Basic Math Examples

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

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

Step 1

Convert

1 \frac{2}{3}

$1 \frac{2}{3}$ to an improper fraction.

Tap for more steps...

Step 1.1

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

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

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

Step 1.2

Add

1

$1$ and

\frac{2}{3}

$\frac{2}{3}$ .

Tap for more steps...

Step 1.2.1

Write

1

$1$ as a fraction with a common denominator.

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

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

Step 1.2.3

Add

3

$3$ and

2

$2$ .

\frac{5}{3} \div 2 \frac{1}{2}

$\frac{5}{3} \div 2 \frac{1}{2}$

\frac{5}{3} \div 2 \frac{1}{2}

$\frac{5}{3} \div 2 \frac{1}{2}$

\frac{5}{3} \div 2 \frac{1}{2}

$\frac{5}{3} \div 2 \frac{1}{2}$

Step 2

Convert

2 \frac{1}{2}

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

Tap for more steps...

Step 2.1

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

\frac{5}{3} \div (2 + \frac{1}{2})

$\frac{5}{3} \div (2 + \frac{1}{2})$

Step 2.2

Add

2

$2$ and

\frac{1}{2}

$\frac{1}{2}$ .

Tap for more steps...

Step 2.2.1

To write

2

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

\frac{2}{2}

$\frac{2}{2}$ .

\frac{5}{3} \div (2 \cdot \frac{2}{2} + \frac{1}{2})

$\frac{5}{3} \div (2 \cdot \frac{2}{2} + \frac{1}{2})$

Step 2.2.2

Combine

2

$2$ and

\frac{2}{2}

$\frac{2}{2}$ .

\frac{5}{3} \div (\frac{2 \cdot 2}{2} + \frac{1}{2})

$\frac{5}{3} \div (\frac{2 \cdot 2}{2} + \frac{1}{2})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{5}{3} \div \frac{2 \cdot 2 + 1}{2}

$\frac{5}{3} \div \frac{2 \cdot 2 + 1}{2}$

Step 2.2.4

Simplify the numerator.

Tap for more steps...

Step 2.2.4.1

Multiply

2

$2$ by

2

$2$ .

\frac{5}{3} \div \frac{4 + 1}{2}

$\frac{5}{3} \div \frac{4 + 1}{2}$

Step 2.2.4.2

Add

4

$4$ and

1

$1$ .

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

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

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

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

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

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

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

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

Step 3

To divide by a fraction, multiply by its reciprocal.

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

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

Step 4

Cancel the common factor of

5

$5$ .

Tap for more steps...

Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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

Step 5

Combine

$\frac{1}{3}$ and

$2$ .

$\frac{2}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$