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 problem:

187×(85)= 187\times(8-5)=

Video Solution

Step-by-Step Solution

Apply the distributive property and proceed to multiply each term inside of the parentheses by 187:

187×8187×5= 187\times8-187\times5=

Solve the first multiplication problem vertically, making sure to solve it in the correct order (ones multiplied by ones, ones multiplied by tens, ones multiplied by hundreds )

187×8 187\\\times8

We should obtain the following result: 1496

Proceed to solve the second multiplication problem vertically, once again making sure to solve it in the correct order (ones multiplied by ones, ones multiplied by tens, ones multiplied by hundreds )

187×5 187\\\times5

We should obtain the following result: 935

Now to tackle the next problem:

1496935= 1496-935=

We should once again solve this vertically. Make sure to align the digits properly, ones under ones, tens under tens, etc.:

1496935 1496\\-935

Subtract ones from ones, tens from tens, etc., to obtain the final result: 561 561

Answer

561 561

Exercise #2

9×(2×1)= 9 \times (2 \times 1) =

Step-by-Step Solution

First, calculate the expression within the parentheses:

2×1=2 2 \times 1 = 2

Now, multiply the result by 9:

9×2=18 9 \times 2 = 18

Thus, the final answer is 18.

Answer

18

Exercise #3

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 #4

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 #5

(4+3)×(52)= (4+3)\times(5-2)=

Step-by-Step Solution

First, solve the expression inside the parentheses:

4+3=7 4+3=7

and

52=3 5-2=3

Thus, the equation becomes:

7×3 7\times3

Now, perform the multiplication:

7×3=21 7 \times 3 = 21 .

Answer

21

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