Basic Math Examples

$14$ $\frac{13}{25} + 10 \frac{1}{3}$

Step 1

Convert $10 \frac{1}{3}$ to an improper fraction.

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Step 1.1

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

$14, \frac{13}{25} + 10 + \frac{1}{3}$

Step 1.2

Add $10$ and $\frac{1}{3}$ .

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Step 1.2.1

To write $10$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$14, \frac{13}{25} + 10 \cdot \frac{3}{3} + \frac{1}{3}$

Step 1.2.2

Combine $10$ and $\frac{3}{3}$ .

$14, \frac{13}{25} + \frac{10 \cdot 3}{3} + \frac{1}{3}$

Step 1.2.3

Combine the numerators over the common denominator.

$14, \frac{13}{25} + \frac{10 \cdot 3 + 1}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $10$ by $3$ .

$14, \frac{13}{25} + \frac{30 + 1}{3}$

Step 1.2.4.2

Add $30$ and $1$ .

$14, \frac{13}{25} + \frac{31}{3}$

Step 2

To write $\frac{13}{25}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$14, \frac{13}{25} \cdot \frac{3}{3} + \frac{31}{3}$

Step 3

To write $\frac{31}{3}$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$14, \frac{13}{25} \cdot \frac{3}{3} + \frac{31}{3} \cdot \frac{25}{25}$

Step 4

Write each expression with a common denominator of $75$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{13}{25}$ by $\frac{3}{3}$ .

$14, \frac{13 \cdot 3}{25 \cdot 3} + \frac{31}{3} \cdot \frac{25}{25}$

Step 4.2

Multiply $25$ by $3$ .

$14, \frac{13 \cdot 3}{75} + \frac{31}{3} \cdot \frac{25}{25}$

Step 4.3

Multiply $\frac{31}{3}$ by $\frac{25}{25}$ .

$14, \frac{13 \cdot 3}{75} + \frac{31 \cdot 25}{3 \cdot 25}$

Step 4.4

Multiply $3$ by $25$ .

$14, \frac{13 \cdot 3}{75} + \frac{31 \cdot 25}{75}$

Step 5

Combine the numerators over the common denominator.

$14, \frac{13 \cdot 3 + 31 \cdot 25}{75}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $13$ by $3$ .

$14, \frac{39 + 31 \cdot 25}{75}$

Step 6.2

Multiply $31$ by $25$ .

$14, \frac{39 + 775}{75}$

Step 6.3

Add $39$ and $775$ .

$14, \frac{814}{75}$

Step 7

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

$\frac{14 + \frac{814}{75}}{2}$

Step 8

Cancel the common factor of $14 + \frac{814}{75}$ and $2$ .

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Step 8.1

Factor $2$ out of $14$ .

$\frac{2 \cdot 7 + \frac{814}{75}}{2}$

Step 8.2

Factor $2$ out of $\frac{814}{75}$ .

$\frac{2 \cdot 7 + 2 (\frac{407}{75})}{2}$

Step 8.3

Factor $2$ out of $2 \cdot 7 + 2 (\frac{407}{75})$ .

$\frac{2 \cdot (7 + \frac{407}{75})}{2}$

Step 8.4

Cancel the common factors.

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Step 8.4.1

Factor $2$ out of $2$ .

$\frac{2 \cdot (7 + \frac{407}{75})}{2 (1)}$

Step 8.4.2

Cancel the common factor.

$\frac{2 \cdot (7 + \frac{407}{75})}{2 \cdot 1}$

Step 8.4.3

Rewrite the expression.

$\frac{7 + \frac{407}{75}}{1}$

Step 8.4.4

Divide $7 + \frac{407}{75}$ by $1$ .

$7 + \frac{407}{75}$

Step 9

To write $7$ as a fraction with a common denominator, multiply by $\frac{75}{75}$ .

$7 \cdot \frac{75}{75} + \frac{407}{75}$

Step 10

Combine $7$ and $\frac{75}{75}$ .

$\frac{7 \cdot 75}{75} + \frac{407}{75}$

Step 11

Combine the numerators over the common denominator.

$\frac{7 \cdot 75 + 407}{75}$

Step 12

Simplify the numerator.

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Step 12.1

Multiply $7$ by $75$ .

$\frac{525 + 407}{75}$

Step 12.2

Add $525$ and $407$ .

$\frac{932}{75}$

Step 13

Divide.

$12.42\overline{6}$

Step 14

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.

$12.4$