Find the Mean 7/8 , 1/4 , 2 2/5

$\frac{7}{8}$ ,

$\frac{1}{4}$ ,

$2 \frac{2}{5}$

Step 1

Convert

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

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

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

Add

$2$ and

$\frac{2}{5}$ .

To write

$2$ as a fraction with a common denominator, multiply by

$\frac{5}{5}$ .

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

Combine

$2$ and

$\frac{5}{5}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply

$2$ by

$5$ .

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

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.

To write

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

$\frac{2}{2}$ .

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

Write each expression with a common denominator of

$8$ , by multiplying each by an appropriate factor of

$1$ .

Multiply

$\frac{1}{4}$ by

$\frac{2}{2}$ .

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

Multiply

$4$ by

$2$ .

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

Combine the numerators over the common denominator.

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

Add

$7$ and

$2$ .

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

To write

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

$\frac{5}{5}$ .

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

To write

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

$\frac{8}{8}$ .

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

Write each expression with a common denominator of

$40$ , by multiplying each by an appropriate factor of

$1$ .

Multiply

$\frac{9}{8}$ by

$\frac{5}{5}$ .

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

Multiply

$8$ by

$5$ .

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

Multiply

$\frac{12}{5}$ by

$\frac{8}{8}$ .

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

Multiply

$5$ by

$8$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply

$9$ by

$5$ .

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

Multiply

$12$ by

$8$ .

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

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

$3$ .

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 7/8 , 1/4 , 2 2/5

Related Questions