Order of Operations with Parentheses

🏆Practice parentheses in advanced order of operations

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!

Solve the following equation:

\( (12 + 8) \div 4 = \)

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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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Example 2

5+83(8:4)=5+8\cdot3-(8:4)=
We'll start by solving the operation inside the parentheses:
5+832=5+8\cdot3-2=
Next, we continue with the multiplications:
5+242=5+24-2=
Finally, we add and subtract:
5+242=275+24-2=27


Example 3

1+915(9:3)=1+9\cdot15-(9:3)=
We'll start by solving the operation inside the parentheses:
1+9153=1+9\cdot15-3=
Next, we continue with the multiplications:
1+1353=1+135-3=
Finally, we add and subtract:
1+1353=1331+135-3=133


Do you know what the answer is?

Example 4

(21+3)24(22:2)= (21+3)\cdot2\operatorname{\cdot}4-(22:2)=

We will start by solving the operation inside the parentheses:
242411= 24\cdot2\operatorname{\cdot}4-11=

Next, we continue with the multiplications:
48411= 48\operatorname{\cdot}4-11=

19211= 192-11=

Finally, we add and subtract:
19211=181 192-11=181


Example 5

(1+9)+(158)(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+1204=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

Solve the following equation:

(12+8)÷4= (12 + 8) \div 4 =

Step-by-Step Solution

To solve the equation, follow these steps:

1. Start by solving the expression inside the parentheses: 12+8 12 + 8 .

2. Calculate 12+8 12 + 8 to get 20 20 .

3. Now divide the result by 4: 20÷4 20 \div 4 .

4. Calculate 20÷4 20 \div 4 to get 5 5 .

Therefore, the final answer is 5 5 .

Answer

5 5

Exercise #2

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)=186=12 18-(3+3)= \\ 18-6= \\ 12

Therefore the correct answer is answer D.

Answer

12

Exercise #3

Solve the following equation:

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

Step-by-Step Solution

First, solve the expression inside the parentheses:
8+5=138 + 5 = 13

Then subtract from 25:
2513=1225 - 13 = 12

Answer

12

Exercise #4

Solve the following equation:

30(10+7)= 30 - (10 + 7) =

Step-by-Step Solution

First, solve the expression inside the parentheses:
10+7=1710 + 7 = 17

Then subtract from 30:
3017=1330 - 17 = 13

Answer

13

Exercise #5

Solve the following equation:

(5010)×2= (50-10) \times 2 =

Step-by-Step Solution

To solve the equation, follow these steps:

1. Start with the expression inside the parentheses: 5010 50 - 10 .

2. Calculate 5010 50 - 10 to get 40 40 .

3. Now multiply the result by 2: 40×2 40 \times 2 .

4. Calculate 40×2 40 \times 2 to get 80 80 .

Therefore, the final answer is 80 80 .

Answer

80 80

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