Basic Math Examples

$\frac{2}{3}$ , $\frac{9}{15}$

Step 1

Cancel the common factor of $9$ and $15$ .

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Step 1.1

Factor $3$ out of $9$ .

$\frac{2}{3}, \frac{3 (3)}{15}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $15$ .

$\frac{2}{3}, \frac{3 \cdot 3}{3 \cdot 5}$

Step 1.2.2

Cancel the common factor.

$\frac{2}{3}, \frac{3 \cdot 3}{3 \cdot 5}$

Step 1.2.3

Rewrite the expression.

$\frac{2}{3}, \frac{3}{5}$

Step 2

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

$\frac{\frac{2}{3} + \frac{3}{5}}{2}$

Step 3

Simplify the numerator.

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Step 3.1

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{\frac{2}{3} \cdot \frac{5}{5} + \frac{3}{5}}{2}$

Step 3.2

To write $\frac{3}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{\frac{2}{3} \cdot \frac{5}{5} + \frac{3}{5} \cdot \frac{3}{3}}{2}$

Step 3.3

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{2}{3}$ by $\frac{5}{5}$ .

$\frac{\frac{2 \cdot 5}{3 \cdot 5} + \frac{3}{5} \cdot \frac{3}{3}}{2}$

Step 3.3.2

Multiply $3$ by $5$ .

$\frac{\frac{2 \cdot 5}{15} + \frac{3}{5} \cdot \frac{3}{3}}{2}$

Step 3.3.3

Multiply $\frac{3}{5}$ by $\frac{3}{3}$ .

$\frac{\frac{2 \cdot 5}{15} + \frac{3 \cdot 3}{5 \cdot 3}}{2}$

Step 3.3.4

Multiply $5$ by $3$ .

$\frac{\frac{2 \cdot 5}{15} + \frac{3 \cdot 3}{15}}{2}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{\frac{2 \cdot 5 + 3 \cdot 3}{15}}{2}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $2$ by $5$ .

$\frac{\frac{10 + 3 \cdot 3}{15}}{2}$

Step 3.5.2

Multiply $3$ by $3$ .

$\frac{\frac{10 + 9}{15}}{2}$

Step 3.5.3

Add $10$ and $9$ .

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

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{19}{15} \cdot \frac{1}{2}$

Step 5

Multiply $\frac{19}{15} \cdot \frac{1}{2}$ .

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Step 5.1

Multiply $\frac{19}{15}$ by $\frac{1}{2}$ .

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

Step 5.2

Multiply $15$ by $2$ .

$\frac{19}{30}$

Step 6

Divide.

$0.6\overline{3}$

Step 7

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.

$0.6$