Basic Math Examples

5 \frac{1}{2} \div 2 \frac{1}{2}

$5 \frac{1}{2} \div 2 \frac{1}{2}$

Step 1

Convert

5 \frac{1}{2}

$5 \frac{1}{2}$ to an improper fraction.

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Step 1.1

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

(5 + \frac{1}{2}) \div 2 \frac{1}{2}

$(5 + \frac{1}{2}) \div 2 \frac{1}{2}$

Step 1.2

Add

5

$5$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 1.2.1

To write

5

$5$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

(5 \cdot \frac{2}{2} + \frac{1}{2}) \div 2 \frac{1}{2}

$(5 \cdot \frac{2}{2} + \frac{1}{2}) \div 2 \frac{1}{2}$

Step 1.2.2

Combine

5

$5$ and

\frac{2}{2}

$\frac{2}{2}$ .

(\frac{5 \cdot 2}{2} + \frac{1}{2}) \div 2 \frac{1}{2}

$(\frac{5 \cdot 2}{2} + \frac{1}{2}) \div 2 \frac{1}{2}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{5 \cdot 2 + 1}{2} \div 2 \frac{1}{2}

$\frac{5 \cdot 2 + 1}{2} \div 2 \frac{1}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

5

$5$ by

2

$2$ .

\frac{10 + 1}{2} \div 2 \frac{1}{2}

$\frac{10 + 1}{2} \div 2 \frac{1}{2}$

Step 1.2.4.2

Add

10

$10$ and

1

$1$ .

\frac{11}{2} \div 2 \frac{1}{2}

$\frac{11}{2} \div 2 \frac{1}{2}$

\frac{11}{2} \div 2 \frac{1}{2}

$\frac{11}{2} \div 2 \frac{1}{2}$

\frac{11}{2} \div 2 \frac{1}{2}

$\frac{11}{2} \div 2 \frac{1}{2}$

\frac{11}{2} \div 2 \frac{1}{2}

$\frac{11}{2} \div 2 \frac{1}{2}$

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{11}{2} \div (2 + \frac{1}{2})

$\frac{11}{2} \div (2 + \frac{1}{2})$

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{11}{2} \div (2 \cdot \frac{2}{2} + \frac{1}{2})

$\frac{11}{2} \div (2 \cdot \frac{2}{2} + \frac{1}{2})$

Step 2.2.2

Combine

2

$2$ and

\frac{2}{2}

$\frac{2}{2}$ .

\frac{11}{2} \div (\frac{2 \cdot 2}{2} + \frac{1}{2})

$\frac{11}{2} \div (\frac{2 \cdot 2}{2} + \frac{1}{2})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{11}{2} \div \frac{2 \cdot 2 + 1}{2}

$\frac{11}{2} \div \frac{2 \cdot 2 + 1}{2}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

2

$2$ by

2

$2$ .

\frac{11}{2} \div \frac{4 + 1}{2}

$\frac{11}{2} \div \frac{4 + 1}{2}$

Step 2.2.4.2

Add

4

$4$ and

1

$1$ .

\frac{11}{2} \div \frac{5}{2}

$\frac{11}{2} \div \frac{5}{2}$

\frac{11}{2} \div \frac{5}{2}

$\frac{11}{2} \div \frac{5}{2}$

\frac{11}{2} \div \frac{5}{2}

$\frac{11}{2} \div \frac{5}{2}$

\frac{11}{2} \div \frac{5}{2}

$\frac{11}{2} \div \frac{5}{2}$

Step 3

To divide by a fraction, multiply by its reciprocal.

\frac{11}{2} \cdot \frac{2}{5}

$\frac{11}{2} \cdot \frac{2}{5}$

Step 4

Cancel the common factor of

2

$2$ .

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Step 4.1

Cancel the common factor.

$\frac{11}{2} \cdot \frac{2}{5}$

Step 4.2

Rewrite the expression.

$11 (\frac{1}{5})$

Step 5

Combine

$11$ and

$\frac{1}{5}$ .

$\frac{11}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{5}$

Decimal Form:

$2.2$

Mixed Number Form:

$2 \frac{1}{5}$