Order of Operations with Parentheses

Parentheses in advanced Order of Operations - Examples, Exercises and Solutions
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In previous articles, we have seen what is the order of operations for addition, subtraction, multiplication, and division and also the order we must follow when there are exponents.

When the exercise we need to solve includes parentheses, we always (always!) start with the operation contained within them.

  1. Parentheses
  2. Exponents and roots
  3. Multiplications and divisions
  4. Additions and subtractions

Reminder: when an exercise presents operations that have the same precedence, that is, multiplications and divisions or additions and subtractions, we will solve the exercise from left to right.

Visual representation of BODMAS/PEMDAS rule emphasizing Brackets (Parentheses) as the first step in arithmetic problem-solving, crucial for accurate mathematical operations

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Test yourself on parentheses in advanced order of operations!

\( (7+2)\times(3+8)= \)

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Below, we present to you some examples

Example 1

4+(6:2)=4+(6:2)=
In this exercise, we will start by solving the operation inside the parentheses, and then the rest:
4+(6:2)=4+(3)=4+3=74+(6:2)=4+(3)= 4+3 = 7

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Test your knowledge
Question 1

\( 8\times(5\times1)= \)

Question 2

\( (2+1\times2)^2= \)

Question 3

Solve the following equation:

\( 18-(3+3)= \)

Example 2

5+8⋅3−(8:4)=5+8\cdot3-(8:4)=
We'll start by solving the operation inside the parentheses:
5+8⋅3−2=5+8\cdot3-2=
Next, we continue with the multiplications:
5+24−2=5+24-2=
Finally, we add and subtract:
5+24−2=275+24-2=27

Example 3

1+9⋅15−(9:3)=1+9\cdot15-(9:3)=
We'll start by solving the operation inside the parentheses:
1+9⋅15−3=1+9\cdot15-3=
Next, we continue with the multiplications:
1+135−3=1+135-3=
Finally, we add and subtract:
1+135−3=1331+135-3=133

Do you know what the answer is?
Question 1

\( 10-(10-4):2= \)

Question 2

Solve the following expression:

\( (85+5):10= \)

Question 3

Solve the following expression:

\( 10-(10-4):2= \)

Example 4

(21+3)⋅2⋅⁡4−(22:2)= (21+3)\cdot2\operatorname{\cdot}4-(22:2)=

We will start by solving the operation inside the parentheses:
24⋅2⋅⁡4−11= 24\cdot2\operatorname{\cdot}4-11=

Next, we continue with the multiplications:
48⋅⁡4−11= 48\operatorname{\cdot}4-11=

192−11= 192-11=

Finally, we add and subtract:
192−11=181 192-11=181

Example 5

(1+9)+(15⋅8)−(8:2)= (1+9)+(15\cdot8)-(8:2)=

Let's start by solving the operation inside the parentheses:
(10)+(120)−(4)= (10)+(120)-(4)=

Finally, we add and subtract:
10+120−4=126 10+120-4=126

That is, the order in all exercises will be as follows:

  1. Parentheses
  2. Exponents and roots
  3. Multiplications and divisions
  4. Additions and subtractions

Reminder: when an exercise includes operations that have the same precedence, that is, multiplication and division or addition and subtraction, we will solve the exercise from left to right.

Examples and Exercises with Solutions on Order of Operations with Parentheses

Exercise #1

(7+2)×(3+8)= (7+2)\times(3+8)=

Video Solution

Step-by-Step Solution

Simplify this expression paying attention to the order of operations. Whereby exponentiation precedes multiplication, division precedes addition and subtraction and that parentheses precede all of the above.

Therefore, let's first start by simplifying the expressions within the parentheses. After which we perform the multiplication between them:

(7+2)⋅(3+8)=9⋅11=99 (7+2)\cdot(3+8)= \\ 9\cdot11=\\ 99 Therefore, the correct answer is option B.

Answer

99

Exercise #2

8×(5×1)= 8\times(5\times1)=

Video Solution

Step-by-Step Solution

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

5×1=5 5\times1=5

Now we multiply:

8×5=40 8\times5=40

Answer

40

Exercise #3

(2+1×2)2= (2+1\times2)^2=

Video Solution

Step-by-Step Solution

Let's solve the expression (2+1×2)2 (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+1×2) (2+1\times2) :

  • Within the parentheses, according to PEMDAS, we first perform the multiplication 1×21\times2 which equals 22.
  • Now, the expression inside the parentheses becomes (2+2) (2+2) .
  • Next, perform the addition: 2+2=42+2=4.

Now the expression simplifies to 424^2.

Second, handle the exponent:

  • Calculate the square of 4: 42=164^2 = 16.

Thus, the final answer is 1616.

Answer

16

Exercise #4

Solve the following equation:

18−(3+3)= 18-(3+3)=

Video Solution

Step-by-Step Solution

Let's begin by simplifying the expression following the order of operations.

P- PARENTHESES

E-EXPONENTS

D-DIVISION

A-ADDITION

S-SUBTRACTION

18−(3+3)=18−6=12 18-(3+3)= \\ 18-6= \\ 12

Therefore the correct answer is answer D.

Answer

12

Exercise #5

10−(10−4):2= 10-(10-4):2=

Video Solution

Step-by-Step Solution

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

Therefore, the correct answer is answer B.

Answer

7

Check your understanding
Question 1

Solve the following equation:

\( (29-4):5= \)

Question 2

Solve the following problem:

\( 187\times(8-5)= \)

Question 3

Solve the following equation:

\( 25 - (8 + 5) = \)

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