Solve: 3/10 Divided by 2½ - Mixed Number Division

$\frac{3}{10}:2\frac{1}{2}=$

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

• Step 1: Convert the mixed number to an improper fraction.
• Step 2: Find the reciprocal of the improper fraction.
• Step 3: Multiply the first fraction by this reciprocal.
• Step 4: Simplify the result to get the final answer.

Let's go through each step in detail:

Step 1: Convert $2\frac{1}{2}$ to an improper fraction:

$2\frac{1}{2}$ is equal to $2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}$.

Step 2: Find the reciprocal of $\frac{5}{2}$:

The reciprocal of $\frac{5}{2}$ is $\frac{2}{5}$.

Step 3: Multiply $\frac{3}{10}$ by $\frac{2}{5}$:

$\frac{3}{10} \times \frac{2}{5} = \frac{3 \times 2}{10 \times 5} = \frac{6}{50}$.

Step 4: Simplify $\frac{6}{50}$:

To simplify, we find the greatest common divisor of 6 and 50, which is 2:

$\frac{6}{50} = \frac{3}{25}$ after dividing the numerator and denominator by 2.

Therefore, the solution to the problem is $\frac{3}{25}$. This matches choice 2.