Divide 4 1/2÷(1/4)

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

Step 1

Convert $4 \frac{1}{2}$ to an improper fraction.

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

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

Add $4$ and $\frac{1}{2}$ .

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Combine $4$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $4$ by $2$ .

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

Add $8$ and $1$ .

$\frac{9}{2} \div \frac{1}{4}$

Step 2

To divide by a fraction, multiply by its reciprocal.

$\frac{9}{2} \cdot 4$

Step 3

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{9}{2} \cdot (2 (2))$

Cancel the common factor.

$\frac{9}{2} \cdot (2 \cdot 2)$

Rewrite the expression.

$9 \cdot 2$

Step 4

Multiply $9$ by $2$ .

$18$