Order of Operations with 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.

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.

Detailed explanation

Start practice

Test yourself on parentheses in advanced order of operations!

Solve the following equation:

$$ 18-(3+3)= $$

Practice more now

Below, we present to you some examples

Example 1

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

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Test your knowledge

Question 1

Solve the following:

$$ 18-(3+3)= $$

Question 2

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

Question 3

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

Example 2

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

Example 3

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

Do you know what the answer is?

Question 1

$187\times(8-5)=$

Question 2

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

Question 3

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

Example 4

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

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

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

$192-11=$

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

Example 5

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

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

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

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

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:

$18-(3+3)=$

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

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

Therefore the correct answer is answer D.

Answer

Exercise #2

Solve the following:

$18-(3+3)=$

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,

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.

Answer

Exercise #3

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

Video Solution

Step-by-Step Solution

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.

Answer

Exercise #4

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

Video Solution

Step-by-Step Solution

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.

Answer

$7$

Exercise #5

$187\times(8-5)=$

Video Solution

Step-by-Step Solution

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: $561$

Answer

$561$

Check your understanding

Question 1

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

Question 2

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

Question 3

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

Start practice

Order of Operations with Parentheses

Test yourself on parentheses in advanced order of operations!

Below, we present to you some examples

Example 1

Example 2

Example 3

Example 4

Example 5

Examples and Exercises with Solutions on Order of Operations with Parentheses

Exercise #1

Video Solution

Step-by-Step Solution

Answer

Exercise #2

Video Solution

Step-by-Step Solution

Answer

Exercise #3

Video Solution

Step-by-Step Solution

Answer

Exercise #4

Video Solution

Step-by-Step Solution

Answer

Exercise #5

Video Solution

Step-by-Step Solution

Answer

More Questions

Parentheses in advanced Order of Operations