Solve Fraction Division: 3/5 ÷ 1½ Step-by-Step Solution

To solve this problem, we will follow the steps below:

• Step 1: Convert the mixed number to an improper fraction.
• Step 2: Divide by using multiplication with the reciprocal.
• Step 3: Simplify the resulting fraction, if necessary.

Step 1: Convert $1\frac{1}{2}$ to an improper fraction.
The mixed number $1\frac{1}{2}$ is converted by multiplying the whole number 1 by the denominator 2, adding the numerator 1, resulting in $\frac{3}{2}$.

Step 2: Divide by multiplying with the reciprocal.
The division $\frac{3}{5} \div \frac{3}{2}$ is performed by multiplying $\frac{3}{5}$ with the reciprocal of $\frac{3}{2}$, which is $\frac{2}{3}$.

Thus, we have:

$\frac{3}{5} \times \frac{2}{3} = \frac{3 \times 2}{5 \times 3} = \frac{6}{15}$.

Step 3: Simplify the result.
The fraction $\frac{6}{15}$ can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3:
$\frac{6 \div 3}{15 \div 3} = \frac{2}{5}$.

Therefore, the final solution to the problem is $\frac{2}{5}$.