Parentheses in advanced Order of Operations: Solving the problem

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 come before all of them,

therefore we'll start by simplifying the expression inside the parentheses and perform the subtraction within them, then since division comes before subtraction, we'll first perform the division operation and then the subtraction operation

$10-(10-4):2= \\ 10-6:2= \\ 10-3=\\ 7$Therefore the correct answer is answer D.

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 come before all of them,

We will therefore start by simplifying the expression inside the parentheses and calculate the result of the addition within them, then - we will first perform the division operation:

$(85+5):10= \\ 90:10= \\ 9$

$$Therefore, the correct answer is answer A.

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 come before all of them,

therefore we'll start by simplifying the expression in parentheses, and perform the addition operation in this expression, then we'll perform the subtraction operation that applies to the expression in parentheses:

$18-(3+3)= \\ 18-6= \\ 12$Therefore the correct answer is answer A.

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 come before all of them,

We will start by simplifying the expression inside the parentheses and calculate the result of the subtraction within them, then - since division comes before subtraction, we will first perform the division operation and then perform the subtraction operation:

$10-(10-4):2= \\ 10-6:2= \\ 10-3= \\ 7$

$$Therefore, the correct answer is answer B.

We'll use the distributive property and multiply each term in parentheses by 187:

$187\times8-187\times5=$

Let's solve the first multiplication problem vertically, making sure to solve it correctly, meaning units times units, units times tens, units times hundreds.

$187\\\times8$

We get the result: 1496

Let's solve the second multiplication problem vertically, making sure to solve it correctly, meaning units times units, units times tens, units times hundreds.

$187\\\times5$

We get the result: 935

Now we'll get the problem:

$1496-935=$

We'll solve this vertically as well. We'll make sure to align the digits properly, units under units, tens under tens, etc.:

$1496\\-935$

We'll subtract units from units, tens from tens, etc., and get the result: $561$

Let's solve the expression $(2+1\times2)^2$ step-by-step, adhering to the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Firstly, handle the expression inside the parentheses $(2+1\times2)$:

• Within the parentheses, according to PEMDAS, we first perform the multiplication $1\times2$ which equals $2$.
• Now, the expression inside the parentheses becomes $(2+2)$.
• Next, perform the addition: $2+2=4$.

Now the expression simplifies to $4^2$.

Second, handle the exponent:

• Calculate the square of 4: $4^2 = 16$.

Thus, the final answer is $16$.

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

$85+5=90$

We should obtain the following expression:

$90:10=9$

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

$(16-6)=10$

$(7-3)=4$

Now we'll get the exercise:

$10\times9+4$

We'll put the multiplication exercise in parentheses to avoid confusion in the rest of the solution:

$(10\times9)+4=$

According to the order of operations, we'll solve the multiplication exercise and then add:

$90+4=94$

First, we perform the operation inside the parentheses:

$12:3(2)$

When there is no mathematical operation between parentheses and a number, we assume it is a multiplication.

Therefore, we can also write the exercise like this:

$12:3\times2$

Here we solve from left to right:

$12:3\times2=4\times2=8$

According to the order of operations, we will first solve the expressions in parentheses and then multiply:

$(12-6+9)=(6+9)=15$

$(7+3)=10$

Then solve the multiplication exercise:

$15\times10=150$

According to the order of operations rules, we must first solve the expressions inside of the parentheses:

$15-9=6$

$7-3=4$

We obtain the following expression:

$6\times4=24$

Let's solve this problem step by step using the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction):

1. First, let's focus on what's inside the parentheses: $\sqrt{36}+9$

2. We need to evaluate the square root first:

• $\sqrt{36} = 6$ (because $6 \times 6 = 36$)

3. Now our expression looks like this: $2\times(6+9)$

4. Next, we perform the addition inside the parentheses:

• $6 + 9 = 15$

5. Our expression is now: $2\times15$

6. Finally, we perform the multiplication:

• $2 \times 15 = 30$

Therefore, $2\times(\sqrt{36}+9) = 30$

This matches the provided correct answer of 30.

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 come before all of them,

In the given expression there is a term in parentheses that needs to be multiplied, we'll start by simplifying this expression, remembering that division comes before addition, so we'll first perform the division operation within the parentheses and then the addition operation in this expression:

$4+(6+6:3)\cdot2= \\ 4+(6+2)\cdot2= \\ 4+8\cdot2=$

Let's continue simplifying the expression we got in the last step, since multiplication comes before addition we'll first calculate the multiplication in the expression and then perform the addition operation:

$4+8\cdot2= \\ 4+16= \\ 20$

Let's summarize the simplification of the given expression, we got that:

$4+(6+6:3)\cdot2= \\ 4+8\cdot2= \\ 20$

Therefore the correct answer is answer C.

According to the order of operations, we will first solve the multiplication exercises in parentheses:

$(13\times2)=26$

$(12\times1.5)=18$

Now we will subtract:

$26-18=8$

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 come before all of them,

Therefore, let's start by simplifying the expression inside the parentheses, remembering that multiplication comes before addition and subtraction and thus we will first perform the multiplications in this expression, then perform the subtraction operations, and finally complete the calculation by performing the subtraction operation on the expression in parentheses:

$17-(3\cdot5-4\cdot2+2\cdot3)= \\ 17-(15-8+6)= \\ 17-13= \\ 4$

Therefore the correct answer is answer C

First, we solve the exercise in the parentheses

$(1+9:9)=$

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

$1+1=2$

Now we obtain the exercise:

$20-2=18$

According to the order of operations, first we solve the exercise within parentheses:

$30+6=36$

Now we solve the exercise

$36:4\times3=$

Since the exercise only involves multiplication and division operations, we solve from left to right:

$36:4=9$

$9\times3=27$

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 come before all of these,

Therefore, we'll start by simplifying the expression in parentheses, and since division comes before addition, we'll first perform the division operation in this expression and then the addition operation:

$4+(6+6:3)\cdot2= \\ 4+(6+2)\cdot2= \\ 4+8\cdot2 \\$We'll continue to simplify the expression we got in the last step, remembering that multiplication comes before addition and therefore we'll first perform the multiplication in the expression and then the addition operation:

$4+8\cdot2= \\ 4+16= \\ 20$Therefore, the correct answer is answer C.

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 come before all of them,

Therefore, we'll start by simplifying the expression in parentheses, since multiplication comes before addition and subtraction we'll first perform the multiplication in the expression and then calculate the result of the addition and subtraction operations in the expression:

$6\cdot(3+5\cdot2-13)= \\ 6\cdot(3+10-13)= \\ 6\cdot0= \\ 0$We completed the calculation above by performing the remaining multiplication, and we also remembered that multiplying any number by 0 will always result in 0.

Therefore, the correct answer is answer B.

According to the rules of the order of operations, we first solve the exercise within parentheses:

$4+5=9$

Now we obtain the exercise:

$2\times3-9:2=$

We place in parentheses the multiplication and division exercises:

$(2\times3)-(9:2)=$

We solve the exercises within parentheses:

$2\times3=6$

$9:2=4.5$

Now we obtain the exercise:

$6-4.5=1.5$