Basic Math Examples

12 \div 5 \frac{9}{11}

$12 \div 5 \frac{9}{11}$

Step 1

Convert

5 \frac{9}{11}

$5 \frac{9}{11}$ to an improper fraction.

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Step 1.1

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

12 \div (5 + \frac{9}{11})

$12 \div (5 + \frac{9}{11})$

Step 1.2

Add

5

$5$ and

\frac{9}{11}

$\frac{9}{11}$ .

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Step 1.2.1

To write

5

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

\frac{11}{11}

$\frac{11}{11}$ .

12 \div (5 \cdot \frac{11}{11} + \frac{9}{11})

$12 \div (5 \cdot \frac{11}{11} + \frac{9}{11})$

Step 1.2.2

Combine

5

$5$ and

\frac{11}{11}

$\frac{11}{11}$ .

12 \div (\frac{5 \cdot 11}{11} + \frac{9}{11})

$12 \div (\frac{5 \cdot 11}{11} + \frac{9}{11})$

Step 1.2.3

Combine the numerators over the common denominator.

12 \div \frac{5 \cdot 11 + 9}{11}

$12 \div \frac{5 \cdot 11 + 9}{11}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

5

$5$ by

11

$11$ .

12 \div \frac{55 + 9}{11}

$12 \div \frac{55 + 9}{11}$

Step 1.2.4.2

Add

55

$55$ and

9

$9$ .

12 \div \frac{64}{11}

$12 \div \frac{64}{11}$

12 \div \frac{64}{11}

$12 \div \frac{64}{11}$

12 \div \frac{64}{11}

$12 \div \frac{64}{11}$

12 \div \frac{64}{11}

$12 \div \frac{64}{11}$

Step 2

To divide by a fraction, multiply by its reciprocal.

12 (\frac{11}{64})

$12 (\frac{11}{64})$

Step 3

Cancel the common factor of

4

$4$ .

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Step 3.1

Factor

4

$4$ out of

12

$12$ .

4 (3) \frac{11}{64}

$4 (3) \frac{11}{64}$

Step 3.2

Factor

4

$4$ out of

64

$64$ .

4 \cdot 3 \frac{11}{4 \cdot 16}

$4 \cdot 3 \frac{11}{4 \cdot 16}$

Step 3.3

Cancel the common factor.

$4 \cdot 3 \frac{11}{4 \cdot 16}$

Step 3.4

Rewrite the expression.

$3 (\frac{11}{16})$

Step 4

Combine

$3$ and

$\frac{11}{16}$ .

$\frac{3 \cdot 11}{16}$

Step 5

Multiply

$3$ by

$11$ .

$\frac{33}{16}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{33}{16}$

Decimal Form:

$2.0625$

Mixed Number Form:

$2 \frac{1}{16}$