Basic Math Examples

$1 \frac{1}{2} \cdot 5$ , $400$

Step 1

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

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Step 1.1

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

$(1 + \frac{1}{2}) \cdot 5, 400$

Step 1.2

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

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Step 1.2.1

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

$(\frac{2}{2} + \frac{1}{2}) \cdot 5, 400$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{2 + 1}{2} \cdot 5, 400$

Step 1.2.3

Add $2$ and $1$ .

$\frac{3}{2} \cdot 5, 400$

Step 2

Multiply $\frac{3}{2} \cdot 5$ .

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Step 2.1

Combine $\frac{3}{2}$ and $5$ .

$\frac{3 \cdot 5}{2}, 400$

Step 2.2

Multiply $3$ by $5$ .

$\frac{15}{2}, 400$

Step 3

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

$\frac{\frac{15}{2} + 400}{2}$

Step 4

Simplify the numerator.

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Step 4.1

To write $400$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{15}{2} + 400 \cdot \frac{2}{2}}{2}$

Step 4.2

Combine $400$ and $\frac{2}{2}$ .

$\frac{\frac{15}{2} + \frac{400 \cdot 2}{2}}{2}$

Step 4.3

Combine the numerators over the common denominator.

$\frac{\frac{15 + 400 \cdot 2}{2}}{2}$

Step 4.4

Simplify the numerator.

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Step 4.4.1

Multiply $400$ by $2$ .

$\frac{\frac{15 + 800}{2}}{2}$

Step 4.4.2

Add $15$ and $800$ .

$\frac{\frac{815}{2}}{2}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{815}{2} \cdot \frac{1}{2}$

Step 6

Multiply $\frac{815}{2} \cdot \frac{1}{2}$ .

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Step 6.1

Multiply $\frac{815}{2}$ by $\frac{1}{2}$ .

$\frac{815}{2 \cdot 2}$

Step 6.2

Multiply $2$ by $2$ .

$\frac{815}{4}$

Step 7

Divide.

$203.75$

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.

$203.8$