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.

Tap for more steps...

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

$\frac{7}{11}$ .

Tap for more steps...

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.

Tap for more steps...

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.

Tap for more steps...

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

$1$ .

Tap for more steps...

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.

Tap for more steps...

Step 3.11.1

Simplify each term.

Tap for more steps...

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.

$3.6$