Basic Math Examples

18 \frac{2}{5} \div \frac{2}{15}

$18 \frac{2}{5} \div \frac{2}{15}$

Step 1

Convert

18 \frac{2}{5}

$18 \frac{2}{5}$ to an improper fraction.

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Step 1.1

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

(18 + \frac{2}{5}) \div \frac{2}{15}

$(18 + \frac{2}{5}) \div \frac{2}{15}$

Step 1.2

Add

18

$18$ and

\frac{2}{5}

$\frac{2}{5}$ .

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Step 1.2.1

To write

18

$18$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

(18 \cdot \frac{5}{5} + \frac{2}{5}) \div \frac{2}{15}

$(18 \cdot \frac{5}{5} + \frac{2}{5}) \div \frac{2}{15}$

Step 1.2.2

Combine

18

$18$ and

\frac{5}{5}

$\frac{5}{5}$ .

(\frac{18 \cdot 5}{5} + \frac{2}{5}) \div \frac{2}{15}

$(\frac{18 \cdot 5}{5} + \frac{2}{5}) \div \frac{2}{15}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{18 \cdot 5 + 2}{5} \div \frac{2}{15}

$\frac{18 \cdot 5 + 2}{5} \div \frac{2}{15}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

18

$18$ by

5

$5$ .

\frac{90 + 2}{5} \div \frac{2}{15}

$\frac{90 + 2}{5} \div \frac{2}{15}$

Step 1.2.4.2

Add

90

$90$ and

2

$2$ .

\frac{92}{5} \div \frac{2}{15}

$\frac{92}{5} \div \frac{2}{15}$

\frac{92}{5} \div \frac{2}{15}

$\frac{92}{5} \div \frac{2}{15}$

\frac{92}{5} \div \frac{2}{15}

$\frac{92}{5} \div \frac{2}{15}$

\frac{92}{5} \div \frac{2}{15}

$\frac{92}{5} \div \frac{2}{15}$

Step 2

To divide by a fraction, multiply by its reciprocal.

\frac{92}{5} \cdot \frac{15}{2}

$\frac{92}{5} \cdot \frac{15}{2}$

Step 3

Cancel the common factor of

2

$2$ .

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Step 3.1

Factor

2

$2$ out of

92

$92$ .

\frac{2 (46)}{5} \cdot \frac{15}{2}

$\frac{2 (46)}{5} \cdot \frac{15}{2}$

Step 3.2

Cancel the common factor.

$\frac{2 \cdot 46}{5} \cdot \frac{15}{2}$

Step 3.3

Rewrite the expression.

$\frac{46}{5} \cdot 15$

Step 4

Cancel the common factor of

$5$ .

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Step 4.1

Factor

$5$ out of

$15$ .

$\frac{46}{5} \cdot (5 (3))$

Step 4.2

Cancel the common factor.

$\frac{46}{5} \cdot (5 \cdot 3)$

Step 4.3

Rewrite the expression.

$46 \cdot 3$

Step 5

Multiply

$46$ by

$3$ .

$138$