Basic Math Examples

10

$10$ ,

35

$35$ ,

45

$45$ ,

50

$50$ ,

50

$50$ ,

50

$50$ ,

55

$55$ ,

55

$55$ ,

60

$60$ ,

90

$90$

Step 1

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

\frac{10 + 35 + 45 + 50 + 50 + 50 + 55 + 55 + 60 + 90}{10}

$\frac{10 + 35 + 45 + 50 + 50 + 50 + 55 + 55 + 60 + 90}{10}$

Step 2

Cancel the common factor of

10 + 35 + 45 + 50 + 50 + 50 + 55 + 55 + 60 + 90

$10 + 35 + 45 + 50 + 50 + 50 + 55 + 55 + 60 + 90$ and

10

$10$ .

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Step 2.1

Factor

5

$5$ out of

10

$10$ .

\frac{5 (2) + 35 + 45 + 50 + 50 + 50 + 55 + 55 + 60 + 90}{10}

$\frac{5 (2) + 35 + 45 + 50 + 50 + 50 + 55 + 55 + 60 + 90}{10}$

Step 2.2

Factor

5

$5$ out of

35

$35$ .

\frac{5 \cdot 2 + 5 \cdot 7 + 45 + 50 + 50 + 50 + 55 + 55 + 60 + 90}{10}

$\frac{5 \cdot 2 + 5 \cdot 7 + 45 + 50 + 50 + 50 + 55 + 55 + 60 + 90}{10}$

Step 2.3

Factor

5

$5$ out of

5 \cdot 2 + 5 \cdot 7

$5 \cdot 2 + 5 \cdot 7$ .

\frac{5 \cdot (2 + 7) + 45 + 50 + 50 + 50 + 55 + 55 + 60 + 90}{10}

$\frac{5 \cdot (2 + 7) + 45 + 50 + 50 + 50 + 55 + 55 + 60 + 90}{10}$

Step 2.4

Factor

5

$5$ out of

45

$45$ .

\frac{5 \cdot (2 + 7) + 5 (9) + 50 + 50 + 50 + 55 + 55 + 60 + 90}{10}

$\frac{5 \cdot (2 + 7) + 5 (9) + 50 + 50 + 50 + 55 + 55 + 60 + 90}{10}$

Step 2.5

Factor

5

$5$ out of

5 \cdot (2 + 7) + 5 (9)

$5 \cdot (2 + 7) + 5 (9)$ .

\frac{5 \cdot (2 + 7 + 9) + 50 + 50 + 50 + 55 + 55 + 60 + 90}{10}

$\frac{5 \cdot (2 + 7 + 9) + 50 + 50 + 50 + 55 + 55 + 60 + 90}{10}$

Step 2.6

Factor

5

$5$ out of

50

$50$ .

\frac{5 \cdot (2 + 7 + 9) + 5 (10) + 50 + 50 + 55 + 55 + 60 + 90}{10}

$\frac{5 \cdot (2 + 7 + 9) + 5 (10) + 50 + 50 + 55 + 55 + 60 + 90}{10}$

Step 2.7

Factor

5

$5$ out of

5 \cdot (2 + 7 + 9) + 5 (10)

$5 \cdot (2 + 7 + 9) + 5 (10)$ .

\frac{5 \cdot (2 + 7 + 9 + 10) + 50 + 50 + 55 + 55 + 60 + 90}{10}

$\frac{5 \cdot (2 + 7 + 9 + 10) + 50 + 50 + 55 + 55 + 60 + 90}{10}$

Step 2.8

Factor

5

$5$ out of

50

$50$ .

\frac{5 \cdot (2 + 7 + 9 + 10) + 5 (10) + 50 + 55 + 55 + 60 + 90}{10}

$\frac{5 \cdot (2 + 7 + 9 + 10) + 5 (10) + 50 + 55 + 55 + 60 + 90}{10}$

Step 2.9

Factor

5

$5$ out of

5 \cdot (2 + 7 + 9 + 10) + 5 (10)

$5 \cdot (2 + 7 + 9 + 10) + 5 (10)$ .

\frac{5 \cdot (2 + 7 + 9 + 10 + 10) + 50 + 55 + 55 + 60 + 90}{10}

$\frac{5 \cdot (2 + 7 + 9 + 10 + 10) + 50 + 55 + 55 + 60 + 90}{10}$

Step 2.10

Factor

5

$5$ out of

50

$50$ .

\frac{5 \cdot (2 + 7 + 9 + 10 + 10) + 5 (10) + 55 + 55 + 60 + 90}{10}

$\frac{5 \cdot (2 + 7 + 9 + 10 + 10) + 5 (10) + 55 + 55 + 60 + 90}{10}$

Step 2.11

Factor

5

$5$ out of

5 \cdot (2 + 7 + 9 + 10 + 10) + 5 (10)

$5 \cdot (2 + 7 + 9 + 10 + 10) + 5 (10)$ .

\frac{5 \cdot (2 + 7 + 9 + 10 + 10 + 10) + 55 + 55 + 60 + 90}{10}

$\frac{5 \cdot (2 + 7 + 9 + 10 + 10 + 10) + 55 + 55 + 60 + 90}{10}$

Step 2.12

Factor

5

$5$ out of

55

$55$ .

\frac{5 \cdot (2 + 7 + 9 + 10 + 10 + 10) + 5 (11) + 55 + 60 + 90}{10}

$\frac{5 \cdot (2 + 7 + 9 + 10 + 10 + 10) + 5 (11) + 55 + 60 + 90}{10}$

Step 2.13

Factor

5

$5$ out of

5 \cdot (2 + 7 + 9 + 10 + 10 + 10) + 5 (11)

$5 \cdot (2 + 7 + 9 + 10 + 10 + 10) + 5 (11)$ .

\frac{5 \cdot (2 + 7 + 9 + 10 + 10 + 10 + 11) + 55 + 60 + 90}{10}

$\frac{5 \cdot (2 + 7 + 9 + 10 + 10 + 10 + 11) + 55 + 60 + 90}{10}$

Step 2.14

Factor

5

$5$ out of

55

$55$ .

\frac{5 \cdot (2 + 7 + 9 + 10 + 10 + 10 + 11) + 5 (11) + 60 + 90}{10}

$\frac{5 \cdot (2 + 7 + 9 + 10 + 10 + 10 + 11) + 5 (11) + 60 + 90}{10}$

Step 2.15

Factor

5

$5$ out of

5 \cdot (2 + 7 + 9 + 10 + 10 + 10 + 11) + 5 (11)

$5 \cdot (2 + 7 + 9 + 10 + 10 + 10 + 11) + 5 (11)$ .

\frac{5 \cdot (2 + 7 + 9 + 10 + 10 + 10 + 11 + 11) + 60 + 90}{10}

$\frac{5 \cdot (2 + 7 + 9 + 10 + 10 + 10 + 11 + 11) + 60 + 90}{10}$

Step 2.16

Factor

5

$5$ out of

$60$ .

$\frac{5 \cdot (2 + 7 + 9 + 10 + 10 + 10 + 11 + 11) + 5 (12) + 90}{10}$

Step 2.17

Factor

$5$ out of

$5 \cdot (2 + 7 + 9 + 10 + 10 + 10 + 11 + 11) + 5 (12)$ .

$\frac{5 \cdot (2 + 7 + 9 + 10 + 10 + 10 + 11 + 11 + 12) + 90}{10}$

Step 2.18

Factor

$5$ out of

$90$ .

$\frac{5 \cdot (2 + 7 + 9 + 10 + 10 + 10 + 11 + 11 + 12) + 5 (18)}{10}$

Step 2.19

Factor

$5$ out of

$5 \cdot (2 + 7 + 9 + 10 + 10 + 10 + 11 + 11 + 12) + 5 (18)$ .

$\frac{5 \cdot (2 + 7 + 9 + 10 + 10 + 10 + 11 + 11 + 12 + 18)}{10}$

Step 2.20

Cancel the common factors.

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Step 2.20.1

Factor

$5$ out of

$10$ .

$\frac{5 \cdot (2 + 7 + 9 + 10 + 10 + 10 + 11 + 11 + 12 + 18)}{5 (2)}$

Step 2.20.2

Cancel the common factor.

$\frac{5 \cdot (2 + 7 + 9 + 10 + 10 + 10 + 11 + 11 + 12 + 18)}{5 \cdot 2}$

Step 2.20.3

Rewrite the expression.

$\frac{2 + 7 + 9 + 10 + 10 + 10 + 11 + 11 + 12 + 18}{2}$

Step 3

Simplify the numerator.

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Step 3.1

Add

$2$ and

$7$ .

$\frac{9 + 9 + 10 + 10 + 10 + 11 + 11 + 12 + 18}{2}$

Step 3.2

Add

$9$ and

$9$ .

$\frac{18 + 10 + 10 + 10 + 11 + 11 + 12 + 18}{2}$

Step 3.3

Add

$18$ and

$10$ .

$\frac{28 + 10 + 10 + 11 + 11 + 12 + 18}{2}$

Step 3.4

Add

$28$ and

$10$ .

$\frac{38 + 10 + 11 + 11 + 12 + 18}{2}$

Step 3.5

Add

$38$ and

$10$ .

$\frac{48 + 11 + 11 + 12 + 18}{2}$

Step 3.6

Add

$48$ and

$11$ .

$\frac{59 + 11 + 12 + 18}{2}$

Step 3.7

Add

$59$ and

$11$ .

$\frac{70 + 12 + 18}{2}$

Step 3.8

Add

$70$ and

$12$ .

$\frac{82 + 18}{2}$

Step 3.9

Add

$82$ and

$18$ .

$\frac{100}{2}$

Step 4

Divide

$100$ by

$2$ .

$50$