Basic Math Examples

$\frac{1}{4}$ , $\frac{3}{10}$ , $\frac{7}{8}$ , $\frac{5}{6}$ , $\frac{1}{2}$ , $\frac{1}{5}$

Step 1

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

$\frac{\frac{1}{4} + \frac{3}{10} + \frac{7}{8} + \frac{5}{6} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2

Simplify the numerator.

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Step 2.1

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{\frac{1}{4} \cdot \frac{5}{5} + \frac{3}{10} + \frac{7}{8} + \frac{5}{6} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.2

To write $\frac{3}{10}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{1}{4} \cdot \frac{5}{5} + \frac{3}{10} \cdot \frac{2}{2} + \frac{7}{8} + \frac{5}{6} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.3

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{1}{4}$ by $\frac{5}{5}$ .

$\frac{\frac{5}{4 \cdot 5} + \frac{3}{10} \cdot \frac{2}{2} + \frac{7}{8} + \frac{5}{6} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.3.2

Multiply $4$ by $5$ .

$\frac{\frac{5}{20} + \frac{3}{10} \cdot \frac{2}{2} + \frac{7}{8} + \frac{5}{6} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.3.3

Multiply $\frac{3}{10}$ by $\frac{2}{2}$ .

$\frac{\frac{5}{20} + \frac{3 \cdot 2}{10 \cdot 2} + \frac{7}{8} + \frac{5}{6} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.3.4

Multiply $10$ by $2$ .

$\frac{\frac{5}{20} + \frac{3 \cdot 2}{20} + \frac{7}{8} + \frac{5}{6} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{\frac{5 + 3 \cdot 2}{20} + \frac{7}{8} + \frac{5}{6} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $3$ by $2$ .

$\frac{\frac{5 + 6}{20} + \frac{7}{8} + \frac{5}{6} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.5.2

Add $5$ and $6$ .

$\frac{\frac{11}{20} + \frac{7}{8} + \frac{5}{6} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.6

To write $\frac{11}{20}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{11}{20} \cdot \frac{2}{2} + \frac{7}{8} + \frac{5}{6} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.7

To write $\frac{7}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{\frac{11}{20} \cdot \frac{2}{2} + \frac{7}{8} \cdot \frac{5}{5} + \frac{5}{6} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.8

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.8.1

Multiply $\frac{11}{20}$ by $\frac{2}{2}$ .

$\frac{\frac{11 \cdot 2}{20 \cdot 2} + \frac{7}{8} \cdot \frac{5}{5} + \frac{5}{6} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.8.2

Multiply $20$ by $2$ .

$\frac{\frac{11 \cdot 2}{40} + \frac{7}{8} \cdot \frac{5}{5} + \frac{5}{6} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.8.3

Multiply $\frac{7}{8}$ by $\frac{5}{5}$ .

$\frac{\frac{11 \cdot 2}{40} + \frac{7 \cdot 5}{8 \cdot 5} + \frac{5}{6} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.8.4

Multiply $8$ by $5$ .

$\frac{\frac{11 \cdot 2}{40} + \frac{7 \cdot 5}{40} + \frac{5}{6} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.9

Combine the numerators over the common denominator.

$\frac{\frac{11 \cdot 2 + 7 \cdot 5}{40} + \frac{5}{6} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.10

Simplify the numerator.

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Step 2.10.1

Multiply $11$ by $2$ .

$\frac{\frac{22 + 7 \cdot 5}{40} + \frac{5}{6} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.10.2

Multiply $7$ by $5$ .

$\frac{\frac{22 + 35}{40} + \frac{5}{6} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.10.3

Add $22$ and $35$ .

$\frac{\frac{57}{40} + \frac{5}{6} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.11

To write $\frac{57}{40}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{\frac{57}{40} \cdot \frac{3}{3} + \frac{5}{6} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.12

To write $\frac{5}{6}$ as a fraction with a common denominator, multiply by $\frac{20}{20}$ .

$\frac{\frac{57}{40} \cdot \frac{3}{3} + \frac{5}{6} \cdot \frac{20}{20} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.13

Write each expression with a common denominator of $120$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.13.1

Multiply $\frac{57}{40}$ by $\frac{3}{3}$ .

$\frac{\frac{57 \cdot 3}{40 \cdot 3} + \frac{5}{6} \cdot \frac{20}{20} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.13.2

Multiply $40$ by $3$ .

$\frac{\frac{57 \cdot 3}{120} + \frac{5}{6} \cdot \frac{20}{20} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.13.3

Multiply $\frac{5}{6}$ by $\frac{20}{20}$ .

$\frac{\frac{57 \cdot 3}{120} + \frac{5 \cdot 20}{6 \cdot 20} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.13.4

Multiply $6$ by $20$ .

$\frac{\frac{57 \cdot 3}{120} + \frac{5 \cdot 20}{120} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.14

Combine the numerators over the common denominator.

$\frac{\frac{57 \cdot 3 + 5 \cdot 20}{120} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.15

Simplify the numerator.

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Step 2.15.1

Multiply $57$ by $3$ .

$\frac{\frac{171 + 5 \cdot 20}{120} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.15.2

Multiply $5$ by $20$ .

$\frac{\frac{171 + 100}{120} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.15.3

Add $171$ and $100$ .

$\frac{\frac{271}{120} + \frac{1}{2} + \frac{1}{5}}{6}$

Step 2.16

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{60}{60}$ .

$\frac{\frac{271}{120} + \frac{1}{2} \cdot \frac{60}{60} + \frac{1}{5}}{6}$

Step 2.17

Write each expression with a common denominator of $120$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.17.1

Multiply $\frac{1}{2}$ by $\frac{60}{60}$ .

$\frac{\frac{271}{120} + \frac{60}{2 \cdot 60} + \frac{1}{5}}{6}$

Step 2.17.2

Multiply $2$ by $60$ .

$\frac{\frac{271}{120} + \frac{60}{120} + \frac{1}{5}}{6}$

Step 2.18

Combine the numerators over the common denominator.

$\frac{\frac{271 + 60}{120} + \frac{1}{5}}{6}$

Step 2.19

Add $271$ and $60$ .

$\frac{\frac{331}{120} + \frac{1}{5}}{6}$

Step 2.20

To write $\frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{24}{24}$ .

$\frac{\frac{331}{120} + \frac{1}{5} \cdot \frac{24}{24}}{6}$

Step 2.21

Write each expression with a common denominator of $120$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.21.1

Multiply $\frac{1}{5}$ by $\frac{24}{24}$ .

$\frac{\frac{331}{120} + \frac{24}{5 \cdot 24}}{6}$

Step 2.21.2

Multiply $5$ by $24$ .

$\frac{\frac{331}{120} + \frac{24}{120}}{6}$

Step 2.22

Combine the numerators over the common denominator.

$\frac{\frac{331 + 24}{120}}{6}$

Step 2.23

Add $331$ and $24$ .

$\frac{\frac{355}{120}}{6}$

Step 2.24

Cancel the common factor of $355$ and $120$ .

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Step 2.24.1

Factor $5$ out of $355$ .

$\frac{\frac{5 (71)}{120}}{6}$

Step 2.24.2

Cancel the common factors.

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Step 2.24.2.1

Factor $5$ out of $120$ .

$\frac{\frac{5 \cdot 71}{5 \cdot 24}}{6}$

Step 2.24.2.2

Cancel the common factor.

$\frac{\frac{5 \cdot 71}{5 \cdot 24}}{6}$

Step 2.24.2.3

Rewrite the expression.

$\frac{\frac{71}{24}}{6}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{71}{24} \cdot \frac{1}{6}$

Step 4

Multiply $\frac{71}{24} \cdot \frac{1}{6}$ .

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Step 4.1

Multiply $\frac{71}{24}$ by $\frac{1}{6}$ .

$\frac{71}{24 \cdot 6}$

Step 4.2

Multiply $24$ by $6$ .

$\frac{71}{144}$

Step 5

Divide.

$0.4930\overline{5}$

Step 6

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.

$0.5$