Pre-Algebra Examples

$13 \frac{5}{32}$ , $21 \frac{3}{16}$ , $12 \frac{7}{8}$

Step 1

Convert $13 \frac{5}{32}$ to an improper fraction.

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Step 1.1

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

$13 + \frac{5}{32}, 21 \frac{3}{16}, 12 \frac{7}{8}$

Step 1.2

Add $13$ and $\frac{5}{32}$ .

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Step 1.2.1

To write $13$ as a fraction with a common denominator, multiply by $\frac{32}{32}$ .

$13 \cdot \frac{32}{32} + \frac{5}{32}, 21 \frac{3}{16}, 12 \frac{7}{8}$

Step 1.2.2

Combine $13$ and $\frac{32}{32}$ .

$\frac{13 \cdot 32}{32} + \frac{5}{32}, 21 \frac{3}{16}, 12 \frac{7}{8}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{13 \cdot 32 + 5}{32}, 21 \frac{3}{16}, 12 \frac{7}{8}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $13$ by $32$ .

$\frac{416 + 5}{32}, 21 \frac{3}{16}, 12 \frac{7}{8}$

Step 1.2.4.2

Add $416$ and $5$ .

$\frac{421}{32}, 21 \frac{3}{16}, 12 \frac{7}{8}$

Step 2

Convert $21 \frac{3}{16}$ to an improper fraction.

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Step 2.1

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

$\frac{421}{32}, 21 + \frac{3}{16}, 12 \frac{7}{8}$

Step 2.2

Add $21$ and $\frac{3}{16}$ .

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Step 2.2.1

To write $21$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

$\frac{421}{32}, 21 \cdot \frac{16}{16} + \frac{3}{16}, 12 \frac{7}{8}$

Step 2.2.2

Combine $21$ and $\frac{16}{16}$ .

$\frac{421}{32}, \frac{21 \cdot 16}{16} + \frac{3}{16}, 12 \frac{7}{8}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{421}{32}, \frac{21 \cdot 16 + 3}{16}, 12 \frac{7}{8}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $21$ by $16$ .

$\frac{421}{32}, \frac{336 + 3}{16}, 12 \frac{7}{8}$

Step 2.2.4.2

Add $336$ and $3$ .

$\frac{421}{32}, \frac{339}{16}, 12 \frac{7}{8}$

Step 3

Convert $12 \frac{7}{8}$ to an improper fraction.

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Step 3.1

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

$\frac{421}{32}, \frac{339}{16}, 12 + \frac{7}{8}$

Step 3.2

Add $12$ and $\frac{7}{8}$ .

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Step 3.2.1

To write $12$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{421}{32}, \frac{339}{16}, 12 \cdot \frac{8}{8} + \frac{7}{8}$

Step 3.2.2

Combine $12$ and $\frac{8}{8}$ .

$\frac{421}{32}, \frac{339}{16}, \frac{12 \cdot 8}{8} + \frac{7}{8}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{421}{32}, \frac{339}{16}, \frac{12 \cdot 8 + 7}{8}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $12$ by $8$ .

$\frac{421}{32}, \frac{339}{16}, \frac{96 + 7}{8}$

Step 3.2.4.2

Add $96$ and $7$ .

$\frac{421}{32}, \frac{339}{16}, \frac{103}{8}$

Step 4

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

$\frac{\frac{421}{32} + \frac{339}{16} + \frac{103}{8}}{3}$

Step 5

Simplify the numerator.

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Step 5.1

To write $\frac{339}{16}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{421}{32} + \frac{339}{16} \cdot \frac{2}{2} + \frac{103}{8}}{3}$

Step 5.2

Write each expression with a common denominator of $32$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.2.1

Multiply $\frac{339}{16}$ by $\frac{2}{2}$ .

$\frac{\frac{421}{32} + \frac{339 \cdot 2}{16 \cdot 2} + \frac{103}{8}}{3}$

Step 5.2.2

Multiply $16$ by $2$ .

$\frac{\frac{421}{32} + \frac{339 \cdot 2}{32} + \frac{103}{8}}{3}$

Step 5.3

Combine the numerators over the common denominator.

$\frac{\frac{421 + 339 \cdot 2}{32} + \frac{103}{8}}{3}$

Step 5.4

Simplify the numerator.

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Step 5.4.1

Multiply $339$ by $2$ .

$\frac{\frac{421 + 678}{32} + \frac{103}{8}}{3}$

Step 5.4.2

Add $421$ and $678$ .

$\frac{\frac{1099}{32} + \frac{103}{8}}{3}$

Step 5.5

To write $\frac{103}{8}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{\frac{1099}{32} + \frac{103}{8} \cdot \frac{4}{4}}{3}$

Step 5.6

Write each expression with a common denominator of $32$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.6.1

Multiply $\frac{103}{8}$ by $\frac{4}{4}$ .

$\frac{\frac{1099}{32} + \frac{103 \cdot 4}{8 \cdot 4}}{3}$

Step 5.6.2

Multiply $8$ by $4$ .

$\frac{\frac{1099}{32} + \frac{103 \cdot 4}{32}}{3}$

Step 5.7

Combine the numerators over the common denominator.

$\frac{\frac{1099 + 103 \cdot 4}{32}}{3}$

Step 5.8

Simplify the numerator.

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Step 5.8.1

Multiply $103$ by $4$ .

$\frac{\frac{1099 + 412}{32}}{3}$

Step 5.8.2

Add $1099$ and $412$ .

$\frac{\frac{1511}{32}}{3}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$\frac{1511}{32} \cdot \frac{1}{3}$

Step 7

Multiply $\frac{1511}{32} \cdot \frac{1}{3}$ .

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Step 7.1

Multiply $\frac{1511}{32}$ by $\frac{1}{3}$ .

$\frac{1511}{32 \cdot 3}$

Step 7.2

Multiply $32$ by $3$ .

$\frac{1511}{96}$

Step 8

Divide.

$15.73958\overline{3}$

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.

$15.7$