Basic Math Examples

$\frac{1}{5}$ , $\frac{3}{2}$ , $\frac{5}{6}$ , $\frac{4}{5}$

Step 1

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

$\frac{\frac{1}{5} + \frac{3}{2} + \frac{5}{6} + \frac{4}{5}}{4}$

Step 2

Simplify the numerator.

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Step 2.1

To write $\frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{1}{5} \cdot \frac{2}{2} + \frac{3}{2} + \frac{5}{6} + \frac{4}{5}}{4}$

Step 2.2

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

$\frac{\frac{1}{5} \cdot \frac{2}{2} + \frac{3}{2} \cdot \frac{5}{5} + \frac{5}{6} + \frac{4}{5}}{4}$

Step 2.3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{1}{5}$ by $\frac{2}{2}$ .

$\frac{\frac{2}{5 \cdot 2} + \frac{3}{2} \cdot \frac{5}{5} + \frac{5}{6} + \frac{4}{5}}{4}$

Step 2.3.2

Multiply $5$ by $2$ .

$\frac{\frac{2}{10} + \frac{3}{2} \cdot \frac{5}{5} + \frac{5}{6} + \frac{4}{5}}{4}$

Step 2.3.3

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

$\frac{\frac{2}{10} + \frac{3 \cdot 5}{2 \cdot 5} + \frac{5}{6} + \frac{4}{5}}{4}$

Step 2.3.4

Multiply $2$ by $5$ .

$\frac{\frac{2}{10} + \frac{3 \cdot 5}{10} + \frac{5}{6} + \frac{4}{5}}{4}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{\frac{2 + 3 \cdot 5}{10} + \frac{5}{6} + \frac{4}{5}}{4}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $3$ by $5$ .

$\frac{\frac{2 + 15}{10} + \frac{5}{6} + \frac{4}{5}}{4}$

Step 2.5.2

Add $2$ and $15$ .

$\frac{\frac{17}{10} + \frac{5}{6} + \frac{4}{5}}{4}$

Step 2.6

To write $\frac{17}{10}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{\frac{17}{10} \cdot \frac{3}{3} + \frac{5}{6} + \frac{4}{5}}{4}$

Step 2.7

To write $\frac{5}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{\frac{17}{10} \cdot \frac{3}{3} + \frac{5}{6} \cdot \frac{5}{5} + \frac{4}{5}}{4}$

Step 2.8

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

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Step 2.8.1

Multiply $\frac{17}{10}$ by $\frac{3}{3}$ .

$\frac{\frac{17 \cdot 3}{10 \cdot 3} + \frac{5}{6} \cdot \frac{5}{5} + \frac{4}{5}}{4}$

Step 2.8.2

Multiply $10$ by $3$ .

$\frac{\frac{17 \cdot 3}{30} + \frac{5}{6} \cdot \frac{5}{5} + \frac{4}{5}}{4}$

Step 2.8.3

Multiply $\frac{5}{6}$ by $\frac{5}{5}$ .

$\frac{\frac{17 \cdot 3}{30} + \frac{5 \cdot 5}{6 \cdot 5} + \frac{4}{5}}{4}$

Step 2.8.4

Multiply $6$ by $5$ .

$\frac{\frac{17 \cdot 3}{30} + \frac{5 \cdot 5}{30} + \frac{4}{5}}{4}$

Step 2.9

Combine the numerators over the common denominator.

$\frac{\frac{17 \cdot 3 + 5 \cdot 5}{30} + \frac{4}{5}}{4}$

Step 2.10

Simplify the numerator.

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Step 2.10.1

Multiply $17$ by $3$ .

$\frac{\frac{51 + 5 \cdot 5}{30} + \frac{4}{5}}{4}$

Step 2.10.2

Multiply $5$ by $5$ .

$\frac{\frac{51 + 25}{30} + \frac{4}{5}}{4}$

Step 2.10.3

Add $51$ and $25$ .

$\frac{\frac{76}{30} + \frac{4}{5}}{4}$

Step 2.11

To write $\frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{\frac{76}{30} + \frac{4}{5} \cdot \frac{6}{6}}{4}$

Step 2.12

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

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Step 2.12.1

Multiply $\frac{4}{5}$ by $\frac{6}{6}$ .

$\frac{\frac{76}{30} + \frac{4 \cdot 6}{5 \cdot 6}}{4}$

Step 2.12.2

Multiply $5$ by $6$ .

$\frac{\frac{76}{30} + \frac{4 \cdot 6}{30}}{4}$

Step 2.13

Combine the numerators over the common denominator.

$\frac{\frac{76 + 4 \cdot 6}{30}}{4}$

Step 2.14

Simplify the numerator.

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Step 2.14.1

Multiply $4$ by $6$ .

$\frac{\frac{76 + 24}{30}}{4}$

Step 2.14.2

Add $76$ and $24$ .

$\frac{\frac{100}{30}}{4}$

Step 2.15

Cancel the common factor of $100$ and $30$ .

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Step 2.15.1

Factor $10$ out of $100$ .

$\frac{\frac{10 (10)}{30}}{4}$

Step 2.15.2

Cancel the common factors.

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Step 2.15.2.1

Factor $10$ out of $30$ .

$\frac{\frac{10 \cdot 10}{10 \cdot 3}}{4}$

Step 2.15.2.2

Cancel the common factor.

$\frac{\frac{10 \cdot 10}{10 \cdot 3}}{4}$

Step 2.15.2.3

Rewrite the expression.

$\frac{\frac{10}{3}}{4}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{10}{3} \cdot \frac{1}{4}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Factor $2$ out of $10$ .

$\frac{2 (5)}{3} \cdot \frac{1}{4}$

Step 4.2

Factor $2$ out of $4$ .

$\frac{2 \cdot 5}{3} \cdot \frac{1}{2 \cdot 2}$

Step 4.3

Cancel the common factor.

$\frac{2 \cdot 5}{3} \cdot \frac{1}{2 \cdot 2}$

Step 4.4

Rewrite the expression.

$\frac{5}{3} \cdot \frac{1}{2}$

Step 5

Multiply $\frac{5}{3}$ by $\frac{1}{2}$ .

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

Step 6

Multiply $3$ by $2$ .

$\frac{5}{6}$

Step 7

Divide.

$0.8\overline{3}$

Step 8

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.

$0.8$