Pre-Algebra Examples

$\frac{2}{3}$ , $\frac{5}{6}$ , $\frac{1}{9}$

Step 1

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

$\frac{\frac{2}{3} + \frac{5}{6} + \frac{1}{9}}{3}$

Step 2

Simplify the numerator.

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Step 2.1

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{2}{3} \cdot \frac{2}{2} + \frac{5}{6} + \frac{1}{9}}{3}$

Step 2.2

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.1

Multiply $\frac{2}{3}$ by $\frac{2}{2}$ .

$\frac{\frac{2 \cdot 2}{3 \cdot 2} + \frac{5}{6} + \frac{1}{9}}{3}$

Step 2.2.2

Multiply $3$ by $2$ .

$\frac{\frac{2 \cdot 2}{6} + \frac{5}{6} + \frac{1}{9}}{3}$

Step 2.3

Combine the numerators over the common denominator.

$\frac{\frac{2 \cdot 2 + 5}{6} + \frac{1}{9}}{3}$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Multiply $2$ by $2$ .

$\frac{\frac{4 + 5}{6} + \frac{1}{9}}{3}$

Step 2.4.2

Add $4$ and $5$ .

$\frac{\frac{9}{6} + \frac{1}{9}}{3}$

Step 2.5

To write $\frac{9}{6}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{\frac{9}{6} \cdot \frac{3}{3} + \frac{1}{9}}{3}$

Step 2.6

To write $\frac{1}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{9}{6} \cdot \frac{3}{3} + \frac{1}{9} \cdot \frac{2}{2}}{3}$

Step 2.7

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.7.1

Multiply $\frac{9}{6}$ by $\frac{3}{3}$ .

$\frac{\frac{9 \cdot 3}{6 \cdot 3} + \frac{1}{9} \cdot \frac{2}{2}}{3}$

Step 2.7.2

Multiply $6$ by $3$ .

$\frac{\frac{9 \cdot 3}{18} + \frac{1}{9} \cdot \frac{2}{2}}{3}$

Step 2.7.3

Multiply $\frac{1}{9}$ by $\frac{2}{2}$ .

$\frac{\frac{9 \cdot 3}{18} + \frac{2}{9 \cdot 2}}{3}$

Step 2.7.4

Multiply $9$ by $2$ .

$\frac{\frac{9 \cdot 3}{18} + \frac{2}{18}}{3}$

Step 2.8

Combine the numerators over the common denominator.

$\frac{\frac{9 \cdot 3 + 2}{18}}{3}$

Step 2.9

Simplify the numerator.

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Step 2.9.1

Multiply $9$ by $3$ .

$\frac{\frac{27 + 2}{18}}{3}$

Step 2.9.2

Add $27$ and $2$ .

$\frac{\frac{29}{18}}{3}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{29}{18} \cdot \frac{1}{3}$

Step 4

Multiply $\frac{29}{18} \cdot \frac{1}{3}$ .

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Step 4.1

Multiply $\frac{29}{18}$ by $\frac{1}{3}$ .

$\frac{29}{18 \cdot 3}$

Step 4.2

Multiply $18$ by $3$ .

$\frac{29}{54}$

Step 5

Divide.

$0.5\overline{370}$

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.

$0.5$