Evaluate 6 2/3÷(2/3)

$6 \frac{2}{3} \div \frac{2}{3}$

Step 1

Convert $6 \frac{2}{3}$ to an improper fraction.

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

$(6 + \frac{2}{3}) \div \frac{2}{3}$

Add $6$ and $\frac{2}{3}$ .

To write $6$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(6 \cdot \frac{3}{3} + \frac{2}{3}) \div \frac{2}{3}$

Combine $6$ and $\frac{3}{3}$ .

$(\frac{6 \cdot 3}{3} + \frac{2}{3}) \div \frac{2}{3}$

Combine the numerators over the common denominator.

$\frac{6 \cdot 3 + 2}{3} \div \frac{2}{3}$

Simplify the numerator.

Multiply $6$ by $3$ .

$\frac{18 + 2}{3} \div \frac{2}{3}$

Add $18$ and $2$ .

$\frac{20}{3} \div \frac{2}{3}$

Step 2

To divide by a fraction, multiply by its reciprocal.

$\frac{20}{3} \cdot \frac{3}{2}$

Step 3

Cancel the common factor of $2$ .

Factor $2$ out of $20$ .

$\frac{2 (10)}{3} \cdot \frac{3}{2}$

Cancel the common factor.

$\frac{2 \cdot 10}{3} \cdot \frac{3}{2}$

Rewrite the expression.

$\frac{10}{3} \cdot 3$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{10}{3} \cdot 3$

Rewrite the expression.

$10$