Basic Math Examples

$\frac{7}{8}$ , $\frac{1}{4}$ , $2 \frac{2}{5}$

Step 1

Convert $2 \frac{2}{5}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{7}{8}, \frac{1}{4}, 2 + \frac{2}{5}$

Step 1.2

Add $2$ and $\frac{2}{5}$ .

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Step 1.2.1

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

$\frac{7}{8}, \frac{1}{4}, 2 \cdot \frac{5}{5} + \frac{2}{5}$

Step 1.2.2

Combine $2$ and $\frac{5}{5}$ .

$\frac{7}{8}, \frac{1}{4}, \frac{2 \cdot 5}{5} + \frac{2}{5}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{7}{8}, \frac{1}{4}, \frac{2 \cdot 5 + 2}{5}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $5$ .

$\frac{7}{8}, \frac{1}{4}, \frac{10 + 2}{5}$

Step 1.2.4.2

Add $10$ and $2$ .

$\frac{7}{8}, \frac{1}{4}, \frac{12}{5}$

Step 2

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

$\frac{\frac{7}{8} + \frac{1}{4} + \frac{12}{5}}{3}$

Step 3

Simplify the numerator.

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Step 3.1

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{7}{8} + \frac{1}{4} \cdot \frac{2}{2} + \frac{12}{5}}{3}$

Step 3.2

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.2.1

Multiply $\frac{1}{4}$ by $\frac{2}{2}$ .

$\frac{\frac{7}{8} + \frac{2}{4 \cdot 2} + \frac{12}{5}}{3}$

Step 3.2.2

Multiply $4$ by $2$ .

$\frac{\frac{7}{8} + \frac{2}{8} + \frac{12}{5}}{3}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{\frac{7 + 2}{8} + \frac{12}{5}}{3}$

Step 3.4

Add $7$ and $2$ .

$\frac{\frac{9}{8} + \frac{12}{5}}{3}$

Step 3.5

To write $\frac{9}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{\frac{9}{8} \cdot \frac{5}{5} + \frac{12}{5}}{3}$

Step 3.6

To write $\frac{12}{5}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{\frac{9}{8} \cdot \frac{5}{5} + \frac{12}{5} \cdot \frac{8}{8}}{3}$

Step 3.7

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.7.1

Multiply $\frac{9}{8}$ by $\frac{5}{5}$ .

$\frac{\frac{9 \cdot 5}{8 \cdot 5} + \frac{12}{5} \cdot \frac{8}{8}}{3}$

Step 3.7.2

Multiply $8$ by $5$ .

$\frac{\frac{9 \cdot 5}{40} + \frac{12}{5} \cdot \frac{8}{8}}{3}$

Step 3.7.3

Multiply $\frac{12}{5}$ by $\frac{8}{8}$ .

$\frac{\frac{9 \cdot 5}{40} + \frac{12 \cdot 8}{5 \cdot 8}}{3}$

Step 3.7.4

Multiply $5$ by $8$ .

$\frac{\frac{9 \cdot 5}{40} + \frac{12 \cdot 8}{40}}{3}$

Step 3.8

Combine the numerators over the common denominator.

$\frac{\frac{9 \cdot 5 + 12 \cdot 8}{40}}{3}$

Step 3.9

Simplify the numerator.

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Step 3.9.1

Multiply $9$ by $5$ .

$\frac{\frac{45 + 12 \cdot 8}{40}}{3}$

Step 3.9.2

Multiply $12$ by $8$ .

$\frac{\frac{45 + 96}{40}}{3}$

Step 3.9.3

Add $45$ and $96$ .

$\frac{\frac{141}{40}}{3}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{141}{40} \cdot \frac{1}{3}$

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Factor $3$ out of $141$ .

$\frac{3 (47)}{40} \cdot \frac{1}{3}$

Step 5.2

Cancel the common factor.

$\frac{3 \cdot 47}{40} \cdot \frac{1}{3}$

Step 5.3

Rewrite the expression.

$\frac{47}{40}$

Step 6

Divide.

$1.175$

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.

$1.2$