Basic Math Examples

$16 \frac{3}{10}$ , $- 16.5$ , $- \frac{50}{3}$ , $- \sqrt{270}$

Step 1

Convert $16 \frac{3}{10}$ to an improper fraction.

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Step 1.1

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

$16 + \frac{3}{10}, - 16.5, - \frac{50}{3}, - \sqrt{270}$

Step 1.2

Add $16$ and $\frac{3}{10}$ .

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Step 1.2.1

To write $16$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$16 \cdot \frac{10}{10} + \frac{3}{10}, - 16.5, - \frac{50}{3}, - \sqrt{270}$

Step 1.2.2

Combine $16$ and $\frac{10}{10}$ .

$\frac{16 \cdot 10}{10} + \frac{3}{10}, - 16.5, - \frac{50}{3}, - \sqrt{270}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{16 \cdot 10 + 3}{10}, - 16.5, - \frac{50}{3}, - \sqrt{270}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $16$ by $10$ .

$\frac{160 + 3}{10}, - 16.5, - \frac{50}{3}, - \sqrt{270}$

Step 1.2.4.2

Add $160$ and $3$ .

$\frac{163}{10}, - 16.5, - \frac{50}{3}, - \sqrt{270}$

Step 2

Rewrite $270$ as $3^{2} \cdot 30$ .

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Step 2.1

Factor $9$ out of $270$ .

$\frac{163}{10}, - 16.5, - \frac{50}{3}, - \sqrt{9 (30)}$

Step 2.2

Rewrite $9$ as $3^{2}$ .

$\frac{163}{10}, - 16.5, - \frac{50}{3}, - \sqrt{3^{2} \cdot 30}$

Step 3

Pull terms out from under the radical.

$\frac{163}{10}, - 16.5, - \frac{50}{3}, - (3 \sqrt{30})$

Step 4

Multiply $3$ by $- 1$ .

$\frac{163}{10}, - 16.5, - \frac{50}{3}, - 3 \sqrt{30}$

Step 5

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

$\frac{\frac{163}{10} - 16.5 - \frac{50}{3} - 3 \sqrt{30}}{4}$

Step 6

Simplify the numerator.

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Step 6.1

To write $- 16.5$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{\frac{163}{10} - 16.5 \cdot \frac{10}{10} - \frac{50}{3} - 3 \sqrt{30}}{4}$

Step 6.2

Combine $- 16.5$ and $\frac{10}{10}$ .

$\frac{\frac{163}{10} + \frac{- 16.5 \cdot 10}{10} - \frac{50}{3} - 3 \sqrt{30}}{4}$

Step 6.3

Combine the numerators over the common denominator.

$\frac{\frac{163 - 16.5 \cdot 10}{10} - \frac{50}{3} - 3 \sqrt{30}}{4}$

Step 6.4

Simplify the numerator.

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Step 6.4.1

Multiply $- 16.5$ by $10$ .

$\frac{\frac{163 - 165}{10} - \frac{50}{3} - 3 \sqrt{30}}{4}$

Step 6.4.2

Subtract $165$ from $163$ .

$\frac{\frac{- 2}{10} - \frac{50}{3} - 3 \sqrt{30}}{4}$

Step 6.5

To write $\frac{- 2}{10}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{\frac{- 2}{10} \cdot \frac{3}{3} - \frac{50}{3} - 3 \sqrt{30}}{4}$

Step 6.6

To write $- \frac{50}{3}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{\frac{- 2}{10} \cdot \frac{3}{3} - \frac{50}{3} \cdot \frac{10}{10} - 3 \sqrt{30}}{4}$

Step 6.7

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

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Step 6.7.1

Multiply $\frac{- 2}{10}$ by $\frac{3}{3}$ .

$\frac{\frac{- 2 \cdot 3}{10 \cdot 3} - \frac{50}{3} \cdot \frac{10}{10} - 3 \sqrt{30}}{4}$

Step 6.7.2

Multiply $10$ by $3$ .

$\frac{\frac{- 2 \cdot 3}{30} - \frac{50}{3} \cdot \frac{10}{10} - 3 \sqrt{30}}{4}$

Step 6.7.3

Multiply $\frac{50}{3}$ by $\frac{10}{10}$ .

$\frac{\frac{- 2 \cdot 3}{30} - \frac{50 \cdot 10}{3 \cdot 10} - 3 \sqrt{30}}{4}$

Step 6.7.4

Multiply $3$ by $10$ .

$\frac{\frac{- 2 \cdot 3}{30} - \frac{50 \cdot 10}{30} - 3 \sqrt{30}}{4}$

Step 6.8

Combine the numerators over the common denominator.

$\frac{\frac{- 2 \cdot 3 - 50 \cdot 10}{30} - 3 \sqrt{30}}{4}$

Step 6.9

Simplify the numerator.

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Step 6.9.1

Multiply $- 2$ by $3$ .

$\frac{\frac{- 6 - 50 \cdot 10}{30} - 3 \sqrt{30}}{4}$

Step 6.9.2

Multiply $- 50$ by $10$ .

$\frac{\frac{- 6 - 500}{30} - 3 \sqrt{30}}{4}$

Step 6.9.3

Subtract $500$ from $- 6$ .

$\frac{\frac{- 506}{30} - 3 \sqrt{30}}{4}$

Step 6.10

Simplify each term.

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Step 6.10.1

Cancel the common factor of $- 506$ and $30$ .

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Step 6.10.1.1

Factor $2$ out of $- 506$ .

$\frac{\frac{2 (- 253)}{30} - 3 \sqrt{30}}{4}$

Step 6.10.1.2

Cancel the common factors.

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Step 6.10.1.2.1

Factor $2$ out of $30$ .

$\frac{\frac{2 \cdot - 253}{2 \cdot 15} - 3 \sqrt{30}}{4}$

Step 6.10.1.2.2

Cancel the common factor.

$\frac{\frac{2 \cdot - 253}{2 \cdot 15} - 3 \sqrt{30}}{4}$

Step 6.10.1.2.3

Rewrite the expression.

$\frac{\frac{- 253}{15} - 3 \sqrt{30}}{4}$

Step 6.10.2

Move the negative in front of the fraction.

$\frac{- \frac{253}{15} - 3 \sqrt{30}}{4}$

Step 6.11

To write $- 3 \sqrt{30}$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$\frac{- \frac{253}{15} - 3 \sqrt{30} \cdot \frac{15}{15}}{4}$

Step 6.12

Combine $- 3 \sqrt{30}$ and $\frac{15}{15}$ .

$\frac{- \frac{253}{15} + \frac{- 3 \sqrt{30} \cdot 15}{15}}{4}$

Step 6.13

Combine the numerators over the common denominator.

$\frac{\frac{- 253 - 3 \sqrt{30} \cdot 15}{15}}{4}$

Step 6.14

Multiply $15$ by $- 3$ .

$\frac{\frac{- 253 - 45 \sqrt{30}}{15}}{4}$

Step 7

Multiply the numerator by the reciprocal of the denominator.

$\frac{- 253 - 45 \sqrt{30}}{15} \cdot \frac{1}{4}$

Step 8

Multiply $\frac{- 253 - 45 \sqrt{30}}{15} \cdot \frac{1}{4}$ .

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Step 8.1

Multiply $\frac{- 253 - 45 \sqrt{30}}{15}$ by $\frac{1}{4}$ .

$\frac{- 253 - 45 \sqrt{30}}{15 \cdot 4}$

Step 8.2

Multiply $15$ by $4$ .

$\frac{- 253 - 45 \sqrt{30}}{60}$

Step 9

Rewrite $- 253$ as $- 1 (253)$ .

$\frac{- 1 (253) - 45 \sqrt{30}}{60}$

Step 10

Factor $- 1$ out of $- 45 \sqrt{30}$ .

$\frac{- 1 (253) - (45 \sqrt{30})}{60}$

Step 11

Factor $- 1$ out of $- 1 (253) - (45 \sqrt{30})$ .

$\frac{- 1 (253 + 45 \sqrt{30})}{60}$

Step 12

Move the negative in front of the fraction.

$- \frac{253 + 45 \sqrt{30}}{60}$

Step 13

Divide.

$- 8.32458584$

Step 14

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.

$- 8.3$