Answer:
It is not possible to get a result of 8 using only the numbers 8, 12, 2, 7, and 4 with the basic arithmetic operations (+, -, x, ÷) and parentheses, following the order of operations.
Here's why:
To get a result of 8, we would need to perform a sequence of arithmetic operations that reduces the given numbers to a single value. However, the given numbers do not have any factors or multiples that combine to give 8, and it is not possible to combine them in a way that gives a result of 8.
To illustrate this, let's consider all the possible arithmetic operations we could perform using the given numbers, following the order of operations:
We could add or subtract the numbers in any order, but none of the possible combinations gives a result of 8. For example:
8 + 12 + 2 + 7 + 4 = 33
8 - 12 - 2 - 7 - 4 = -17
8 + 12 - 2 + 7 - 4 = 21
8 - 12 + 2 - 7 + 4 = -5
We could multiply or divide the numbers in any order, but again none of the possible combinations gives a result of 8:
8 x 12 x 2 x 7 x 4 = 2688
8 ÷ 12 ÷ 2 ÷ 7 ÷ 4 = 0.00119
8 x 12 ÷ 2 - 7 + 4 = 41
8 ÷ 12 x 2 + 7 - 4 = 1.83
We could use parentheses to change the order of operations, but again none of the possible combinations gives a result of 8:
(8 + 12) x (2 + 7) - 4 = 170
8 + (12 ÷ 2) x (7 - 4) = 26
(8 - 12) x (2 + 7) + 4 = -40
8 + 12 x (2 + 7) ÷ 4 = 38
Therefore, there is no way to get a result of 8 using only the numbers 8, 12, 2, 7, and 4 with the basic arithmetic operations and parentheses, following the order of operations.