Solve Complex Fraction Operation: (44-3×0)/11 ÷ 4 - (3×4+5)/17

This simple rule is the emphasis on the order of operations which states that exponentiation precedes multiplication and division, which precede addition and subtraction, and that parentheses precede all,

Initially, we pay very close attention to the given rule, given that in the rule the existence of a number that is multiplied by 0, since multiplying any number by 0 always yields the result of 0, we disregard this multiplication, of course, meaning that it does not contribute anything, in contrast we focus on the second break from the left (as all the break from the right) and simplify the rule that is in it, this in accordance to the order of operations mentioned above, therefore we start with the multiplication that is in the break and continue to perform the division operation that is in this break:

$\frac{44-3\cdot0}{11}:4-\frac{3\cdot4+5}{17}= \\ \frac{44}{11}:4-\frac{12+5}{17}= \\ \frac{44}{11}:4-\frac{17}{17} \\$

We continue and simplify the rule we received in the last step, again, of course in accordance to the order of operations mentioned above, therefore we start with performing the division operation of the breaks, this is done sequentially, and continue to perform the division operation that is across the first, and finally perform the subtraction operation:

$\frac{\not{44}}{\not{11}}:4-\frac{\not{17}}{\not{17}}= \\ 4:4-1=\\ 1-1=\\ 0$ Simply put, this rule is short, therefore there is no need to elaborate,

We received whether the correct answer is answer c'.

Note:

Keep in mind that in the group of the last breaks in the solution to the problem, we can start recording the break and the division operation that is easy on it even without the break, but with the help of the division operation:

$\frac{44}{11}:4\\ \downarrow\\ 44:11:4$And in continuation we will calculate the division operation in the break and only after that we performed the division by the number 4, we emphasize that in total we simplified this rule in accordance to the natural order of operations, meaning we performed the operations one after the other from left to right, and this means that there is no precedence of one division operation in this rule over the other defined by the natural order of operations, meaning- in calculation from left to right, (Keep in mind in addition that the order of operations mentioned at the beginning, which states that exponentiation precedes multiplication and division, which precede addition and subtraction, and that parentheses precede all, it does not define precedence also between the multiplication and division operations, and therefore the rule between these two operations, in the absence of parentheses that constitute a different order, is in calculation from left to right).