Basic Math Examples

$7 \frac{5}{6}$ , $6 \frac{4}{9}$ , $8 \frac{2}{3}$

Step 1

Convert $7 \frac{5}{6}$ to an improper fraction.

Tap for more steps...

Step 1.1

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

$7 + \frac{5}{6}, 6 \frac{4}{9}, 8 \frac{2}{3}$

Step 1.2

Add $7$ and $\frac{5}{6}$ .

Tap for more steps...

Step 1.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$7 \cdot \frac{6}{6} + \frac{5}{6}, 6 \frac{4}{9}, 8 \frac{2}{3}$

Step 1.2.2

Combine $7$ and $\frac{6}{6}$ .

$\frac{7 \cdot 6}{6} + \frac{5}{6}, 6 \frac{4}{9}, 8 \frac{2}{3}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{7 \cdot 6 + 5}{6}, 6 \frac{4}{9}, 8 \frac{2}{3}$

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply $7$ by $6$ .

$\frac{42 + 5}{6}, 6 \frac{4}{9}, 8 \frac{2}{3}$

Step 1.2.4.2

Add $42$ and $5$ .

$\frac{47}{6}, 6 \frac{4}{9}, 8 \frac{2}{3}$

Step 2

Convert $6 \frac{4}{9}$ to an improper fraction.

Tap for more steps...

Step 2.1

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

$\frac{47}{6}, 6 + \frac{4}{9}, 8 \frac{2}{3}$

Step 2.2

Add $6$ and $\frac{4}{9}$ .

Tap for more steps...

Step 2.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{47}{6}, 6 \cdot \frac{9}{9} + \frac{4}{9}, 8 \frac{2}{3}$

Step 2.2.2

Combine $6$ and $\frac{9}{9}$ .

$\frac{47}{6}, \frac{6 \cdot 9}{9} + \frac{4}{9}, 8 \frac{2}{3}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{47}{6}, \frac{6 \cdot 9 + 4}{9}, 8 \frac{2}{3}$

Step 2.2.4

Simplify the numerator.

Tap for more steps...

Step 2.2.4.1

Multiply $6$ by $9$ .

$\frac{47}{6}, \frac{54 + 4}{9}, 8 \frac{2}{3}$

Step 2.2.4.2

Add $54$ and $4$ .

$\frac{47}{6}, \frac{58}{9}, 8 \frac{2}{3}$

Step 3

Convert $8 \frac{2}{3}$ to an improper fraction.

Tap for more steps...

Step 3.1

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

$\frac{47}{6}, \frac{58}{9}, 8 + \frac{2}{3}$

Step 3.2

Add $8$ and $\frac{2}{3}$ .

Tap for more steps...

Step 3.2.1

To write $8$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{47}{6}, \frac{58}{9}, 8 \cdot \frac{3}{3} + \frac{2}{3}$

Step 3.2.2

Combine $8$ and $\frac{3}{3}$ .

$\frac{47}{6}, \frac{58}{9}, \frac{8 \cdot 3}{3} + \frac{2}{3}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{47}{6}, \frac{58}{9}, \frac{8 \cdot 3 + 2}{3}$

Step 3.2.4

Simplify the numerator.

Tap for more steps...

Step 3.2.4.1

Multiply $8$ by $3$ .

$\frac{47}{6}, \frac{58}{9}, \frac{24 + 2}{3}$

Step 3.2.4.2

Add $24$ and $2$ .

$\frac{47}{6}, \frac{58}{9}, \frac{26}{3}$

Step 4

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

$\frac{\frac{47}{6} + \frac{58}{9} + \frac{26}{3}}{3}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

To write $\frac{47}{6}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{\frac{47}{6} \cdot \frac{3}{3} + \frac{58}{9} + \frac{26}{3}}{3}$

Step 5.2

To write $\frac{58}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{47}{6} \cdot \frac{3}{3} + \frac{58}{9} \cdot \frac{2}{2} + \frac{26}{3}}{3}$

Step 5.3

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 5.3.1

Multiply $\frac{47}{6}$ by $\frac{3}{3}$ .

$\frac{\frac{47 \cdot 3}{6 \cdot 3} + \frac{58}{9} \cdot \frac{2}{2} + \frac{26}{3}}{3}$

Step 5.3.2

Multiply $6$ by $3$ .

$\frac{\frac{47 \cdot 3}{18} + \frac{58}{9} \cdot \frac{2}{2} + \frac{26}{3}}{3}$

Step 5.3.3

Multiply $\frac{58}{9}$ by $\frac{2}{2}$ .

$\frac{\frac{47 \cdot 3}{18} + \frac{58 \cdot 2}{9 \cdot 2} + \frac{26}{3}}{3}$

Step 5.3.4

Multiply $9$ by $2$ .

$\frac{\frac{47 \cdot 3}{18} + \frac{58 \cdot 2}{18} + \frac{26}{3}}{3}$

Step 5.4

Combine the numerators over the common denominator.

$\frac{\frac{47 \cdot 3 + 58 \cdot 2}{18} + \frac{26}{3}}{3}$

Step 5.5

Simplify the numerator.

Tap for more steps...

Step 5.5.1

Multiply $47$ by $3$ .

$\frac{\frac{141 + 58 \cdot 2}{18} + \frac{26}{3}}{3}$

Step 5.5.2

Multiply $58$ by $2$ .

$\frac{\frac{141 + 116}{18} + \frac{26}{3}}{3}$

Step 5.5.3

Add $141$ and $116$ .

$\frac{\frac{257}{18} + \frac{26}{3}}{3}$

Step 5.6

To write $\frac{26}{3}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{\frac{257}{18} + \frac{26}{3} \cdot \frac{6}{6}}{3}$

Step 5.7

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 5.7.1

Multiply $\frac{26}{3}$ by $\frac{6}{6}$ .

$\frac{\frac{257}{18} + \frac{26 \cdot 6}{3 \cdot 6}}{3}$

Step 5.7.2

Multiply $3$ by $6$ .

$\frac{\frac{257}{18} + \frac{26 \cdot 6}{18}}{3}$

Step 5.8

Combine the numerators over the common denominator.

$\frac{\frac{257 + 26 \cdot 6}{18}}{3}$

Step 5.9

Simplify the numerator.

Tap for more steps...

Step 5.9.1

Multiply $26$ by $6$ .

$\frac{\frac{257 + 156}{18}}{3}$

Step 5.9.2

Add $257$ and $156$ .

$\frac{\frac{413}{18}}{3}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$\frac{413}{18} \cdot \frac{1}{3}$

Step 7

Multiply $\frac{413}{18} \cdot \frac{1}{3}$ .

Tap for more steps...

Step 7.1

Multiply $\frac{413}{18}$ by $\frac{1}{3}$ .

$\frac{413}{18 \cdot 3}$

Step 7.2

Multiply $18$ by $3$ .

$\frac{413}{54}$

Step 8

Divide.

$7.6\overline{481}$

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.

$7.6$