Find the Mean 5/8 , 3/20 , 4/15

$\frac{5}{8}$ , $\frac{3}{20}$ , $\frac{4}{15}$

Step 1

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

$\frac{\frac{5}{8} + \frac{3}{20} + \frac{4}{15}}{3}$

Step 2

Simplify the numerator.

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

$\frac{\frac{5}{8} \cdot \frac{5}{5} + \frac{3}{20} + \frac{4}{15}}{3}$

To write $\frac{3}{20}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{5}{8} \cdot \frac{5}{5} + \frac{3}{20} \cdot \frac{2}{2} + \frac{4}{15}}{3}$

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

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

$\frac{\frac{5 \cdot 5}{8 \cdot 5} + \frac{3}{20} \cdot \frac{2}{2} + \frac{4}{15}}{3}$

Multiply $8$ by $5$ .

$\frac{\frac{5 \cdot 5}{40} + \frac{3}{20} \cdot \frac{2}{2} + \frac{4}{15}}{3}$

Multiply $\frac{3}{20}$ by $\frac{2}{2}$ .

$\frac{\frac{5 \cdot 5}{40} + \frac{3 \cdot 2}{20 \cdot 2} + \frac{4}{15}}{3}$

Multiply $20$ by $2$ .

$\frac{\frac{5 \cdot 5}{40} + \frac{3 \cdot 2}{40} + \frac{4}{15}}{3}$

Combine the numerators over the common denominator.

$\frac{\frac{5 \cdot 5 + 3 \cdot 2}{40} + \frac{4}{15}}{3}$

Simplify the numerator.

Multiply $5$ by $5$ .

$\frac{\frac{25 + 3 \cdot 2}{40} + \frac{4}{15}}{3}$

Multiply $3$ by $2$ .

$\frac{\frac{25 + 6}{40} + \frac{4}{15}}{3}$

Add $25$ and $6$ .

$\frac{\frac{31}{40} + \frac{4}{15}}{3}$

To write $\frac{31}{40}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{\frac{31}{40} \cdot \frac{3}{3} + \frac{4}{15}}{3}$

To write $\frac{4}{15}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{\frac{31}{40} \cdot \frac{3}{3} + \frac{4}{15} \cdot \frac{8}{8}}{3}$

Write each expression with a common denominator of $120$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{31}{40}$ by $\frac{3}{3}$ .

$\frac{\frac{31 \cdot 3}{40 \cdot 3} + \frac{4}{15} \cdot \frac{8}{8}}{3}$

Multiply $40$ by $3$ .

$\frac{\frac{31 \cdot 3}{120} + \frac{4}{15} \cdot \frac{8}{8}}{3}$

Multiply $\frac{4}{15}$ by $\frac{8}{8}$ .

$\frac{\frac{31 \cdot 3}{120} + \frac{4 \cdot 8}{15 \cdot 8}}{3}$

Multiply $15$ by $8$ .

$\frac{\frac{31 \cdot 3}{120} + \frac{4 \cdot 8}{120}}{3}$

Combine the numerators over the common denominator.

$\frac{\frac{31 \cdot 3 + 4 \cdot 8}{120}}{3}$

Simplify the numerator.

Multiply $31$ by $3$ .

$\frac{\frac{93 + 4 \cdot 8}{120}}{3}$

Multiply $4$ by $8$ .

$\frac{\frac{93 + 32}{120}}{3}$

Add $93$ and $32$ .

$\frac{\frac{125}{120}}{3}$

Cancel the common factor of $125$ and $120$ .

Factor $5$ out of $125$ .

$\frac{\frac{5 (25)}{120}}{3}$

Cancel the common factors.

Factor $5$ out of $120$ .

$\frac{\frac{5 \cdot 25}{5 \cdot 24}}{3}$

Cancel the common factor.

$\frac{\frac{5 \cdot 25}{5 \cdot 24}}{3}$

Rewrite the expression.

$\frac{\frac{25}{24}}{3}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{25}{24} \cdot \frac{1}{3}$

Step 4

Multiply $\frac{25}{24} \cdot \frac{1}{3}$ .

Multiply $\frac{25}{24}$ by $\frac{1}{3}$ .

$\frac{25}{24 \cdot 3}$

Multiply $24$ by $3$ .

$\frac{25}{72}$

Step 5

Divide.

$0.347\overline{2}$

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.

$0.3$

Find the Mean 5/8 , 3/20 , 4/15

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