# Order of Operations with Parentheses

🏆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.

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.

## Test yourself on parentheses!

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

## 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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### 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:
$5+24-2=$
$5+24-2=27$

### 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:
$1+135-3=$
$1+135-3=133$

Do you know what the answer is?

### 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:
$48\operatorname{\cdot}4-11=$

$192-11=$

$192-11=181$

### Example 5

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

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

$10+120-4=126$

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

$(85+5):10=$

### Step-by-Step Solution

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

$85+5=90$

Now we'll get the expression:

$90:10=9$

9

### Exercise #2

$8\times(5\times1)=$

### Step-by-Step Solution

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

$5\times1=5$

Now we multiply:

$8\times5=40$

40

### Exercise #3

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

### Step-by-Step Solution

Simplify this expression paying attention to the order of operations which states that exponentiation precedes multiplication and division before addition and subtraction and that parentheses precede all of them.

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

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

99

### Exercise #4

$[(5-2):3-1]\times4=$

### Step-by-Step Solution

In the order of operations, parentheses come before everything else.

We start by solving the inner parentheses in the subtraction operation:

$((3):3-1)\times4=$ We continue with the inner parentheses in the division operation and then subtraction:

$(1-1)\times4=$

We continue solving the subtraction exercise within parentheses and then multiply:

$0\times4=0$

$0$

### Exercise #5

$12:3(1+1)=$

### Step-by-Step Solution

First, we perform the operation inside the parentheses:

$12:3(2)$

When there is no mathematical operation between parentheses and a number, we assume it is a multiplication.

Therefore, we can also write the exercise like this:

$12:3\times2$

Here we solve from left to right:

$12:3\times2=4\times2=8$