Basic Math Examples

$\frac{1}{3}$ , $\frac{9}{10}$ , $\frac{1}{30}$

Step 1

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

$\frac{\frac{1}{3} + \frac{9}{10} + \frac{1}{30}}{3}$

Step 2

Simplify the numerator.

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Step 2.1

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{\frac{1}{3} \cdot \frac{10}{10} + \frac{9}{10} + \frac{1}{30}}{3}$

Step 2.2

To write $\frac{9}{10}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{\frac{1}{3} \cdot \frac{10}{10} + \frac{9}{10} \cdot \frac{3}{3} + \frac{1}{30}}{3}$

Step 2.3

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{1}{3}$ by $\frac{10}{10}$ .

$\frac{\frac{10}{3 \cdot 10} + \frac{9}{10} \cdot \frac{3}{3} + \frac{1}{30}}{3}$

Step 2.3.2

Multiply $3$ by $10$ .

$\frac{\frac{10}{30} + \frac{9}{10} \cdot \frac{3}{3} + \frac{1}{30}}{3}$

Step 2.3.3

Multiply $\frac{9}{10}$ by $\frac{3}{3}$ .

$\frac{\frac{10}{30} + \frac{9 \cdot 3}{10 \cdot 3} + \frac{1}{30}}{3}$

Step 2.3.4

Multiply $10$ by $3$ .

$\frac{\frac{10}{30} + \frac{9 \cdot 3}{30} + \frac{1}{30}}{3}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{\frac{10 + 9 \cdot 3}{30} + \frac{1}{30}}{3}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $9$ by $3$ .

$\frac{\frac{10 + 27}{30} + \frac{1}{30}}{3}$

Step 2.5.2

Add $10$ and $27$ .

$\frac{\frac{37}{30} + \frac{1}{30}}{3}$

Step 2.6

Combine the numerators over the common denominator.

$\frac{\frac{37 + 1}{30}}{3}$

Step 2.7

Add $37$ and $1$ .

$\frac{\frac{38}{30}}{3}$

Step 2.8

Cancel the common factor of $38$ and $30$ .

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Step 2.8.1

Factor $2$ out of $38$ .

$\frac{\frac{2 (19)}{30}}{3}$

Step 2.8.2

Cancel the common factors.

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Step 2.8.2.1

Factor $2$ out of $30$ .

$\frac{\frac{2 \cdot 19}{2 \cdot 15}}{3}$

Step 2.8.2.2

Cancel the common factor.

$\frac{\frac{2 \cdot 19}{2 \cdot 15}}{3}$

Step 2.8.2.3

Rewrite the expression.

$\frac{\frac{19}{15}}{3}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{19}{15} \cdot \frac{1}{3}$

Step 4

Multiply $\frac{19}{15} \cdot \frac{1}{3}$ .

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Step 4.1

Multiply $\frac{19}{15}$ by $\frac{1}{3}$ .

$\frac{19}{15 \cdot 3}$

Step 4.2

Multiply $15$ by $3$ .

$\frac{19}{45}$

Step 5

Divide.

$0.4\overline{2}$

Step 6

The mean should be rounded to one more decimal place than the original data. If the original data were mixed, round to one decimal place more than the least precise.

$0.4$