Verified Answer :

Multiplying fractions is always easier when you multiply impartial fractions.
2 3/4 = 11/4
1 1/8 = 9/8

Something that will make your life a lot easier is always to take advantage of the fact that you have whole numbers available (in this case the 32). You know that 41/4 = 1, and one times anything is itself and can be crossed out.
You can turn the 32 into 4
8, and use that 4 to multiple with 11/4 (or 11 1/4) to get 11. Now you're left with:
11
9/8 8

Then 8
1/8 = 1 as well. So use the 8 you have remaining to multiple with 9/8 (or 9 1/8) to get 9. Now you're left with:
11
9.

11 * 9 = 99. 99 is your answer.

\(2\frac{3}{4}\times1\frac{1}{8}\times32=\frac{2\times4+3}{4}\times\frac{1\times8+1}{8}\times\frac{32}{1}=(8+3)\times(8+1)\\\\=11\times9=\fbox{99}\)