Solve Mixed Number Division: 2½ ÷ ⅔ Step-by-Step

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

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

• Step 1: Convert the mixed number to an improper fraction.
• Step 2: Find the reciprocal of the divisor fraction.
• Step 3: Multiply the two fractions.
• Step 4: Convert the result back to a mixed number.

Now, let's work through each step:

Step 1: Convert the mixed number.
The mixed number $2\frac{1}{2}$ is converted to an improper fraction as follows:
$2\frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}$

Step 2: Find the reciprocal of the divisor.
The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$.

Step 3: Multiply the two fractions.
Now we multiply $\frac{5}{2}$ by $\frac{3}{2}$:
$\frac{5}{2} \times \frac{3}{2} = \frac{5 \times 3}{2 \times 2} = \frac{15}{4}$

Step 4: Convert the result back to a mixed number.
Convert $\frac{15}{4}$ to a mixed number:
15 divided by 4 gives a quotient of 3 and a remainder of 3, so:
$\frac{15}{4} = 3\frac{3}{4}$

Therefore, the solution to the problem is $3\frac{3}{4}$.