Divide 12 3/8÷2 3/4

$12 \frac{3}{8} \div 2 \frac{3}{4}$

Step 1

Convert $12 \frac{3}{8}$ to an improper fraction.

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

$(12 + \frac{3}{8}) \div 2 \frac{3}{4}$

Add $12$ and $\frac{3}{8}$ .

To write $12$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$(12 \cdot \frac{8}{8} + \frac{3}{8}) \div 2 \frac{3}{4}$

Combine $12$ and $\frac{8}{8}$ .

$(\frac{12 \cdot 8}{8} + \frac{3}{8}) \div 2 \frac{3}{4}$

Combine the numerators over the common denominator.

$\frac{12 \cdot 8 + 3}{8} \div 2 \frac{3}{4}$

Simplify the numerator.

Multiply $12$ by $8$ .

$\frac{96 + 3}{8} \div 2 \frac{3}{4}$

Add $96$ and $3$ .

$\frac{99}{8} \div 2 \frac{3}{4}$

Step 2

Convert $2 \frac{3}{4}$ to an improper fraction.

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

$\frac{99}{8} \div (2 + \frac{3}{4})$

Add $2$ and $\frac{3}{4}$ .

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

$\frac{99}{8} \div (2 \cdot \frac{4}{4} + \frac{3}{4})$

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

$\frac{99}{8} \div (\frac{2 \cdot 4}{4} + \frac{3}{4})$

Combine the numerators over the common denominator.

$\frac{99}{8} \div \frac{2 \cdot 4 + 3}{4}$

Simplify the numerator.

Multiply $2$ by $4$ .

$\frac{99}{8} \div \frac{8 + 3}{4}$

Add $8$ and $3$ .

$\frac{99}{8} \div \frac{11}{4}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{99}{8} \cdot \frac{4}{11}$

Step 4

Cancel the common factor of $11$ .

Factor $11$ out of $99$ .

$\frac{11 (9)}{8} \cdot \frac{4}{11}$

Cancel the common factor.

$\frac{11 \cdot 9}{8} \cdot \frac{4}{11}$

Rewrite the expression.

$\frac{9}{8} \cdot 4$

Step 5

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{9}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{2}$

Decimal Form:

$4.5$

Mixed Number Form:

$4 \frac{1}{2}$

Divide 12 3/8÷2 3/4

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