Solve Mixed Number Division: 6⅔ ÷ 2½ Step-by-Step

$6\frac{2}{3}:2\frac{1}{2}=$

To solve this problem, we'll follow these steps:

• Step 1: Convert each mixed number to an improper fraction.
• Step 2: Divide the fractions by multiplying by the reciprocal of the divisor.
• Step 3: Simplify the resulting improper fraction and convert it back to a mixed number.

Let's work through these steps:

Step 1: Convert the mixed numbers:
$6\frac{2}{3} = \frac{6 \times 3 + 2}{3} = \frac{20}{3}$
$2\frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}$

Step 2: Divide the fractions:
To divide $\frac{20}{3}$ by $\frac{5}{2}$, we multiply by the reciprocal of $\frac{5}{2}$:
$\frac{20}{3} \times \frac{2}{5} = \frac{20 \times 2}{3 \times 5} = \frac{40}{15}$

Step 3: Simplify and convert back:
Simplify $\frac{40}{15}$:
The greatest common divisor of 40 and 15 is 5:
$\frac{40}{15} = \frac{8}{3}$
Convert $\frac{8}{3}$ to a mixed number:
$8\div3 = 2$ remainder $2$, so $\frac{8}{3} = 2\frac{2}{3}$.

Therefore, the solution to the problem is $2\frac{2}{3}$.