

\frac{306 + 104 + 105 + 106 + 107 + 108 + 109 + 110 + 111 + 112}{12}

$\frac{306 + 104 + 105 + 106 + 107 + 108 + 109 + 110 + 111 + 112}{12}$

Step 2.3

Add

306

$306$ and

104

$104$ .

\frac{410 + 105 + 106 + 107 + 108 + 109 + 110 + 111 + 112}{12}

$\frac{410 + 105 + 106 + 107 + 108 + 109 + 110 + 111 + 112}{12}$

Step 2.4

Add

410

$410$ and

105

$105$ .

\frac{515 + 106 + 107 + 108 + 109 + 110 + 111 + 112}{12}

$\frac{515 + 106 + 107 + 108 + 109 + 110 + 111 + 112}{12}$

Step 2.5

Add

515

$515$ and

106

$106$ .

\frac{621 + 107 + 108 + 109 + 110 + 111 + 112}{12}

$\frac{621 + 107 + 108 + 109 + 110 + 111 + 112}{12}$

Step 2.6

Add

621

$621$ and

107

$107$ .

\frac{728 + 108 + 109 + 110 + 111 + 112}{12}

$\frac{728 + 108 + 109 + 110 + 111 + 112}{12}$

Step 2.7

Add

728

$728$ and

108

$108$ .

\frac{836 + 109 + 110 + 111 + 112}{12}

$\frac{836 + 109 + 110 + 111 + 112}{12}$

Step 2.8

Add

836

$836$ and

109

$109$ .

\frac{945 + 110 + 111 + 112}{12}

$\frac{945 + 110 + 111 + 112}{12}$

Step 2.9

Add

945

$945$ and

110

$110$ .

\frac{1055 + 111 + 112}{12}

$\frac{1055 + 111 + 112}{12}$

Step 2.10

Add

1055

$1055$ and

111

$111$ .

\frac{1166 + 112}{12}

$\frac{1166 + 112}{12}$

Step 2.11

Add

1166

$1166$ and

112

$112$ .

\frac{1278}{12}

$\frac{1278}{12}$

\frac{1278}{12}

$\frac{1278}{12}$

Step 3

Cancel the common factor of

1278

$1278$ and

12

$12$ .

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Step 3.1

Factor

6

$6$ out of

1278

$1278$ .

\frac{6 (213)}{12}

$\frac{6 (213)}{12}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor

6

$6$ out of

12

$12$ .

\frac{6 \cdot 213}{6 \cdot 2}

$\frac{6 \cdot 213}{6 \cdot 2}$

Step 3.2.2

Cancel the common factor.

\frac{6 \cdot 213}{6 \cdot 2}

$\frac{6 \cdot 213}{6 \cdot 2}$

Step 3.2.3

Rewrite the expression.

\frac{213}{2}

$\frac{213}{2}$

\frac{213}{2}

$\frac{213}{2}$

\frac{213}{2}

$\frac{213}{2}$

Step 4

Divide.

106.5

$106.5$