To simplify the expression, follow the order of operations (PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division - from left to right, Addition and Subtraction - from left to right):
Start with the innermost parentheses:
3/2 ÷ 4 ½ = (1.5 ÷ 4.5) = 1/3
Now, the expression becomes:
10 - 15/8 × (1/3) ÷ (-¼)
Next, perform the multiplications and divisions:
15/8 × (1/3) = (15/8) * (1/3) = 5/8
Also, remember that dividing by a negative number flips the sign:
(-¼) = -(1/4)
Now, the expression becomes:
10 - 5/8 ÷ -(1/4)
Perform the division:
5/8 ÷ -(1/4) = (5/8) / -(1/4)
To divide fractions, multiply by the reciprocal of the second fraction:
(5/8) * (-4/1) = -20/8 = -5/2
Finally, subtract:
10 - (-5/2)
To subtract a negative number, you can think of it as adding the positive:
10 + 5/2 = 20/2 + 5/2 = 25/2
So, the simplified result is 25/2, which can also be expressed as 12.5.