Solve Mixed Number Division: 3¾ ÷ 1⅓ Step-by-Step

Let's solve the problem step by step:

• Step 1: Convert the mixed numbers to improper fractions.
• Step 2: Divide the first improper fraction by the second.
• Step 3: Simplify the result and convert back to a mixed number if needed.

Step 1: Convert the mixed numbers to improper fractions.
For $3\frac{3}{4}$:
- The whole number is 3, the numerator is 3, and the denominator is 4.
- Convert: $3 \frac{3}{4} = \frac{(3 \times 4) + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4}$.

For $1\frac{1}{3}$:
- The whole number is 1, the numerator is 1, and the denominator is 3.
- Convert: $1 \frac{1}{3} = \frac{(1 \times 3) + 1}{3} = \frac{3 + 1}{3} = \frac{4}{3}$.

Step 2: Divide the fractions by multiplying by the reciprocal of the second fraction.
$\frac{15}{4} \div \frac{4}{3} = \frac{15}{4} \times \frac{3}{4} = \frac{15 \times 3}{4 \times 4} = \frac{45}{16}$.

Step 3: Convert the improper fraction back to a mixed number.
Divide 45 by 16:
- 45 divided by 16 is 2, remainder 13, giving us $2\frac{13}{16}$.

Thus, the solution to the problem is $2\frac{13}{16}$, which matches choice (1).