Solve (7-8)+3/2:1+(5-4): Order of Operations Challenge

This simple equation emphasizes the order of operations, indicating that exponentiation precedes multiplication and division, which come before addition and subtraction, and that operations within parentheses take precedence over all others,

Let's start by discussing the given equation, the first step from the left is division by the number 1, remember that dividing any number by 1 always yields the same number, so we can simply disregard the division by 1 operation, which essentially leaves the equation (with the division by 1 operation, or without it) unchanged, namely:

$\frac{(7-8)+3}{2}:1+(5-4)= \\ \downarrow\\ \frac{(7-8)+3}{2}+(5-4)=$

Continuing with this equation,

Let's note that both the numerator and the denominator in a fraction (every fraction) are equations (in their entirety) between which a division operation is performed, namely- they can be treated as the numerator and the denominator in a fraction as equations that are closed, thus we can rewrite the given equation and write it in the following form:

$\frac{(7-8)+3}{2}+(5-4)= \\ \downarrow\\ \big((7-8)+3\big):2+(5-4)$We highlight this to emphasize that fractions which are the numerator and similarly in its denominator should be treated separately, indeed as if they are closed,

Returning to the original equation, namely - in the given form, and simplifying, we simplify the equation that is in the numerator of the fraction and, this is done in accordance with the order of operations mentioned above and in a systematic manner:

$\frac{(7-8)+3}{2}+(5-4)= \\ \frac{-1+3}{2}+1= \\ \frac{2}{2}+1$In the first stage, we simplified the equation that is in the numerator of the fraction, this in accordance with the order of operations mentioned above hence we started with the equation that is closed, and only then did we perform the multiplication operation that is in the numerator of the fraction, in contrast, we simplified the equation that is in closed parentheses,

Continuing we simplify the equation in accordance with the order of operations mentioned above,thus the division operation of the fraction (this is done mechanically), and continuing we perform the multiplication operation:

$\frac{\not{2}}{\not{2}}+1 =\\ 1+1 =\\ 2$In this case, the simplification process is very short, hence we won't elaborate,

Therefore, the correct answer is option B.