To multiply \( \frac{5}{6} \) by \( 2\frac{3}{4} \), we first need to convert the mixed number \( 2\frac{3}{4} \) into an improper fraction.
- Convert \( 2\frac{3}{4} \) to an improper fraction:
\[ 2\frac{3}{4} = 2 \times 4 + 3 = 8 + 3 = 11 \quad \text{so,} \quad 2\frac{3}{4} = \frac{11}{4} \]
- Now, multiply \( \frac{5}{6} \) by \( \frac{11}{4} \):
\[ \frac{5}{6} \times \frac{11}{4} = \frac{5 \times 11}{6 \times 4} = \frac{55}{24} \]
- Next, we need to convert \( \frac{55}{24} \) into a mixed number. To do this, divide 55 by 24:
- \( 55 \div 24 = 2 \) (the whole number part)
- The remainder is \( 55 - (24 \times 2) = 55 - 48 = 7 \)
Thus, we can express \( \frac{55}{24} \) as a mixed number:
\[ \frac{55}{24} = 2 \frac{7}{24} \]
Therefore, the product of \( \frac{5}{6} \) and \( 2\frac{3}{4} \) expressed as a mixed number is:
\[ \boxed{2 \frac{7}{24}} \]