Solve Mixed Number Division: 3⅝ ÷ 1½ Step-by-Step

To solve this problem, we need to proceed through the following steps:

• Step 1: Convert the mixed numbers to improper fractions.
• Step 2: Divide the improper fractions using multiplication by the reciprocal.
• Step 3: Simplify the resulting fraction and convert back to a mixed number.

Now, let's work through each step:

Step 1: Convert
For $3\frac{5}{8}$, multiply the whole number 3 by the denominator 8 and add the numerator 5:
$3 \times 8 + 5 = 24 + 5 = 29$
$<=>$ This gives us the improper fraction $\frac{29}{8}$.

For $1\frac{1}{2}$, multiply the whole number 1 by the denominator 2 and add the numerator 1:
$1 \times 2 + 1 = 2 + 1 = 3$
$<=>$ This gives us the improper fraction $\frac{3}{2}$.

Step 2: Divide the improper fractions.
$\frac{29}{8} \div \frac{3}{2}$ becomes $\frac{29}{8} \times \frac{2}{3}$.
Multiply the numerators and the denominators:
$\frac{29 \times 2}{8 \times 3} = \frac{58}{24}$.

Step 3: Simplify the resulting fraction.
Divide both the numerator and the denominator by their greatest common divisor, which is 2:
$\frac{58 \div 2}{24 \div 2} = \frac{29}{12}$.
Convert $\frac{29}{12}$ into a mixed number:
$29 \div 12 = 2 \text{ remainder } 5$
Thus, it becomes $2\frac{5}{12}$.

Therefore, the division of $3\frac{5}{8}$ by $1\frac{1}{2}$ yields $2\frac{5}{12}$.