Basic Math Examples

15 \div 6 \frac{2}{3}

$15 \div 6 \frac{2}{3}$

Step 1

Convert

6 \frac{2}{3}

$6 \frac{2}{3}$ to an improper fraction.

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Step 1.1

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

15 \div (6 + \frac{2}{3})

$15 \div (6 + \frac{2}{3})$

Step 1.2

Add

6

$6$ and

\frac{2}{3}

$\frac{2}{3}$ .

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Step 1.2.1

To write

6

$6$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

15 \div (6 \cdot \frac{3}{3} + \frac{2}{3})

$15 \div (6 \cdot \frac{3}{3} + \frac{2}{3})$

Step 1.2.2

Combine

6

$6$ and

\frac{3}{3}

$\frac{3}{3}$ .

15 \div (\frac{6 \cdot 3}{3} + \frac{2}{3})

$15 \div (\frac{6 \cdot 3}{3} + \frac{2}{3})$

Step 1.2.3

Combine the numerators over the common denominator.

15 \div \frac{6 \cdot 3 + 2}{3}

$15 \div \frac{6 \cdot 3 + 2}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

6

$6$ by

3

$3$ .

15 \div \frac{18 + 2}{3}

$15 \div \frac{18 + 2}{3}$

Step 1.2.4.2

Add

18

$18$ and

2

$2$ .

15 \div \frac{20}{3}

$15 \div \frac{20}{3}$

15 \div \frac{20}{3}

$15 \div \frac{20}{3}$

15 \div \frac{20}{3}

$15 \div \frac{20}{3}$

15 \div \frac{20}{3}

$15 \div \frac{20}{3}$

Step 2

To divide by a fraction, multiply by its reciprocal.

15 (\frac{3}{20})

$15 (\frac{3}{20})$

Step 3

Cancel the common factor of

5

$5$ .

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Step 3.1

Factor

5

$5$ out of

15

$15$ .

5 (3) \frac{3}{20}

$5 (3) \frac{3}{20}$

Step 3.2

Factor

5

$5$ out of

20

$20$ .

5 \cdot 3 \frac{3}{5 \cdot 4}

$5 \cdot 3 \frac{3}{5 \cdot 4}$

Step 3.3

Cancel the common factor.

$5 \cdot 3 \frac{3}{5 \cdot 4}$

Step 3.4

Rewrite the expression.

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

Step 4

Combine

$3$ and

$\frac{3}{4}$ .

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

Step 5

Multiply

$3$ by

$3$ .

$\frac{9}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{4}$

Decimal Form:

$2.25$

Mixed Number Form:

$2 \frac{1}{4}$