Find the Mean 3/8 , 2/5 , 2 3/4

$\frac{3}{8}$ , $\frac{2}{5}$ , $2 \frac{3}{4}$

Step 1

Convert $2 \frac{3}{4}$ to an improper fraction.

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

$\frac{3}{8}, \frac{2}{5}, 2 + \frac{3}{4}$

Add $2$ and $\frac{3}{4}$ .

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

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

Combine $2$ and $\frac{4}{4}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $4$ .

$\frac{3}{8}, \frac{2}{5}, \frac{8 + 3}{4}$

Add $8$ and $3$ .

$\frac{3}{8}, \frac{2}{5}, \frac{11}{4}$

Step 2

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

$\frac{\frac{3}{8} + \frac{2}{5} + \frac{11}{4}}{3}$

Step 3

Simplify the numerator.

To write $\frac{3}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{\frac{3}{8} \cdot \frac{5}{5} + \frac{2}{5} + \frac{11}{4}}{3}$

To write $\frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{\frac{3}{8} \cdot \frac{5}{5} + \frac{2}{5} \cdot \frac{8}{8} + \frac{11}{4}}{3}$

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

Multiply $\frac{3}{8}$ by $\frac{5}{5}$ .

$\frac{\frac{3 \cdot 5}{8 \cdot 5} + \frac{2}{5} \cdot \frac{8}{8} + \frac{11}{4}}{3}$

Multiply $8$ by $5$ .

$\frac{\frac{3 \cdot 5}{40} + \frac{2}{5} \cdot \frac{8}{8} + \frac{11}{4}}{3}$

Multiply $\frac{2}{5}$ by $\frac{8}{8}$ .

$\frac{\frac{3 \cdot 5}{40} + \frac{2 \cdot 8}{5 \cdot 8} + \frac{11}{4}}{3}$

Multiply $5$ by $8$ .

$\frac{\frac{3 \cdot 5}{40} + \frac{2 \cdot 8}{40} + \frac{11}{4}}{3}$

Combine the numerators over the common denominator.

$\frac{\frac{3 \cdot 5 + 2 \cdot 8}{40} + \frac{11}{4}}{3}$

Simplify the numerator.

Multiply $3$ by $5$ .

$\frac{\frac{15 + 2 \cdot 8}{40} + \frac{11}{4}}{3}$

Multiply $2$ by $8$ .

$\frac{\frac{15 + 16}{40} + \frac{11}{4}}{3}$

Add $15$ and $16$ .

$\frac{\frac{31}{40} + \frac{11}{4}}{3}$

To write $\frac{11}{4}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{\frac{31}{40} + \frac{11}{4} \cdot \frac{10}{10}}{3}$

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

Multiply $\frac{11}{4}$ by $\frac{10}{10}$ .

$\frac{\frac{31}{40} + \frac{11 \cdot 10}{4 \cdot 10}}{3}$

Multiply $4$ by $10$ .

$\frac{\frac{31}{40} + \frac{11 \cdot 10}{40}}{3}$

Combine the numerators over the common denominator.

$\frac{\frac{31 + 11 \cdot 10}{40}}{3}$

Simplify the numerator.

Multiply $11$ by $10$ .

$\frac{\frac{31 + 110}{40}}{3}$

Add $31$ and $110$ .

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

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 $3$ .

Factor $3$ out of $141$ .

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

Cancel the common factor.

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

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.

$1.2$

Find the Mean 3/8 , 2/5 , 2 3/4

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