Basic Math Examples

12 \div 2 \frac{2}{3}

$12 \div 2 \frac{2}{3}$

Step 1

Convert

2 \frac{2}{3}

$2 \frac{2}{3}$ 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 (2 + \frac{2}{3})

$12 \div (2 + \frac{2}{3})$

Step 1.2

Add

2

$2$ and

\frac{2}{3}

$\frac{2}{3}$ .

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Step 1.2.1

To write

2

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

\frac{3}{3}

$\frac{3}{3}$ .

12 \div (2 \cdot \frac{3}{3} + \frac{2}{3})

$12 \div (2 \cdot \frac{3}{3} + \frac{2}{3})$

Step 1.2.2

Combine

2

$2$ and

\frac{3}{3}

$\frac{3}{3}$ .

12 \div (\frac{2 \cdot 3}{3} + \frac{2}{3})

$12 \div (\frac{2 \cdot 3}{3} + \frac{2}{3})$

Step 1.2.3

Combine the numerators over the common denominator.

12 \div \frac{2 \cdot 3 + 2}{3}

$12 \div \frac{2 \cdot 3 + 2}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

3

$3$ .

12 \div \frac{6 + 2}{3}

$12 \div \frac{6 + 2}{3}$

Step 1.2.4.2

Add

6

$6$ and

2

$2$ .

12 \div \frac{8}{3}

$12 \div \frac{8}{3}$

12 \div \frac{8}{3}

$12 \div \frac{8}{3}$

12 \div \frac{8}{3}

$12 \div \frac{8}{3}$

12 \div \frac{8}{3}

$12 \div \frac{8}{3}$

Step 2

To divide by a fraction, multiply by its reciprocal.

12 (\frac{3}{8})

$12 (\frac{3}{8})$

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{3}{8}

$4 (3) \frac{3}{8}$

Step 3.2

Factor

4

$4$ out of

8

$8$ .

4 \cdot 3 \frac{3}{4 \cdot 2}

$4 \cdot 3 \frac{3}{4 \cdot 2}$

Step 3.3

Cancel the common factor.

$4 \cdot 3 \frac{3}{4 \cdot 2}$

Step 3.4

Rewrite the expression.

$3 (\frac{3}{2})$

Step 4

Combine

$3$ and

$\frac{3}{2}$ .

$\frac{3 \cdot 3}{2}$

Step 5

Multiply

$3$ by

$3$ .

$\frac{9}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{2}$

Decimal Form:

$4.5$

Mixed Number Form:

$4 \frac{1}{2}$