(2 3\4+0.15-1 8\25):(21\2-13\4+0.04)

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To solve this, we need to follow the order of operations (PEMDAS/BODMAS):

First, let's convert the mixed numbers and fractions to improper fractions:

2 3/4 = 11/4
1 8/25 = 33/25

Next, perform the operations inside the parentheses:

21/2 = 10.5
13/4 = 3.25
(10.5 - 3.25 + 0.04) = 7.29

Now, the expression becomes:

(11/4 + 0.15 - 33/25) ÷ 7.29

Next, subtract the fractions and convert the mixed numbers to improper fractions:

11/4 + 0.15 = 11/4 + 3/20 = 265/80 + 12/80 = 277/80

Now, divide the result by 7.29:

(277/80 - 33/25) ÷ 7.29

Now, find a common denominator for the fractions:

(277/80 - 1056/80) ÷ 7.29
(277 - 1056)/80 ÷ 7.29
(-779)/80 ÷ 7.29
-779/80 ÷ 7.29
-779/80 * 1/7.29
-779/581.1

Therefore, the final result is approximately -1.34.