Basic Math Examples

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

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

Step 1

Convert

1 \frac{1}{2}

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

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Step 1.1

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

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

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

Step 1.2

Add

1

$1$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 1.2.1

Write

1

$1$ as a fraction with a common denominator.

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

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

Step 1.2.3

Add

2

$2$ and

1

$1$ .

\frac{3}{2} \div \frac{2}{5}

$\frac{3}{2} \div \frac{2}{5}$

\frac{3}{2} \div \frac{2}{5}

$\frac{3}{2} \div \frac{2}{5}$

\frac{3}{2} \div \frac{2}{5}

$\frac{3}{2} \div \frac{2}{5}$

Step 2

To divide by a fraction, multiply by its reciprocal.

\frac{3}{2} \cdot \frac{5}{2}

$\frac{3}{2} \cdot \frac{5}{2}$

Step 3

Multiply

\frac{3}{2} \cdot \frac{5}{2}

$\frac{3}{2} \cdot \frac{5}{2}$ .

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Step 3.1

Multiply

\frac{3}{2}

$\frac{3}{2}$ by

\frac{5}{2}

$\frac{5}{2}$ .

\frac{3 \cdot 5}{2 \cdot 2}

$\frac{3 \cdot 5}{2 \cdot 2}$

Step 3.2

Multiply

3

$3$ by

5

$5$ .

\frac{15}{2 \cdot 2}

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

Step 3.3

Multiply

2

$2$ by

2

$2$ .

\frac{15}{4}

$\frac{15}{4}$

\frac{15}{4}

$\frac{15}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

\frac{15}{4}

$\frac{15}{4}$

Decimal Form:

3.75

$3.75$

Mixed Number Form:

3 \frac{3}{4}

$3 \frac{3}{4}$