Question

multply 3 2/3 times 3/4 express your answer in simplest form A 2 3/4, B 8 1/4, C 11/12, D 11

Answer 1

To multiply \( 3 \frac{2}{3} \) by \( \frac{3}{4} \), we first convert \( 3 \frac{2}{3} \) into an improper fraction.

1. Convert \( 3 \frac{2}{3} \):
\[
3 \frac{2}{3} = \frac{3 \times 3 + 2}{3} = \frac{9 + 2}{3} = \frac{11}{3}
\]

2. Now multiply \( \frac{11}{3} \) by \( \frac{3}{4} \):
\[
\frac{11}{3} \times \frac{3}{4} = \frac{11 \times 3}{3 \times 4} = \frac{33}{12}
\]

3. 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:
\[
\frac{33 \div 3}{12 \div 3} = \frac{11}{4}
\]

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**.