Basic Math Examples

$\frac{1}{4}$ ,

$\frac{1}{6}$ ,

$\frac{1}{2}$

Step 1

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

$\frac{\frac{1}{4} + \frac{1}{6} + \frac{1}{2}}{3}$

Step 2

Simplify the numerator.

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Step 2.1

To write

$\frac{1}{4}$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{\frac{1}{4} \cdot \frac{3}{3} + \frac{1}{6} + \frac{1}{2}}{3}$

Step 2.2

To write

$\frac{1}{6}$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$\frac{\frac{1}{4} \cdot \frac{3}{3} + \frac{1}{6} \cdot \frac{2}{2} + \frac{1}{2}}{3}$

Step 2.3

Write each expression with a common denominator of

$12$ , by multiplying each by an appropriate factor of

$1$ .

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Step 2.3.1

Multiply

$\frac{1}{4}$ by

$\frac{3}{3}$ .

$\frac{\frac{3}{4 \cdot 3} + \frac{1}{6} \cdot \frac{2}{2} + \frac{1}{2}}{3}$

Step 2.3.2

Multiply

$4$ by

$3$ .

$\frac{\frac{3}{12} + \frac{1}{6} \cdot \frac{2}{2} + \frac{1}{2}}{3}$

Step 2.3.3

Multiply

$\frac{1}{6}$ by

$\frac{2}{2}$ .

$\frac{\frac{3}{12} + \frac{2}{6 \cdot 2} + \frac{1}{2}}{3}$

Step 2.3.4

Multiply

$6$ by

$2$ .

$\frac{\frac{3}{12} + \frac{2}{12} + \frac{1}{2}}{3}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{\frac{3 + 2}{12} + \frac{1}{2}}{3}$

Step 2.5

Add

$3$ and

$2$ .

$\frac{\frac{5}{12} + \frac{1}{2}}{3}$

Step 2.6

To write

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

$\frac{6}{6}$ .

$\frac{\frac{5}{12} + \frac{1}{2} \cdot \frac{6}{6}}{3}$

Step 2.7

Write each expression with a common denominator of

$12$ , by multiplying each by an appropriate factor of

$1$ .

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Step 2.7.1

Multiply

$\frac{1}{2}$ by

$\frac{6}{6}$ .

$\frac{\frac{5}{12} + \frac{6}{2 \cdot 6}}{3}$

Step 2.7.2

Multiply

$2$ by

$6$ .

$\frac{\frac{5}{12} + \frac{6}{12}}{3}$

Step 2.8

Combine the numerators over the common denominator.

$\frac{\frac{5 + 6}{12}}{3}$

Step 2.9

Add

$5$ and

$6$ .

$\frac{\frac{11}{12}}{3}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{11}{12} \cdot \frac{1}{3}$

Step 4

Multiply

$\frac{11}{12} \cdot \frac{1}{3}$ .

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Step 4.1

Multiply

$\frac{11}{12}$ by

$\frac{1}{3}$ .

$\frac{11}{12 \cdot 3}$

Step 4.2

Multiply

$12$ by

$3$ .

$\frac{11}{36}$

Step 5

Divide.

$0.30\overline{5}$

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.

$0.3$