Basic Math Examples

$3.569$ , $3 \frac{7}{11}$ , $3.59$ , $\frac{71}{20}$

Step 1

Convert $3 \frac{7}{11}$ to an improper fraction.

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Step 1.1

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

$3.569, 3 + \frac{7}{11}, 3.59, \frac{71}{20}$

Step 1.2

Add $3$ and $\frac{7}{11}$ .

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Step 1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$3.569, 3 \cdot \frac{11}{11} + \frac{7}{11}, 3.59, \frac{71}{20}$

Step 1.2.2

Combine $3$ and $\frac{11}{11}$ .

$3.569, \frac{3 \cdot 11}{11} + \frac{7}{11}, 3.59, \frac{71}{20}$

Step 1.2.3

Combine the numerators over the common denominator.

$3.569, \frac{3 \cdot 11 + 7}{11}, 3.59, \frac{71}{20}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $11$ .

$3.569, \frac{33 + 7}{11}, 3.59, \frac{71}{20}$

Step 1.2.4.2

Add $33$ and $7$ .

$3.569, \frac{40}{11}, 3.59, \frac{71}{20}$

Step 2

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

$\frac{3.569 + \frac{40}{11} + 3.59 + \frac{71}{20}}{4}$

Step 3

Simplify the numerator.

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Step 3.1

To write $3.569$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$\frac{3.569 \cdot \frac{11}{11} + \frac{40}{11} + 3.59 + \frac{71}{20}}{4}$

Step 3.2

Combine $3.569$ and $\frac{11}{11}$ .

$\frac{\frac{3.569 \cdot 11}{11} + \frac{40}{11} + 3.59 + \frac{71}{20}}{4}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{\frac{3.569 \cdot 11 + 40}{11} + 3.59 + \frac{71}{20}}{4}$

Step 3.4

To write $3.59$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$\frac{\frac{3.569 \cdot 11 + 40}{11} + 3.59 \cdot \frac{11}{11} + \frac{71}{20}}{4}$

Step 3.5

Combine $3.59$ and $\frac{11}{11}$ .

$\frac{\frac{3.569 \cdot 11 + 40}{11} + \frac{3.59 \cdot 11}{11} + \frac{71}{20}}{4}$

Step 3.6

Combine the numerators over the common denominator.

$\frac{\frac{3.569 \cdot 11 + 40 + 3.59 \cdot 11}{11} + \frac{71}{20}}{4}$

Step 3.7

To write $\frac{3.569 \cdot 11 + 40 + 3.59 \cdot 11}{11}$ as a fraction with a common denominator, multiply by $\frac{20}{20}$ .

$\frac{\frac{3.569 \cdot 11 + 40 + 3.59 \cdot 11}{11} \cdot \frac{20}{20} + \frac{71}{20}}{4}$

Step 3.8

To write $\frac{71}{20}$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$\frac{\frac{3.569 \cdot 11 + 40 + 3.59 \cdot 11}{11} \cdot \frac{20}{20} + \frac{71}{20} \cdot \frac{11}{11}}{4}$

Step 3.9

Write each expression with a common denominator of $220$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.9.1

Multiply $\frac{3.569 \cdot 11 + 40 + 3.59 \cdot 11}{11}$ by $\frac{20}{20}$ .

$\frac{\frac{(3.569 \cdot 11 + 40 + 3.59 \cdot 11) \cdot 20}{11 \cdot 20} + \frac{71}{20} \cdot \frac{11}{11}}{4}$

Step 3.9.2

Multiply $11$ by $20$ .

$\frac{\frac{(3.569 \cdot 11 + 40 + 3.59 \cdot 11) \cdot 20}{220} + \frac{71}{20} \cdot \frac{11}{11}}{4}$

Step 3.9.3

Multiply $\frac{71}{20}$ by $\frac{11}{11}$ .

$\frac{\frac{(3.569 \cdot 11 + 40 + 3.59 \cdot 11) \cdot 20}{220} + \frac{71 \cdot 11}{20 \cdot 11}}{4}$

Step 3.9.4

Multiply $20$ by $11$ .

$\frac{\frac{(3.569 \cdot 11 + 40 + 3.59 \cdot 11) \cdot 20}{220} + \frac{71 \cdot 11}{220}}{4}$

Step 3.10

Combine the numerators over the common denominator.

$\frac{\frac{(3.569 \cdot 11 + 40 + 3.59 \cdot 11) \cdot 20 + 71 \cdot 11}{220}}{4}$

Step 3.11

Rewrite $\frac{(3.569 \cdot 11 + 40 + 3.59 \cdot 11) \cdot 20 + 71 \cdot 11}{220}$ in a factored form.

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Step 3.11.1

Simplify each term.

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Step 3.11.1.1

Multiply $3.569$ by $11$ .

$\frac{\frac{(39.259 + 40 + 3.59 \cdot 11) \cdot 20 + 71 \cdot 11}{220}}{4}$

Step 3.11.1.2

Multiply $3.59$ by $11$ .

$\frac{\frac{(39.259 + 40 + 39.49) \cdot 20 + 71 \cdot 11}{220}}{4}$

Step 3.11.2

Add $39.259$ and $40$ .

$\frac{\frac{(79.259 + 39.49) \cdot 20 + 71 \cdot 11}{220}}{4}$

Step 3.11.3

Add $79.259$ and $39.49$ .

$\frac{\frac{118.749 \cdot 20 + 71 \cdot 11}{220}}{4}$

Step 3.11.4

Multiply $118.749$ by $20$ .

$\frac{\frac{2374.98 + 71 \cdot 11}{220}}{4}$

Step 3.11.5

Multiply $71$ by $11$ .

$\frac{\frac{2374.98 + 781}{220}}{4}$

Step 3.11.6

Add $2374.98$ and $781$ .

$\frac{\frac{3155.98}{220}}{4}$

Step 3.11.7

Divide $3155.98$ by $220$ .

$\frac{14.345\overline{36}}{4}$

Step 4

Divide $14.345\overline{36}$ by $4$ .

$3.58634\overline{09}$

Step 5

Divide.

$3.58634\overline{09}$

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.

$3.6$