To multiply \( 3 \frac{2}{3} \) by \( \frac{3}{4} \), we first convert \( 3 \frac{2}{3} \) into an improper fraction.
-
Convert \( 3 \frac{2}{3} \): \[ 3 \frac{2}{3} = \frac{3 \times 3 + 2}{3} = \frac{9 + 2}{3} = \frac{11}{3} \]
-
Now multiply \( \frac{11}{3} \) by \( \frac{3}{4} \): \[ \frac{11}{3} \times \frac{3}{4} = \frac{11 \times 3}{3 \times 4} = \frac{33}{12} \]
-
Simplify \( \frac{33}{12} \):
- Find the greatest common divisor (GCD) of 33 and 12, which is 3.
- Divide both the numerator and the denominator by 3: \[ \frac{33 \div 3}{12 \div 3} = \frac{11}{4} \]
-
Convert \( \frac{11}{4} \) to a mixed number: \[ 11 \div 4 = 2 \quad \text{(with a remainder of 3)} \implies 2 \frac{3}{4} \]
Thus, the final answer in simplest form is \( 2 \frac{3}{4} \).
So, the answer is A 2 3/4.