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

First, calculate the expression within the parentheses:

$2 \times 1 = 2$

Now, multiply the result by 9:

$9 \times 2 = 18$

Thus, the final answer is 18.

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

$5\times1=5$

Now we multiply:

$8\times5=40$

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, we first solve the expression in parentheses:

$18-0=18$

Now we divide:

$18:3=6$

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 must first solve the expression inside of the parentheses:

$7\times1=7$

Resulting in the following expression:

$8\times7=56$

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:

$0\times18=0$

$0+2=2$

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 rules, we first solve the expression in parentheses:

$19-1=18$

We obtain the following expression:

$0\times18+2=$

We insert the multiplication expression into parentheses:

$(0\times18)+2=$

We solve the expression in parentheses and then combine:

$0\times18=0$

$0+2=2$

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

Following the simple rule, multiplication comes before division and subtraction, therefore we calculate the values of the multiplications and then proceed with the operations of division and subtraction

$3\cdot5-15\cdot1+3-2= \\ 15-15+3-2= \\ 1$ Therefore, the correct answer is answer B.

Let's simplify this expression while following the order of operations which states that exponents come before multiplication and division, which come before addition and subtraction, and that parentheses must be performed before all else.

We'll start by simplifying the expression inside the parentheses, since multiplication comes before addition and subtraction we'll first perform the multiplication in this expression, while remembering that multiplying any number by 0 will always yield the result 0. Then we'll perform the addition and subtraction operations within the parentheses:

$20\cdot4:5\cdot(3+0\cdot7-1)= \\ 20\cdot4:5\cdot(3+0-1)= \\ 20\cdot4:5\cdot2$

We'll continue and simplify the expression obtained in the last step. Since between multiplication and division operations there is no priority according to the order of operations, we'll perform the multiplication and division operations, etc., one after another from left to right:

$20\cdot4:5\cdot2 =\\ 80:5\cdot2 =\\ 16\cdot2 =\\ 32$

Let's summarize the steps of simplifying the given expression:

$20\cdot4:5\cdot(3+0\cdot7-1)= \\ 20\cdot4:5\cdot2 =\\ 16\cdot2 =\\ 32$

Therefore, the correct answer is answer A.

This simple rule is the foundation of the order of operations which states that exponentiation precedes multiplication and division, which precede addition and subtraction, and that operations enclosed in parentheses precede all others,

First, we pay special attention to the given rule, the first break from the left is the number 0, remember that dividing the number 0 by any number always yields the result 0, (except dividing by the number 0 itself, which is generally forbidden, even though this simple rule that breaks in the given rule, in accordance with the order of operations mentioned, means that this break is worth nothing) therefore the value of this break is 0 and therefore we can simply omit it entirely (as if - the entire break) from the given rule, as this is a common practice that does not contribute anything in terms of numerical value,

$\frac{0}{5+4:2}-(5+3):4= \\ \downarrow\\ 0-(5+3):4= \\ -(5+3):4=$As usual we should not forget to keep the negative sign after the break, as this minus sign indicates multiplication by negative one,

We will continue and simplify this rule,

In accordance with the order of operations mentioned we will start with the multiplication and division operations, next we will calculate the result of the division operation:

$-(5+3):4=\\ -8:4=\\ -2$In the last step we did not forget that dividing a positive number by a negative number yields a negative result,

We received that the correct answer is answer c.

We begin by addressing the numerator of the fraction.

First we solve the division exercise and the exercise within the parentheses:

$400:(-5)=-80$

$(93-61)=32$

We obtain the following:

$\frac{-80-(-2\times32)}{4}=$

We then solve the parentheses in the numerator of the fraction:

$\frac{-80-(-64)}{4}=$

Let's remember that a negative times a negative equals a positive:

$\frac{-80+64}{4}=$

$\frac{-16}{4}=-4$

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 operations within parentheses precede all others,

Let's consider that the numerator is the whole and the denominator is the part which breaks (every break) into whole pieces (in their entirety) among which division operation is performed, meaning- we can relate the numerator and the denominator of the break as whole pieces in closures, thus we can express the given fraction and write it in the following form:

$\frac{(25-2-16)^2+3}{8+5}:\sqrt{9}= \\ \downarrow\\ \big((25-2-16)^2+3\big):(8+5):\sqrt{9}$We highlight this by noting that fractions in the numerator of the break and in its denominator are considered separately, as if they are in closures,

Let's return to the original fraction in question, meaning - in the given form, and simplify, separately, the fraction in the numerator of the break which causes it and the fraction in its denominator, this is done in accordance to the order of operations mentioned and in a systematic way,

Let's consider that in the numerator of the break the fraction we get changes into a fraction in closures which indicates strength, therefore we will start simplifying this fraction, given that this fraction includes only addition and subtraction operations, perform the operations in accordance to the natural order of operations, meaning- from left to right, simplifying the fraction in the numerator of the break:

$\frac{(25-2-16)^2+3}{8+5}:\sqrt{9}=\\ \frac{7^2+3}{13}:\sqrt{9}\\$We will continue and simplify the fraction we received in the previous step, this of course, in accordance to the natural order of operations (which states that exponentiation precedes multiplication and division, which precede addition and subtraction, and that operations within parentheses precede all others), therefore we will start from calculating the numerical values of the exponents in strength (while we remember that in defining the root as strength, the root itself is strength for everything), and then perform the division operation which is in the numerator of the break:

$\frac{7^2+3}{13}:\sqrt{9}=\\ \frac{49+3}{13}:3=\\ \frac{52}{13}:3\\$We will continue and simplify the fraction we received in the previous step, starting with performing the division operation of the break, this is done by approximation, and then perform the remaining division operation:

$\frac{\not{52}}{\not{13}}:3=\\ 4:3=\\ \frac{4}{3}$In the previous step, given that the outcome of the division operation is different from a whole (greater than whole for the numerator, given that the divisor is greater than the dividend) we marked its outcome as a fraction in approximation (where the numerator is greater than the denominator),

We conclude the steps of simplifying the given fraction, we found that:

$\frac{(25-2-16)^2+3}{8+5}:\sqrt{9}=\\ \frac{7^2+3}{13}:\sqrt{9}=\\ \frac{52}{13}:3=\\ \frac{4}{3}$Therefore, the correct answer is answer b'.

Note:

Let's consider that in the group of the previous steps in solving the problem, we can start recording the break and the division operation that affects it even without the break, but with the help of the division operation:

$\frac{52}{13}:3\\ \downarrow\\ 52:13:3$And from here on we will start calculating the division operation in the break and only after that we performed the division in number 3, we emphasize that in general we simplify this fraction in accordance to the natural order of operations, meaning we perform the operations one after the other from left to right, and this means that there is no precedence of one division operation in the given fraction over the other except as defined by the natural order of operations, meaning- in calculating from left to right, (Let's consider additionally that defining the order of operations mentioned at the beginning of the solution, which states that exponentiation precedes multiplication and division, which precede addition and subtraction, and that operations within parentheses precede all others, does not define precedence even among multiplication and division, and therefore the judgment between these two operations, in different closures, is in a different order, it is in calculating from left to right).