Basic Math Examples

$2$ , $5 - 0.4 \cdot 3 \frac{1}{3}$

Step 1

Convert $3 \frac{1}{3}$ to an improper fraction.

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Step 1.1

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

$2, 5 - 0.4 \cdot (3 + \frac{1}{3})$

Step 1.2

Add $3$ and $\frac{1}{3}$ .

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Step 1.2.1

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

$2, 5 - 0.4 \cdot (3 \cdot \frac{3}{3} + \frac{1}{3})$

Step 1.2.2

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

$2, 5 - 0.4 \cdot (\frac{3 \cdot 3}{3} + \frac{1}{3})$

Step 1.2.3

Combine the numerators over the common denominator.

$2, 5 - 0.4 \cdot \frac{3 \cdot 3 + 1}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $3$ .

$2, 5 - 0.4 \cdot \frac{9 + 1}{3}$

Step 1.2.4.2

Add $9$ and $1$ .

$2, 5 - 0.4 \cdot \frac{10}{3}$

Step 2

Simplify each term.

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Step 2.1

Multiply $- 0.4 (\frac{10}{3})$ .

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Step 2.1.1

Combine $- 0.4$ and $\frac{10}{3}$ .

$2, 5 + \frac{- 0.4 \cdot 10}{3}$

Step 2.1.2

Multiply $- 0.4$ by $10$ .

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

Step 2.2

Cancel the common factor of $- 4$ and $3$ .

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Step 2.2.1

Rewrite $- 4$ as $1 (- 4)$ .

$2, 5 + \frac{1 (- 4)}{3}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Rewrite $3$ as $1 (3)$ .

$2, 5 + \frac{1 \cdot - 4}{1 \cdot 3}$

Step 2.2.2.2

Cancel the common factor.

$2, 5 + \frac{1 \cdot - 4}{1 \cdot 3}$

Step 2.2.2.3

Rewrite the expression.

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

Step 2.3

Move the negative in front of the fraction.

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

Step 3

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

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

Step 4

Combine $5$ and $\frac{3}{3}$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

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Step 6.1

Multiply $5$ by $3$ .

$2, \frac{15 - 4}{3}$

Step 6.2

Subtract $4$ from $15$ .

$2, \frac{11}{3}$

Step 7

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

$\frac{2 + \frac{11}{3}}{2}$

Step 8

Simplify the numerator.

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Step 8.1

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

$\frac{2 \cdot \frac{3}{3} + \frac{11}{3}}{2}$

Step 8.2

Combine $2$ and $\frac{3}{3}$ .

$\frac{\frac{2 \cdot 3}{3} + \frac{11}{3}}{2}$

Step 8.3

Combine the numerators over the common denominator.

$\frac{\frac{2 \cdot 3 + 11}{3}}{2}$

Step 8.4

Simplify the numerator.

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Step 8.4.1

Multiply $2$ by $3$ .

$\frac{\frac{6 + 11}{3}}{2}$

Step 8.4.2

Add $6$ and $11$ .

$\frac{\frac{17}{3}}{2}$

Step 9

Multiply the numerator by the reciprocal of the denominator.

$\frac{17}{3} \cdot \frac{1}{2}$

Step 10

Multiply $\frac{17}{3} \cdot \frac{1}{2}$ .

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Step 10.1

Multiply $\frac{17}{3}$ by $\frac{1}{2}$ .

$\frac{17}{3 \cdot 2}$

Step 10.2

Multiply $3$ by $2$ .

$\frac{17}{6}$

Step 11

Divide.

$2.8\overline{3}$

Step 12

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.

$2.8$