Special Cases (0 and 1, Inverse, Fraction Line): Using 0

According to the order of operations rules, since the exercise only involves addition and subtraction, we will solve the problem from left to right:

$9-0=9$

$9+0.5=9.5$

According to the order of operations, the exercise is solved from left to right as it contains only an addition operation:

$0+0.2=0.2$

$0.2+0.6=0.8$

According to the order of operations, we first multiply and then add:

$12+(3\cdot0)=$

$3\times0=0$

$12+0=12$

This simple rule is the order of operations which states that multiplication precedes addition and subtraction, and division precedes all of them,

In the given example, a multiplication occurs between two sets of parentheses, thus we simplify the expressions within each pair of parentheses separately,

We start with simplifying the expression within the parentheses on the left, this is done in accordance with the order of operations mentioned above, meaning that multiplication comes before subtraction, we perform the multiplications in this expression first and then proceed with the subtraction operations within it, in reverse we simplify the expression within the parentheses on the right and perform the subtraction operation within them:

What remains for us is to perform the last multiplication that was deferred, it is the multiplication that occurred between the expressions within the parentheses in the original expression, we perform it while remembering that multiplying any number by 0 will result in 0:

Therefore, the correct answer is answer d.

According to the order of operations, the exercise is solved from left to right as it only involves an addition operation:

$12+1=13$

$13+0=13$

According to the order of operations rules, since the exercise only involves addition and subtraction operations, we will solve the problem from left to right:

$19+1=20$

$20-0=20$

According to the order of operations rules, we first divide and then add:

$2+(0:3)=$

$0:3=0$

$2+0=2$

According to the order of operations, we first multiply and then add:

$3\times0=0$

$12+0=12$

According to the order of operations, since the exercise only involves addition operations, we will solve the problem from left to right:

$\frac{1}{2}+0=\frac{1}{2}$

$\frac{1}{2}+\frac{1}{2}=\frac{1}{1}=1$

According to the order of operations rules, we first divide and then add:

$0:3=0$

$2+0=2$

According to the order of operations rules, we first divide and then add:

$0:7=0$

$0+1=1$

This simple rule is the order of operations which states that multiplication and division come before addition and subtraction, and operations enclosed in parentheses come first,

In the given example of division between two given numbers in parentheses, therefore according to the order of operations mentioned above, we start by calculating the values of each of the numbers within the parentheses, there is no prohibition against calculating the result of the addition operation in the given number, for the sake of proper order, this operation is performed later:

$(3+2-1):(1+3)-1+5= \\ 4:4-1+5$In continuation of the principle that division comes before addition and subtraction the division operation is performed first and then the operations of subtraction and addition which were received in the given number and in the last stage:

$4:4-1+5= \\ 1-1+5=\\ 5$Therefore the correct answer here is answer B.

According to the order of operations, we'll first solve the expression in parentheses:

$19-1=18$

We obtain the following expression:

$0\times18+2=$

According to the order of operations, we'll multiply first and then add:

$0\times18=0$

$0+2=2$

According to the order of operations, we will solve the exercise from left to right.

$\frac{1}{2}=0.5$

$0.5+0.5=1$

$1-0=1$

According to the order of operations rules, we must first solve the expression inside of the parentheses. Following this we will perform the division:

$18-0=18$

$18:3=6$

Simplifying this expression emphasizes the order of operations, which states that multiplication precedes addition and subtraction, and that division precedes all of them,

In the given expression, the establishment of division operations between the parentheses (the outermost) to a number, therefore according to the order of operations as mentioned, is handled by simplifying the expression in these parentheses, this expression includes division operations that begin on the expression within the parentheses (the innermost), therefore according to the order of operations as mentioned is handled by simplifying the expression in these parentheses and performing the subtraction operations in it, there is no hindrance to calculate the outcome of the division operations in the expression in the outermost parentheses, but for the sake of good order this is done afterwards:

$\lbrack(4+3):7+2:2-2\rbrack:5= \\ \lbrack7:7+2:2-2\rbrack:5$Continuing and simplifying the expression in the parentheses we noted, since division precedes addition and subtraction, start with the division operations in the expression and only then calculate the outcome of the addition and subtraction, ultimately perform the division operations on this expression in the parentheses:

$\lbrack7:7+2:2-2\rbrack:5 \\ \lbrack1+1-2\rbrack:5=\\ 0:5=\\0$In the last stage we mentioned that multiplying a number by 0 gives the result 0,

Therefore, this simplifying expression is short so there is no need to elaborate,

And the correct answer here is answer A.

In the order of operations, parentheses come before everything else.

We start by solving the inner parentheses in the subtraction operation:

$((3):3-1)\times4=$ We continue with the inner parentheses in the division operation and then subtraction:

$(1-1)\times4=$

We continue solving the subtraction exercise within parentheses and then multiply:

$0\times4=0$

According to the order of operations rules, we first solve the expression in parentheses:

$1-1=0$

And we get the expression:

$0.18+0=0.18$

According to the order of operations, we first solve the expression in parentheses:

$18-0=18$

Now we divide:

$18:3=6$

This simple example demonstrates the order of operations, which states that exponentiation precedes multiplication and division, which come before addition and subtraction, and that operations within parentheses come first,

In the given example, the operation of division between parentheses (the denominators) by a number (which is also in parentheses but only for clarification purposes), thus according to the order of operations mentioned we start with the parentheses that contain the denominators first, this parentheses that contain the denominators includes multiplication between two numbers which are also in parentheses, therefore according to the order of operations mentioned, we start with the numbers inside them, paying attention that each of these numbers, including the ones in strength, and therefore assuming that exponentiation precedes multiplication and division we consider their numerical values only in the first step and only then do we perform the operations of multiplication and division on these numbers:

$$$$$\lbrack(3^2-4-5)\cdot(4+\sqrt{16})-5 \rbrack:(-5)=\\ \lbrack(9-4-5)\cdot(4+4)-5 \rbrack:(-5)=\\ \lbrack0\cdot8-5 \rbrack:(-5)\\$Continuing with the simple division in parentheses ,and according to the order of operations mentioned, we proceed from the multiplication calculation and remember that the multiplication of the number 0 by any number will yield the result 0, in the first step the operation of subtraction is performed and finally the operation of division is initiated on the number in parentheses:

$\lbrack0\cdot8-5 \rbrack:(-5)= \\ \lbrack0-5 \rbrack:(-5)= \\ -5 :(-5)=\\ 1$ Therefore, the correct answer is answer c.