Simplify the following expression.

$(\mathrm{4.2 }\text{of}\mathrm{ 2.5}÷3.5)-(3.6÷2.4+2.5\text{ of}\mathrm{ 3}÷7.5)+(6-3\text{ of}\mathrm{ 2}+4\text{ of}\mathrm{ 3}÷6)$

The correct answer is 2.5.

To simplify the given expression, we follow the BODMAS rule, which states the order of operations as: Bracket (B), Of (O), Division (D), Multiplication (M), Addition (A), and Subtraction (S).

The original expression is:

$(4.2\text{ of }2.5÷3.5)-(3.6÷2.4+2.5\text{ of }3÷7.5)+(6-3\text{ of }2+4\text{ of }3÷6)$

Let's simplify each bracketed term one by one:

Step 1: Simplify the first bracket
$(4.2\text{ of }2.5÷3.5)$
First, evaluate the "of" operation (which represents multiplication):
$4.2\times 2.5=10.5$
Next, perform the division:
$10.5÷3.5=3$
So, the value of the first bracket is 3.

Step 2: Simplify the second bracket
$(3.6÷2.4+2.5\text{ of }3÷7.5)$
First, evaluate the "of" operation:
$2.5\times 3=7.5$
Now we substitute this back into the bracket:
$3.6÷2.4+7.5÷7.5$
Perform the divisions:
$3.6÷2.4=1.5$
$7.5÷7.5=1$
Now, add the results together:
$1.5+1=2.5$
So, the value of the second bracket is 2.5.

Step 3: Simplify the third bracket
$(6-3\text{ of }2+4\text{ of }3÷6)$
First, evaluate the "of" operations:
$3\text{ of }2=6$
$4\text{ of }3=12$
Substitute these back:
$6-6+12÷6$
Perform the division:
$12÷6=2$
Substitute the division result:
$6-6+2=2$
So, the value of the third bracket is 2.

Step 4: Combine all simplified parts
Now we substitute the values back into the main expression:
$\text{First Bracket}-\text{Second Bracket}+\text{Third Bracket}$
$=3-2.5+2$
$=0.5+2$
$=2.5$