Finite Math Examples

$\frac{7}{12}$ , $1 \frac{1}{3} \cdot 2 \frac{1}{12} \cdot 2 \frac{5}{6}$

Step 1

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

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Step 1.1

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

$\frac{7}{12}, (1 + \frac{1}{3}) \cdot 2 \frac{1}{12} \cdot 2 \frac{5}{6}$

Step 1.2

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

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Step 1.2.1

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

$\frac{7}{12}, (\frac{3}{3} + \frac{1}{3}) \cdot 2 \frac{1}{12} \cdot 2 \frac{5}{6}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{7}{12}, \frac{3 + 1}{3} \cdot 2 \frac{1}{12} \cdot 2 \frac{5}{6}$

Step 1.2.3

Add $3$ and $1$ .

$\frac{7}{12}, \frac{4}{3} \cdot 2 \frac{1}{12} \cdot 2 \frac{5}{6}$

Step 2

Convert $2 \frac{1}{12}$ to an improper fraction.

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Step 2.1

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

$\frac{7}{12}, \frac{4}{3} \cdot (2 + \frac{1}{12}) \cdot 2 \frac{5}{6}$

Step 2.2

Add $2$ and $\frac{1}{12}$ .

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Step 2.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$\frac{7}{12}, \frac{4}{3} \cdot (2 \cdot \frac{12}{12} + \frac{1}{12}) \cdot 2 \frac{5}{6}$

Step 2.2.2

Combine $2$ and $\frac{12}{12}$ .

$\frac{7}{12}, \frac{4}{3} \cdot (\frac{2 \cdot 12}{12} + \frac{1}{12}) \cdot 2 \frac{5}{6}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{7}{12}, \frac{4}{3} \cdot \frac{2 \cdot 12 + 1}{12} \cdot 2 \frac{5}{6}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $12$ .

$\frac{7}{12}, \frac{4}{3} \cdot \frac{24 + 1}{12} \cdot 2 \frac{5}{6}$

Step 2.2.4.2

Add $24$ and $1$ .

$\frac{7}{12}, \frac{4}{3} \cdot \frac{25}{12} \cdot 2 \frac{5}{6}$

Step 3

Convert $2 \frac{5}{6}$ to an improper fraction.

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Step 3.1

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

$\frac{7}{12}, \frac{4}{3} \cdot \frac{25}{12} \cdot (2 + \frac{5}{6})$

Step 3.2

Add $2$ and $\frac{5}{6}$ .

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Step 3.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{7}{12}, \frac{4}{3} \cdot \frac{25}{12} \cdot (2 \cdot \frac{6}{6} + \frac{5}{6})$

Step 3.2.2

Combine $2$ and $\frac{6}{6}$ .

$\frac{7}{12}, \frac{4}{3} \cdot \frac{25}{12} \cdot (\frac{2 \cdot 6}{6} + \frac{5}{6})$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{7}{12}, \frac{4}{3} \cdot \frac{25}{12} \cdot \frac{2 \cdot 6 + 5}{6}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $2$ by $6$ .

$\frac{7}{12}, \frac{4}{3} \cdot \frac{25}{12} \cdot \frac{12 + 5}{6}$

Step 3.2.4.2

Add $12$ and $5$ .

$\frac{7}{12}, \frac{4}{3} \cdot \frac{25}{12} \cdot \frac{17}{6}$

Step 4

Cancel the common factor of $4$ .

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Step 4.1

Factor $4$ out of $12$ .

$\frac{7}{12}, \frac{4}{3} \cdot \frac{25}{4 (3)} \cdot \frac{17}{6}$

Step 4.2

Cancel the common factor.

$\frac{7}{12}, \frac{4}{3} \cdot \frac{25}{4 \cdot 3} \cdot \frac{17}{6}$

Step 4.3

Rewrite the expression.

$\frac{7}{12}, \frac{1}{3} \cdot \frac{25}{3} \cdot \frac{17}{6}$

Step 5

Multiply $\frac{1}{3}$ by $\frac{25}{3}$ .

$\frac{7}{12}, \frac{25}{3 \cdot 3} \cdot \frac{17}{6}$

Step 6

Multiply $3$ by $3$ .

$\frac{7}{12}, \frac{25}{9} \cdot \frac{17}{6}$

Step 7

Multiply $\frac{25}{9} \cdot \frac{17}{6}$ .

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Step 7.1

Multiply $\frac{25}{9}$ by $\frac{17}{6}$ .

$\frac{7}{12}, \frac{25 \cdot 17}{9 \cdot 6}$

Step 7.2

Multiply $25$ by $17$ .

$\frac{7}{12}, \frac{425}{9 \cdot 6}$

Step 7.3

Multiply $9$ by $6$ .

$\frac{7}{12}, \frac{425}{54}$

Step 8

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

$\frac{\frac{7}{12} + \frac{425}{54}}{2}$

Step 9

Simplify the numerator.

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Step 9.1

To write $\frac{7}{12}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{\frac{7}{12} \cdot \frac{9}{9} + \frac{425}{54}}{2}$

Step 9.2

To write $\frac{425}{54}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{7}{12} \cdot \frac{9}{9} + \frac{425}{54} \cdot \frac{2}{2}}{2}$

Step 9.3

Write each expression with a common denominator of $108$ , by multiplying each by an appropriate factor of $1$ .

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Step 9.3.1

Multiply $\frac{7}{12}$ by $\frac{9}{9}$ .

$\frac{\frac{7 \cdot 9}{12 \cdot 9} + \frac{425}{54} \cdot \frac{2}{2}}{2}$

Step 9.3.2

Multiply $12$ by $9$ .

$\frac{\frac{7 \cdot 9}{108} + \frac{425}{54} \cdot \frac{2}{2}}{2}$

Step 9.3.3

Multiply $\frac{425}{54}$ by $\frac{2}{2}$ .

$\frac{\frac{7 \cdot 9}{108} + \frac{425 \cdot 2}{54 \cdot 2}}{2}$

Step 9.3.4

Multiply $54$ by $2$ .

$\frac{\frac{7 \cdot 9}{108} + \frac{425 \cdot 2}{108}}{2}$

Step 9.4

Combine the numerators over the common denominator.

$\frac{\frac{7 \cdot 9 + 425 \cdot 2}{108}}{2}$

Step 9.5

Simplify the numerator.

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Step 9.5.1

Multiply $7$ by $9$ .

$\frac{\frac{63 + 425 \cdot 2}{108}}{2}$

Step 9.5.2

Multiply $425$ by $2$ .

$\frac{\frac{63 + 850}{108}}{2}$

Step 9.5.3

Add $63$ and $850$ .

$\frac{\frac{913}{108}}{2}$

Step 10

Multiply the numerator by the reciprocal of the denominator.

$\frac{913}{108} \cdot \frac{1}{2}$

Step 11

Multiply $\frac{913}{108} \cdot \frac{1}{2}$ .

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Step 11.1

Multiply $\frac{913}{108}$ by $\frac{1}{2}$ .

$\frac{913}{108 \cdot 2}$

Step 11.2

Multiply $108$ by $2$ .

$\frac{913}{216}$

Step 12

Divide.

$4.226\overline{851}$

Step 13

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.

$4.2$