Find the Mean 16/4 , -13/6 , 3/5 , -6/7 , -5/4

$\frac{16}{4}$ , $- \frac{13}{6}$ , $\frac{3}{5}$ , $- \frac{6}{7}$ , $- \frac{5}{4}$

Step 1

Divide $16$ by $4$ .

$4, - \frac{13}{6}, \frac{3}{5}, - \frac{6}{7}, - \frac{5}{4}$

Step 2

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

$\frac{4 - \frac{13}{6} + \frac{3}{5} - \frac{6}{7} - \frac{5}{4}}{5}$

Step 3

Simplify the numerator.

To write $4$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{4 \cdot \frac{6}{6} - \frac{13}{6} + \frac{3}{5} - \frac{6}{7} - \frac{5}{4}}{5}$

Combine $4$ and $\frac{6}{6}$ .

$\frac{\frac{4 \cdot 6}{6} - \frac{13}{6} + \frac{3}{5} - \frac{6}{7} - \frac{5}{4}}{5}$

Combine the numerators over the common denominator.

$\frac{\frac{4 \cdot 6 - 13}{6} + \frac{3}{5} - \frac{6}{7} - \frac{5}{4}}{5}$

Simplify the numerator.

Multiply $4$ by $6$ .

$\frac{\frac{24 - 13}{6} + \frac{3}{5} - \frac{6}{7} - \frac{5}{4}}{5}$

Subtract $13$ from $24$ .

$\frac{\frac{11}{6} + \frac{3}{5} - \frac{6}{7} - \frac{5}{4}}{5}$

To write $\frac{11}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{\frac{11}{6} \cdot \frac{5}{5} + \frac{3}{5} - \frac{6}{7} - \frac{5}{4}}{5}$

To write $\frac{3}{5}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{\frac{11}{6} \cdot \frac{5}{5} + \frac{3}{5} \cdot \frac{6}{6} - \frac{6}{7} - \frac{5}{4}}{5}$

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{11}{6}$ by $\frac{5}{5}$ .

$\frac{\frac{11 \cdot 5}{6 \cdot 5} + \frac{3}{5} \cdot \frac{6}{6} - \frac{6}{7} - \frac{5}{4}}{5}$

Multiply $6$ by $5$ .

$\frac{\frac{11 \cdot 5}{30} + \frac{3}{5} \cdot \frac{6}{6} - \frac{6}{7} - \frac{5}{4}}{5}$

Multiply $\frac{3}{5}$ by $\frac{6}{6}$ .

$\frac{\frac{11 \cdot 5}{30} + \frac{3 \cdot 6}{5 \cdot 6} - \frac{6}{7} - \frac{5}{4}}{5}$

Multiply $5$ by $6$ .

$\frac{\frac{11 \cdot 5}{30} + \frac{3 \cdot 6}{30} - \frac{6}{7} - \frac{5}{4}}{5}$

Combine the numerators over the common denominator.

$\frac{\frac{11 \cdot 5 + 3 \cdot 6}{30} - \frac{6}{7} - \frac{5}{4}}{5}$

Simplify the numerator.

Multiply $11$ by $5$ .

$\frac{\frac{55 + 3 \cdot 6}{30} - \frac{6}{7} - \frac{5}{4}}{5}$

Multiply $3$ by $6$ .

$\frac{\frac{55 + 18}{30} - \frac{6}{7} - \frac{5}{4}}{5}$

Add $55$ and $18$ .

$\frac{\frac{73}{30} - \frac{6}{7} - \frac{5}{4}}{5}$

To write $\frac{73}{30}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{\frac{73}{30} \cdot \frac{7}{7} - \frac{6}{7} - \frac{5}{4}}{5}$

To write $- \frac{6}{7}$ as a fraction with a common denominator, multiply by $\frac{30}{30}$ .

$\frac{\frac{73}{30} \cdot \frac{7}{7} - \frac{6}{7} \cdot \frac{30}{30} - \frac{5}{4}}{5}$

Write each expression with a common denominator of $210$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{73}{30}$ by $\frac{7}{7}$ .

$\frac{\frac{73 \cdot 7}{30 \cdot 7} - \frac{6}{7} \cdot \frac{30}{30} - \frac{5}{4}}{5}$

Multiply $30$ by $7$ .

$\frac{\frac{73 \cdot 7}{210} - \frac{6}{7} \cdot \frac{30}{30} - \frac{5}{4}}{5}$

Multiply $\frac{6}{7}$ by $\frac{30}{30}$ .

$\frac{\frac{73 \cdot 7}{210} - \frac{6 \cdot 30}{7 \cdot 30} - \frac{5}{4}}{5}$

Multiply $7$ by $30$ .

$\frac{\frac{73 \cdot 7}{210} - \frac{6 \cdot 30}{210} - \frac{5}{4}}{5}$

Combine the numerators over the common denominator.

$\frac{\frac{73 \cdot 7 - 6 \cdot 30}{210} - \frac{5}{4}}{5}$

Simplify the numerator.

Multiply $73$ by $7$ .

$\frac{\frac{511 - 6 \cdot 30}{210} - \frac{5}{4}}{5}$

Multiply $- 6$ by $30$ .

$\frac{\frac{511 - 180}{210} - \frac{5}{4}}{5}$

Subtract $180$ from $511$ .

$\frac{\frac{331}{210} - \frac{5}{4}}{5}$

To write $\frac{331}{210}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{331}{210} \cdot \frac{2}{2} - \frac{5}{4}}{5}$

To write $- \frac{5}{4}$ as a fraction with a common denominator, multiply by $\frac{105}{105}$ .

$\frac{\frac{331}{210} \cdot \frac{2}{2} - \frac{5}{4} \cdot \frac{105}{105}}{5}$

Write each expression with a common denominator of $420$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{331}{210}$ by $\frac{2}{2}$ .

$\frac{\frac{331 \cdot 2}{210 \cdot 2} - \frac{5}{4} \cdot \frac{105}{105}}{5}$

Multiply $210$ by $2$ .

$\frac{\frac{331 \cdot 2}{420} - \frac{5}{4} \cdot \frac{105}{105}}{5}$

Multiply $\frac{5}{4}$ by $\frac{105}{105}$ .

$\frac{\frac{331 \cdot 2}{420} - \frac{5 \cdot 105}{4 \cdot 105}}{5}$

Multiply $4$ by $105$ .

$\frac{\frac{331 \cdot 2}{420} - \frac{5 \cdot 105}{420}}{5}$

Combine the numerators over the common denominator.

$\frac{\frac{331 \cdot 2 - 5 \cdot 105}{420}}{5}$

Simplify the numerator.

Multiply $331$ by $2$ .

$\frac{\frac{662 - 5 \cdot 105}{420}}{5}$

Multiply $- 5$ by $105$ .

$\frac{\frac{662 - 525}{420}}{5}$

Subtract $525$ from $662$ .

$\frac{\frac{137}{420}}{5}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{137}{420} \cdot \frac{1}{5}$

Step 5

Multiply $\frac{137}{420} \cdot \frac{1}{5}$ .

Multiply $\frac{137}{420}$ by $\frac{1}{5}$ .

$\frac{137}{420 \cdot 5}$

Multiply $420$ by $5$ .

$\frac{137}{2100}$

Step 6

Divide.

$0.06523809$

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.

$0.1$

Find the Mean 16/4 , -13/6 , 3/5 , -6/7 , -5/4

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