Basic Math Examples

2 \frac{1}{2} \div \frac{2}{3}

$2 \frac{1}{2} \div \frac{2}{3}$

Step 1

Convert

2 \frac{1}{2}

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

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Step 1.1

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

(2 + \frac{1}{2}) \div \frac{2}{3}

$(2 + \frac{1}{2}) \div \frac{2}{3}$

Step 1.2

Add

2

$2$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 1.2.1

To write

2

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

\frac{2}{2}

$\frac{2}{2}$ .

(2 \cdot \frac{2}{2} + \frac{1}{2}) \div \frac{2}{3}

$(2 \cdot \frac{2}{2} + \frac{1}{2}) \div \frac{2}{3}$

Step 1.2.2

Combine

2

$2$ and

\frac{2}{2}

$\frac{2}{2}$ .

(\frac{2 \cdot 2}{2} + \frac{1}{2}) \div \frac{2}{3}

$(\frac{2 \cdot 2}{2} + \frac{1}{2}) \div \frac{2}{3}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{2 \cdot 2 + 1}{2} \div \frac{2}{3}

$\frac{2 \cdot 2 + 1}{2} \div \frac{2}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

2

$2$ .

\frac{4 + 1}{2} \div \frac{2}{3}

$\frac{4 + 1}{2} \div \frac{2}{3}$

Step 1.2.4.2

Add

4

$4$ and

1

$1$ .

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

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

Step 2

To divide by a fraction, multiply by its reciprocal.

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

Step 3

Multiply

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

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Step 3.1

Multiply

$\frac{5}{2}$ by

$\frac{3}{2}$ .

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

Step 3.2

Multiply

$5$ by

$3$ .

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

Step 3.3

Multiply

$2$ by

$2$ .

$\frac{15}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{15}{4}$

Decimal Form:

$3.75$

Mixed Number Form:

$3 \frac{3}{4}$