Simplify 12÷5 2/5

$12 \div 5 \frac{2}{5}$

Step 1

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

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

$12 \div (5 + \frac{2}{5})$

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

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

$12 \div (5 \cdot \frac{5}{5} + \frac{2}{5})$

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

$12 \div (\frac{5 \cdot 5}{5} + \frac{2}{5})$

Combine the numerators over the common denominator.

$12 \div \frac{5 \cdot 5 + 2}{5}$

Simplify the numerator.

Multiply $5$ by $5$ .

$12 \div \frac{25 + 2}{5}$

Add $25$ and $2$ .

$12 \div \frac{27}{5}$

Step 2

To divide by a fraction, multiply by its reciprocal.

$12 (\frac{5}{27})$

Step 3

Cancel the common factor of $3$ .

Factor $3$ out of $12$ .

$3 (4) \frac{5}{27}$

Factor $3$ out of $27$ .

$3 \cdot 4 \frac{5}{3 \cdot 9}$

Cancel the common factor.

$3 \cdot 4 \frac{5}{3 \cdot 9}$

Rewrite the expression.

$4 (\frac{5}{9})$

Step 4

Combine $4$ and $\frac{5}{9}$ .

$\frac{4 \cdot 5}{9}$

Step 5

Multiply $4$ by $5$ .

$\frac{20}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{20}{9}$

Decimal Form:

$2.\overline{2}$

Mixed Number Form:

$2 \frac{2}{9}$