Basic Math Examples

1 \frac{1}{4}

$1 \frac{1}{4}$ ,

2 \frac{1}{2}

$2 \frac{1}{2}$ ,

3

$3$ ,

2 \frac{1}{4}

$2 \frac{1}{4}$

Step 1

Convert

1 \frac{1}{4}

$1 \frac{1}{4}$ to an improper fraction.

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Step 1.1

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

1 + \frac{1}{4}, 2 \frac{1}{2}, 3, 2 \frac{1}{4}

$1 + \frac{1}{4}, 2 \frac{1}{2}, 3, 2 \frac{1}{4}$

Step 1.2

Add

1

$1$ and

\frac{1}{4}

$\frac{1}{4}$ .

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Step 1.2.1

Write

1

$1$ as a fraction with a common denominator.

\frac{4}{4} + \frac{1}{4}, 2 \frac{1}{2}, 3, 2 \frac{1}{4}

$\frac{4}{4} + \frac{1}{4}, 2 \frac{1}{2}, 3, 2 \frac{1}{4}$

Step 1.2.2

Combine the numerators over the common denominator.

\frac{4 + 1}{4}, 2 \frac{1}{2}, 3, 2 \frac{1}{4}

$\frac{4 + 1}{4}, 2 \frac{1}{2}, 3, 2 \frac{1}{4}$

Step 1.2.3

Add

4

$4$ and

1

$1$ .

\frac{5}{4}, 2 \frac{1}{2}, 3, 2 \frac{1}{4}

$\frac{5}{4}, 2 \frac{1}{2}, 3, 2 \frac{1}{4}$

\frac{5}{4}, 2 \frac{1}{2}, 3, 2 \frac{1}{4}

$\frac{5}{4}, 2 \frac{1}{2}, 3, 2 \frac{1}{4}$

\frac{5}{4}, 2 \frac{1}{2}, 3, 2 \frac{1}{4}

$\frac{5}{4}, 2 \frac{1}{2}, 3, 2 \frac{1}{4}$

Step 2

Convert

2 \frac{1}{2}

$2 \frac{1}{2}$ to an improper fraction.

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Step 2.1

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

\frac{5}{4}, 2 + \frac{1}{2}, 3, 2 \frac{1}{4}

$\frac{5}{4}, 2 + \frac{1}{2}, 3, 2 \frac{1}{4}$

Step 2.2

Add

2

$2$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 2.2.1

To write

2

$2$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{5}{4}, 2 \cdot \frac{2}{2} + \frac{1}{2}, 3, 2 \frac{1}{4}

$\frac{5}{4}, 2 \cdot \frac{2}{2} + \frac{1}{2}, 3, 2 \frac{1}{4}$

Step 2.2.2

Combine

2

$2$ and

\frac{2}{2}

$\frac{2}{2}$ .

\frac{5}{4}, \frac{2 \cdot 2}{2} + \frac{1}{2}, 3, 2 \frac{1}{4}

$\frac{5}{4}, \frac{2 \cdot 2}{2} + \frac{1}{2}, 3, 2 \frac{1}{4}$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{5}{4}, \frac{2 \cdot 2 + 1}{2}, 3, 2 \frac{1}{4}

$\frac{5}{4}, \frac{2 \cdot 2 + 1}{2}, 3, 2 \frac{1}{4}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

2

$2$ by

2

$2$ .

\frac{5}{4}, \frac{4 + 1}{2}, 3, 2 \frac{1}{4}

$\frac{5}{4}, \frac{4 + 1}{2}, 3, 2 \frac{1}{4}$

Step 2.2.4.2

Add

4

$4$ and

1

$1$ .

\frac{5}{4}, \frac{5}{2}, 3, 2 \frac{1}{4}

$\frac{5}{4}, \frac{5}{2}, 3, 2 \frac{1}{4}$

\frac{5}{4}, \frac{5}{2}, 3, 2 \frac{1}{4}

$\frac{5}{4}, \frac{5}{2}, 3, 2 \frac{1}{4}$

\frac{5}{4}, \frac{5}{2}, 3, 2 \frac{1}{4}

$\frac{5}{4}, \frac{5}{2}, 3, 2 \frac{1}{4}$

\frac{5}{4}, \frac{5}{2}, 3, 2 \frac{1}{4}

$\frac{5}{4}, \frac{5}{2}, 3, 2 \frac{1}{4}$

Step 3

Convert

2 \frac{1}{4}

$2 \frac{1}{4}$ to an improper fraction.

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Step 3.1

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

\frac{5}{4}, \frac{5}{2}, 3, 2 + \frac{1}{4}

$\frac{5}{4}, \frac{5}{2}, 3, 2 + \frac{1}{4}$

Step 3.2

Add

2

$2$ and

\frac{1}{4}

$\frac{1}{4}$ .

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Step 3.2.1

To write

2

$2$ as a fraction with a common denominator, multiply by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{5}{4}, \frac{5}{2}, 3, 2 \cdot \frac{4}{4} + \frac{1}{4}

$\frac{5}{4}, \frac{5}{2}, 3, 2 \cdot \frac{4}{4} + \frac{1}{4}$

Step 3.2.2

Combine

2

$2$ and

\frac{4}{4}

$\frac{4}{4}$ .

\frac{5}{4}, \frac{5}{2}, 3, \frac{2 \cdot 4}{4} + \frac{1}{4}

$\frac{5}{4}, \frac{5}{2}, 3, \frac{2 \cdot 4}{4} + \frac{1}{4}$

Step 3.2.3

Combine the numerators over the common denominator.

\frac{5}{4}, \frac{5}{2}, 3, \frac{2 \cdot 4 + 1}{4}

$\frac{5}{4}, \frac{5}{2}, 3, \frac{2 \cdot 4 + 1}{4}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply

2

$2$ by

4

$4$ .

\frac{5}{4}, \frac{5}{2}, 3, \frac{8 + 1}{4}

$\frac{5}{4}, \frac{5}{2}, 3, \frac{8 + 1}{4}$

Step 3.2.4.2

Add

8

$8$ and

1

$1$ .

\frac{5}{4}, \frac{5}{2}, 3, \frac{9}{4}

$\frac{5}{4}, \frac{5}{2}, 3, \frac{9}{4}$

\frac{5}{4}, \frac{5}{2}, 3, \frac{9}{4}

$\frac{5}{4}, \frac{5}{2}, 3, \frac{9}{4}$

\frac{5}{4}, \frac{5}{2}, 3, \frac{9}{4}

$\frac{5}{4}, \frac{5}{2}, 3, \frac{9}{4}$

\frac{5}{4}, \frac{5}{2}, 3, \frac{9}{4}

$\frac{5}{4}, \frac{5}{2}, 3, \frac{9}{4}$

Step 4

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

\frac{\frac{5}{4} + \frac{5}{2} + 3 + \frac{9}{4}}{4}

$\frac{\frac{5}{4} + \frac{5}{2} + 3 + \frac{9}{4}}{4}$

Step 5

Simplify the numerator.

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Step 5.1

To write

\frac{5}{2}

$\frac{5}{2}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{\frac{5}{4} + \frac{5}{2} \cdot \frac{2}{2} + 3 + \frac{9}{4}}{4}

$\frac{\frac{5}{4} + \frac{5}{2} \cdot \frac{2}{2} + 3 + \frac{9}{4}}{4}$

Step 5.2

Write each expression with a common denominator of

4

$4$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 5.2.1

Multiply

\frac{5}{2}

$\frac{5}{2}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{\frac{5}{4} + \frac{5 \cdot 2}{2 \cdot 2} + 3 + \frac{9}{4}}{4}

$\frac{\frac{5}{4} + \frac{5 \cdot 2}{2 \cdot 2} + 3 + \frac{9}{4}}{4}$

Step 5.2.2

Multiply

2

$2$ by

2

$2$ .

\frac{\frac{5}{4} + \frac{5 \cdot 2}{4} + 3 + \frac{9}{4}}{4}

$\frac{\frac{5}{4} + \frac{5 \cdot 2}{4} + 3 + \frac{9}{4}}{4}$

Step 5.3

Combine the numerators over the common denominator.

$\frac{\frac{5 + 5 \cdot 2}{4} + 3 + \frac{9}{4}}{4}$

Step 5.4

Simplify the numerator.

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Step 5.4.1

Multiply

$5$ by

$2$ .

$\frac{\frac{5 + 10}{4} + 3 + \frac{9}{4}}{4}$

Step 5.4.2

Add

$5$ and

$10$ .

$\frac{\frac{15}{4} + 3 + \frac{9}{4}}{4}$

Step 5.5

To write

$3$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$\frac{\frac{15}{4} + 3 \cdot \frac{4}{4} + \frac{9}{4}}{4}$

Step 5.6

Combine

$3$ and

$\frac{4}{4}$ .

$\frac{\frac{15}{4} + \frac{3 \cdot 4}{4} + \frac{9}{4}}{4}$

Step 5.7

Combine the numerators over the common denominator.

$\frac{\frac{15 + 3 \cdot 4}{4} + \frac{9}{4}}{4}$

Step 5.8

Simplify the numerator.

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Step 5.8.1

Multiply

$3$ by

$4$ .

$\frac{\frac{15 + 12}{4} + \frac{9}{4}}{4}$

Step 5.8.2

Add

$15$ and

$12$ .

$\frac{\frac{27}{4} + \frac{9}{4}}{4}$

Step 5.9

Combine the numerators over the common denominator.

$\frac{\frac{27 + 9}{4}}{4}$

Step 5.10

Add

$27$ and

$9$ .

$\frac{\frac{36}{4}}{4}$

Step 5.11

Divide

$36$ by

$4$ .

$\frac{9}{4}$

Step 6

Divide.

$2.25$

Step 7

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.

$2.3$