Basic Math Examples

$8 \frac{1}{2}$ , $38 \frac{1}{4}$

Step 1

Convert $8 \frac{1}{2}$ to an improper fraction.

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Step 1.1

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

$8 + \frac{1}{2}, 38 \frac{1}{4}$

Step 1.2

Add $8$ and $\frac{1}{2}$ .

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Step 1.2.1

To write $8$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$8 \cdot \frac{2}{2} + \frac{1}{2}, 38 \frac{1}{4}$

Step 1.2.2

Combine $8$ and $\frac{2}{2}$ .

$\frac{8 \cdot 2}{2} + \frac{1}{2}, 38 \frac{1}{4}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{8 \cdot 2 + 1}{2}, 38 \frac{1}{4}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $8$ by $2$ .

$\frac{16 + 1}{2}, 38 \frac{1}{4}$

Step 1.2.4.2

Add $16$ and $1$ .

$\frac{17}{2}, 38 \frac{1}{4}$

Step 2

Convert $38 \frac{1}{4}$ to an improper fraction.

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Step 2.1

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

$\frac{17}{2}, 38 + \frac{1}{4}$

Step 2.2

Add $38$ and $\frac{1}{4}$ .

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Step 2.2.1

To write $38$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{17}{2}, 38 \cdot \frac{4}{4} + \frac{1}{4}$

Step 2.2.2

Combine $38$ and $\frac{4}{4}$ .

$\frac{17}{2}, \frac{38 \cdot 4}{4} + \frac{1}{4}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{17}{2}, \frac{38 \cdot 4 + 1}{4}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $38$ by $4$ .

$\frac{17}{2}, \frac{152 + 1}{4}$

Step 2.2.4.2

Add $152$ and $1$ .

$\frac{17}{2}, \frac{153}{4}$

Step 3

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

$\frac{\frac{17}{2} + \frac{153}{4}}{2}$

Step 4

Simplify the numerator.

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Step 4.1

To write $\frac{17}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{17}{2} \cdot \frac{2}{2} + \frac{153}{4}}{2}$

Step 4.2

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.2.1

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

$\frac{\frac{17 \cdot 2}{2 \cdot 2} + \frac{153}{4}}{2}$

Step 4.2.2

Multiply $2$ by $2$ .

$\frac{\frac{17 \cdot 2}{4} + \frac{153}{4}}{2}$

Step 4.3

Combine the numerators over the common denominator.

$\frac{\frac{17 \cdot 2 + 153}{4}}{2}$

Step 4.4

Simplify the numerator.

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Step 4.4.1

Multiply $17$ by $2$ .

$\frac{\frac{34 + 153}{4}}{2}$

Step 4.4.2

Add $34$ and $153$ .

$\frac{\frac{187}{4}}{2}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{187}{4} \cdot \frac{1}{2}$

Step 6

Multiply $\frac{187}{4} \cdot \frac{1}{2}$ .

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Step 6.1

Multiply $\frac{187}{4}$ by $\frac{1}{2}$ .

$\frac{187}{4 \cdot 2}$

Step 6.2

Multiply $4$ by $2$ .

$\frac{187}{8}$

Step 7

Divide.

$23.375$

Step 8

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.

$23.4$