Divide 5 1/2÷(3/4)

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

Convert $5 \frac{1}{2}$ to an improper fraction.

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

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

Add $5$ and $\frac{1}{2}$ .

To write $5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Combine $5$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $5$ by $2$ .

$\frac{10 + 1}{2} \div \frac{3}{4}$

Add $10$ and $1$ .

$\frac{11}{2} \div \frac{3}{4}$

To divide by a fraction, multiply by its reciprocal.

$\frac{11}{2} \cdot \frac{4}{3}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{11}{2} \cdot \frac{2 (2)}{3}$

Cancel the common factor.

$\frac{11}{2} \cdot \frac{2 \cdot 2}{3}$

Rewrite the expression.

$11 (\frac{2}{3})$

Combine $11$ and $\frac{2}{3}$ .

$\frac{11 \cdot 2}{3}$

Multiply $11$ by $2$ .

$\frac{22}{3}$

The result can be shown in multiple forms.

Exact Form:

$\frac{22}{3}$

Decimal Form:

$7.\overline{3}$

Mixed Number Form:

$7 \frac{1}{3}$