Order of Operations with Parentheses

πŸ†Practice parentheses

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.

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Test yourself on parentheses!

einstein

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

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


Example 3

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


Do you know what the answer is?

Example 4

(21+3)β‹…2⋅⁑4βˆ’(22:2)= (21+3)\cdot2\operatorname{\cdot}4-(22:2)=

We will start by solving the operation inside the parentheses:
24β‹…2⋅⁑4βˆ’11= 24\cdot2\operatorname{\cdot}4-11=

Next, we continue with the multiplications:
48⋅⁑4βˆ’11= 48\operatorname{\cdot}4-11=

192βˆ’11= 192-11=

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


Example 5

(1+9)+(15β‹…8)βˆ’(8:2)= (1+9)+(15\cdot8)-(8:2)=

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

Finally, we add and subtract:
10+120βˆ’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.


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