Basic Math Examples

$- 2 \frac{3}{4}$ , $\frac{5}{4}$

Step 1

Convert $2 \frac{3}{4}$ to an improper fraction.

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Step 1.1

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

$- (2 + \frac{3}{4}), \frac{5}{4}$

Step 1.2

Add $2$ and $\frac{3}{4}$ .

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- (2 \cdot \frac{4}{4} + \frac{3}{4}), \frac{5}{4}$

Step 1.2.2

Combine $2$ and $\frac{4}{4}$ .

$- (\frac{2 \cdot 4}{4} + \frac{3}{4}), \frac{5}{4}$

Step 1.2.3

Combine the numerators over the common denominator.

$- \frac{2 \cdot 4 + 3}{4}, \frac{5}{4}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $4$ .

$- \frac{8 + 3}{4}, \frac{5}{4}$

Step 1.2.4.2

Add $8$ and $3$ .

$- \frac{11}{4}, \frac{5}{4}$

Step 2

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

$\frac{- \frac{11}{4} + \frac{5}{4}}{2}$

Step 3

Simplify the numerator.

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Step 3.1

Combine the numerators over the common denominator.

$\frac{\frac{- 11 + 5}{4}}{2}$

Step 3.2

Add $- 11$ and $5$ .

$\frac{\frac{- 6}{4}}{2}$

Step 3.3

Reduce the expression by cancelling the common factors.

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Step 3.3.1

Cancel the common factor of $- 6$ and $4$ .

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Step 3.3.1.1

Factor $2$ out of $- 6$ .

$\frac{\frac{2 (- 3)}{4}}{2}$

Step 3.3.1.2

Cancel the common factors.

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Step 3.3.1.2.1

Factor $2$ out of $4$ .

$\frac{\frac{2 \cdot - 3}{2 \cdot 2}}{2}$

Step 3.3.1.2.2

Cancel the common factor.

$\frac{\frac{2 \cdot - 3}{2 \cdot 2}}{2}$

Step 3.3.1.2.3

Rewrite the expression.

$\frac{\frac{- 3}{2}}{2}$

Step 3.3.2

Move the negative in front of the fraction.

$\frac{- \frac{3}{2}}{2}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

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

Step 5

Multiply $- \frac{3}{2} \cdot \frac{1}{2}$ .

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Step 5.1

Multiply $\frac{1}{2}$ by $\frac{3}{2}$ .

$- \frac{3}{2 \cdot 2}$

Step 5.2

Multiply $2$ by $2$ .

$- \frac{3}{4}$

Step 6

Divide.

$- 0.75$

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.

$- 0.8$