Find the Mean 9/10 , 6/7 , 1/70

$\frac{9}{10}$ , $\frac{6}{7}$ , $\frac{1}{70}$

Step 1

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

$\frac{\frac{9}{10} + \frac{6}{7} + \frac{1}{70}}{3}$

Step 2

Simplify the numerator.

To write $\frac{9}{10}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{\frac{9}{10} \cdot \frac{7}{7} + \frac{6}{7} + \frac{1}{70}}{3}$

To write $\frac{6}{7}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{\frac{9}{10} \cdot \frac{7}{7} + \frac{6}{7} \cdot \frac{10}{10} + \frac{1}{70}}{3}$

Write each expression with a common denominator of $70$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{9}{10}$ by $\frac{7}{7}$ .

$\frac{\frac{9 \cdot 7}{10 \cdot 7} + \frac{6}{7} \cdot \frac{10}{10} + \frac{1}{70}}{3}$

Multiply $10$ by $7$ .

$\frac{\frac{9 \cdot 7}{70} + \frac{6}{7} \cdot \frac{10}{10} + \frac{1}{70}}{3}$

Multiply $\frac{6}{7}$ by $\frac{10}{10}$ .

$\frac{\frac{9 \cdot 7}{70} + \frac{6 \cdot 10}{7 \cdot 10} + \frac{1}{70}}{3}$

Multiply $7$ by $10$ .

$\frac{\frac{9 \cdot 7}{70} + \frac{6 \cdot 10}{70} + \frac{1}{70}}{3}$

Combine the numerators over the common denominator.

$\frac{\frac{9 \cdot 7 + 6 \cdot 10}{70} + \frac{1}{70}}{3}$

Simplify the numerator.

Multiply $9$ by $7$ .

$\frac{\frac{63 + 6 \cdot 10}{70} + \frac{1}{70}}{3}$

Multiply $6$ by $10$ .

$\frac{\frac{63 + 60}{70} + \frac{1}{70}}{3}$

Add $63$ and $60$ .

$\frac{\frac{123}{70} + \frac{1}{70}}{3}$

Combine the numerators over the common denominator.

$\frac{\frac{123 + 1}{70}}{3}$

Add $123$ and $1$ .

$\frac{\frac{124}{70}}{3}$

Cancel the common factor of $124$ and $70$ .

Factor $2$ out of $124$ .

$\frac{\frac{2 (62)}{70}}{3}$

Cancel the common factors.

Factor $2$ out of $70$ .

$\frac{\frac{2 \cdot 62}{2 \cdot 35}}{3}$

Cancel the common factor.

$\frac{\frac{2 \cdot 62}{2 \cdot 35}}{3}$

Rewrite the expression.

$\frac{\frac{62}{35}}{3}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{62}{35} \cdot \frac{1}{3}$

Step 4

Multiply $\frac{62}{35} \cdot \frac{1}{3}$ .

Multiply $\frac{62}{35}$ by $\frac{1}{3}$ .

$\frac{62}{35 \cdot 3}$

Multiply $35$ by $3$ .

$\frac{62}{105}$

Step 5

Divide.

$0.59047619$

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.

$0.6$

Find the Mean 9/10 , 6/7 , 1/70

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