Question

Multiply 5/6
by 2 3/4
. Convert the product to be a mixed number.

Answer 1

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.

1. Convert \( 2 \frac{3}{4} \) to an improper fraction:
\[
2 \frac{3}{4} = 2 \times 4 + 3 = 8 + 3 = 11
\]
Therefore, \( 2 \frac{3}{4} = \frac{11}{4} \).

2. Now we can multiply the fractions:
\[
\frac{5}{6} \times \frac{11}{4} = \frac{5 \times 11}{6 \times 4} = \frac{55}{24}.
\]

3. Next, we convert \( \frac{55}{24} \) to a mixed number. To do this, we 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:
\[
2 \frac{7}{24}.
\]

Therefore, the product of \( \frac{5}{6} \) and \( 2 \frac{3}{4} \) is \( 2 \frac{7}{24} \).