Divide 2 1/2÷(3/8)

$2 \frac{1}{2} \div \frac{3}{8}$

Step 1

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

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

$(2 + \frac{1}{2}) \div \frac{3}{8}$

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

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

$(2 \cdot \frac{2}{2} + \frac{1}{2}) \div \frac{3}{8}$

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

$(\frac{2 \cdot 2}{2} + \frac{1}{2}) \div \frac{3}{8}$

Combine the numerators over the common denominator.

$\frac{2 \cdot 2 + 1}{2} \div \frac{3}{8}$

Simplify the numerator.

Multiply $2$ by $2$ .

$\frac{4 + 1}{2} \div \frac{3}{8}$

Add $4$ and $1$ .

$\frac{5}{2} \div \frac{3}{8}$

Step 2

To divide by a fraction, multiply by its reciprocal.

$\frac{5}{2} \cdot \frac{8}{3}$

Step 3

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

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

Cancel the common factor.

$\frac{5}{2} \cdot \frac{2 \cdot 4}{3}$

Rewrite the expression.

$5 (\frac{4}{3})$

Step 4

Combine $5$ and $\frac{4}{3}$ .

$\frac{5 \cdot 4}{3}$

Step 5

Multiply $5$ by $4$ .

$\frac{20}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{20}{3}$

Decimal Form:

$6.\overline{6}$

Mixed Number Form:

$6 \frac{2}{3}$