Basic Math Examples

$- 7$ , $- \frac{7}{3}$ , $- \frac{7}{9}$ , $- \frac{7}{27}$ , $- \frac{7}{81}$ , $- \frac{7}{729}$

Step 1

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

$\frac{- 7 - \frac{7}{3} - \frac{7}{9} - \frac{7}{27} - \frac{7}{81} - \frac{7}{729}}{6}$

Step 2

Simplify the numerator.

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Step 2.1

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{- 7 \cdot \frac{3}{3} - \frac{7}{3} - \frac{7}{9} - \frac{7}{27} - \frac{7}{81} - \frac{7}{729}}{6}$

Step 2.2

Combine $- 7$ and $\frac{3}{3}$ .

$\frac{\frac{- 7 \cdot 3}{3} - \frac{7}{3} - \frac{7}{9} - \frac{7}{27} - \frac{7}{81} - \frac{7}{729}}{6}$

Step 2.3

Combine the numerators over the common denominator.

$\frac{\frac{- 7 \cdot 3 - 7}{3} - \frac{7}{9} - \frac{7}{27} - \frac{7}{81} - \frac{7}{729}}{6}$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Multiply $- 7$ by $3$ .

$\frac{\frac{- 21 - 7}{3} - \frac{7}{9} - \frac{7}{27} - \frac{7}{81} - \frac{7}{729}}{6}$

Step 2.4.2

Subtract $7$ from $- 21$ .

$\frac{\frac{- 28}{3} - \frac{7}{9} - \frac{7}{27} - \frac{7}{81} - \frac{7}{729}}{6}$

Step 2.5

To write $\frac{- 28}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{\frac{- 28}{3} \cdot \frac{3}{3} - \frac{7}{9} - \frac{7}{27} - \frac{7}{81} - \frac{7}{729}}{6}$

Step 2.6

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.6.1

Multiply $\frac{- 28}{3}$ by $\frac{3}{3}$ .

$\frac{\frac{- 28 \cdot 3}{3 \cdot 3} - \frac{7}{9} - \frac{7}{27} - \frac{7}{81} - \frac{7}{729}}{6}$

Step 2.6.2

Multiply $3$ by $3$ .

$\frac{\frac{- 28 \cdot 3}{9} - \frac{7}{9} - \frac{7}{27} - \frac{7}{81} - \frac{7}{729}}{6}$

Step 2.7

Combine the numerators over the common denominator.

$\frac{\frac{- 28 \cdot 3 - 7}{9} - \frac{7}{27} - \frac{7}{81} - \frac{7}{729}}{6}$

Step 2.8

Simplify the numerator.

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Step 2.8.1

Multiply $- 28$ by $3$ .

$\frac{\frac{- 84 - 7}{9} - \frac{7}{27} - \frac{7}{81} - \frac{7}{729}}{6}$

Step 2.8.2

Subtract $7$ from $- 84$ .

$\frac{\frac{- 91}{9} - \frac{7}{27} - \frac{7}{81} - \frac{7}{729}}{6}$

Step 2.9

To write $\frac{- 91}{9}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{\frac{- 91}{9} \cdot \frac{3}{3} - \frac{7}{27} - \frac{7}{81} - \frac{7}{729}}{6}$

Step 2.10

Write each expression with a common denominator of $27$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.10.1

Multiply $\frac{- 91}{9}$ by $\frac{3}{3}$ .

$\frac{\frac{- 91 \cdot 3}{9 \cdot 3} - \frac{7}{27} - \frac{7}{81} - \frac{7}{729}}{6}$

Step 2.10.2

Multiply $9$ by $3$ .

$\frac{\frac{- 91 \cdot 3}{27} - \frac{7}{27} - \frac{7}{81} - \frac{7}{729}}{6}$

Step 2.11

Combine the numerators over the common denominator.

$\frac{\frac{- 91 \cdot 3 - 7}{27} - \frac{7}{81} - \frac{7}{729}}{6}$

Step 2.12

Simplify the numerator.

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Step 2.12.1

Multiply $- 91$ by $3$ .

$\frac{\frac{- 273 - 7}{27} - \frac{7}{81} - \frac{7}{729}}{6}$

Step 2.12.2

Subtract $7$ from $- 273$ .

$\frac{\frac{- 280}{27} - \frac{7}{81} - \frac{7}{729}}{6}$

Step 2.13

To write $\frac{- 280}{27}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{\frac{- 280}{27} \cdot \frac{3}{3} - \frac{7}{81} - \frac{7}{729}}{6}$

Step 2.14

Write each expression with a common denominator of $81$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.14.1

Multiply $\frac{- 280}{27}$ by $\frac{3}{3}$ .

$\frac{\frac{- 280 \cdot 3}{27 \cdot 3} - \frac{7}{81} - \frac{7}{729}}{6}$

Step 2.14.2

Multiply $27$ by $3$ .

$\frac{\frac{- 280 \cdot 3}{81} - \frac{7}{81} - \frac{7}{729}}{6}$

Step 2.15

Combine the numerators over the common denominator.

$\frac{\frac{- 280 \cdot 3 - 7}{81} - \frac{7}{729}}{6}$

Step 2.16

Simplify the numerator.

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Step 2.16.1

Multiply $- 280$ by $3$ .

$\frac{\frac{- 840 - 7}{81} - \frac{7}{729}}{6}$

Step 2.16.2

Subtract $7$ from $- 840$ .

$\frac{\frac{- 847}{81} - \frac{7}{729}}{6}$

Step 2.17

To write $\frac{- 847}{81}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{\frac{- 847}{81} \cdot \frac{9}{9} - \frac{7}{729}}{6}$

Step 2.18

Write each expression with a common denominator of $729$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.18.1

Multiply $\frac{- 847}{81}$ by $\frac{9}{9}$ .

$\frac{\frac{- 847 \cdot 9}{81 \cdot 9} - \frac{7}{729}}{6}$

Step 2.18.2

Multiply $81$ by $9$ .

$\frac{\frac{- 847 \cdot 9}{729} - \frac{7}{729}}{6}$

Step 2.19

Combine the numerators over the common denominator.

$\frac{\frac{- 847 \cdot 9 - 7}{729}}{6}$

Step 2.20

Simplify the numerator.

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Step 2.20.1

Multiply $- 847$ by $9$ .

$\frac{\frac{- 7623 - 7}{729}}{6}$

Step 2.20.2

Subtract $7$ from $- 7623$ .

$\frac{\frac{- 7630}{729}}{6}$

Step 2.21

Move the negative in front of the fraction.

$\frac{- \frac{7630}{729}}{6}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$- \frac{7630}{729} \cdot \frac{1}{6}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Move the leading negative in $- \frac{7630}{729}$ into the numerator.

$\frac{- 7630}{729} \cdot \frac{1}{6}$

Step 4.2

Factor $2$ out of $- 7630$ .

$\frac{2 (- 3815)}{729} \cdot \frac{1}{6}$

Step 4.3

Factor $2$ out of $6$ .

$\frac{2 \cdot - 3815}{729} \cdot \frac{1}{2 \cdot 3}$

Step 4.4

Cancel the common factor.

$\frac{2 \cdot - 3815}{729} \cdot \frac{1}{2 \cdot 3}$

Step 4.5

Rewrite the expression.

$\frac{- 3815}{729} \cdot \frac{1}{3}$

Step 5

Multiply $\frac{- 3815}{729}$ by $\frac{1}{3}$ .

$\frac{- 3815}{729 \cdot 3}$

Step 6

Simplify the expression.

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Step 6.1

Multiply $729$ by $3$ .

$\frac{- 3815}{2187}$

Step 6.2

Move the negative in front of the fraction.

$- \frac{3815}{2187}$

Step 7

Divide.

$- 1.74439871$

Step 8

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.

$- 1.7$