Divide 16 1/2÷2 1/4

$16 \frac{1}{2} \div 2 \frac{1}{4}$

Step 1

Convert $16 \frac{1}{2}$ to an improper fraction.

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

$(16 + \frac{1}{2}) \div 2 \frac{1}{4}$

Add $16$ and $\frac{1}{2}$ .

To write $16$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(16 \cdot \frac{2}{2} + \frac{1}{2}) \div 2 \frac{1}{4}$

Combine $16$ and $\frac{2}{2}$ .

$(\frac{16 \cdot 2}{2} + \frac{1}{2}) \div 2 \frac{1}{4}$

Combine the numerators over the common denominator.

$\frac{16 \cdot 2 + 1}{2} \div 2 \frac{1}{4}$

Simplify the numerator.

Multiply $16$ by $2$ .

$\frac{32 + 1}{2} \div 2 \frac{1}{4}$

Add $32$ and $1$ .

$\frac{33}{2} \div 2 \frac{1}{4}$

Step 2

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

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

$\frac{33}{2} \div (2 + \frac{1}{4})$

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

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

$\frac{33}{2} \div (2 \cdot \frac{4}{4} + \frac{1}{4})$

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

$\frac{33}{2} \div (\frac{2 \cdot 4}{4} + \frac{1}{4})$

Combine the numerators over the common denominator.

$\frac{33}{2} \div \frac{2 \cdot 4 + 1}{4}$

Simplify the numerator.

Multiply $2$ by $4$ .

$\frac{33}{2} \div \frac{8 + 1}{4}$

Add $8$ and $1$ .

$\frac{33}{2} \div \frac{9}{4}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{33}{2} \cdot \frac{4}{9}$

Step 4

Cancel the common factor of $3$ .

Factor $3$ out of $33$ .

$\frac{3 (11)}{2} \cdot \frac{4}{9}$

Factor $3$ out of $9$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

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.

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

Step 6

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

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

Step 7

Multiply $11$ by $2$ .

$\frac{22}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{22}{3}$

Decimal Form:

$7.\overline{3}$

Mixed Number Form:

$7 \frac{1}{3}$

Divide 16 1/2÷2 1/4

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