Basic Math Examples

$2 \frac{2}{3} \cdot 1 \frac{5}{7}$

Step 1

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

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Step 1.1

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

$(2 + \frac{2}{3}) \cdot 1 \frac{5}{7}$

Step 1.2

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

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Step 1.2.1

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

$(2 \cdot \frac{3}{3} + \frac{2}{3}) \cdot 1 \frac{5}{7}$

Step 1.2.2

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

$(\frac{2 \cdot 3}{3} + \frac{2}{3}) \cdot 1 \frac{5}{7}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 3 + 2}{3} \cdot 1 \frac{5}{7}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $3$ .

$\frac{6 + 2}{3} \cdot 1 \frac{5}{7}$

Step 1.2.4.2

Add $6$ and $2$ .

$\frac{8}{3} \cdot 1 \frac{5}{7}$

Step 2

Convert $1 \frac{5}{7}$ to an improper fraction.

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Step 2.1

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

$\frac{8}{3} \cdot (1 + \frac{5}{7})$

Step 2.2

Add $1$ and $\frac{5}{7}$ .

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Step 2.2.1

Write $1$ as a fraction with a common denominator.

$\frac{8}{3} \cdot (\frac{7}{7} + \frac{5}{7})$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{8}{3} \cdot \frac{7 + 5}{7}$

Step 2.2.3

Add $7$ and $5$ .

$\frac{8}{3} \cdot \frac{12}{7}$

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Factor $3$ out of $12$ .

$\frac{8}{3} \cdot \frac{3 (4)}{7}$

Step 3.2

Cancel the common factor.

$\frac{8}{3} \cdot \frac{3 \cdot 4}{7}$

Step 3.3

Rewrite the expression.

$8 \cdot \frac{4}{7}$

Step 4

Combine $8$ and $\frac{4}{7}$ .

$\frac{8 \cdot 4}{7}$

Step 5

Multiply $8$ by $4$ .

$\frac{32}{7}$

Step 6

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

$\frac{\frac{32}{7}}{1}$

Step 7

Divide $\frac{32}{7}$ by $1$ .

$\frac{32}{7}$

Step 8

Divide.

$4.\overline{571428}$

Step 9

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.

$4.6$