The order of operations is a convention used to determine which operations are performed first. In every math exercise that combines more than one operation (addition, subtraction, multiplication, division, etc.), each operation must be performed in a specific order:

It is important to perform the operations in the right order to arrive at the correct result.

The first operations we have to solve are those in parentheses. Once solved, we can continue. Some exercises include parentheses inside other parentheses. In such cases, we must first solve the internal parentheses before solving the external ones.

The next operations that we must solve are powers and roots, also referred to as 'exponents'. When these are inside parentheses, we solve them first in order to solve the parentheses.

The next operations we must perform are multiplication and division. When there is more than one in the exercise, they must be solved in order from left to right.

The last operations to perform are addition and subtraction. These must also be solved from left to right in instances when there is more than one in the same exercise.

Order of Elementary Operations with Combined Operations

Before talking about more advanced mathematical operations, it is important to know the order in which the elementary mathematical operations (addition, subtraction, multiplication and division) are solved.

In each exercise we will solve these operations in the following order:

Multiplication and division

Addition and subtraction

For example, in the exercise:

$4+5\times7$

First, we solve the multiplication $\left(5\times7=35\right)$ before adding the $4$. The result is $39$.

When we have only one type of operation (only multiplication and division, or only addition and subtraction), we solve the exercise from left to right.

Let's look at the following example:

$4-3+7-5$

In this exercise, we have only one type of operation (addition and subtraction). Therefore, we solve it from left to right:

$4-3=1$

$1+7=8$

$8-5=3$

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Order of Operations โ Addition and Subtraction (from left to right)

Parentheses

Powers and roots

Multiplication and division

Addition and subtraction

Review Questions

What is the order when solving an equation?

It depends on the type of equation. However, it is important not to confuse the term 'equation' with the term 'expression'. This article deals with arithmetic expressions.

To solve an equation, for example a first-degree equation, both sides must be simplified using the order of operations. If there are unknown variables on both sides, they must be put together on a single side.

What is solved first in an expression?

Operations inside parentheses

Powers and roots

Multiplication and division

Addition and subtraction

Which is performed first, addition or subtraction?

They are performed in order from left to right.

What is a combined operation?

An arithmetic expression which include several operations.

What is the order of combined operations without parentheses?

Powers and roots

Multiplication and division

Addition and subtraction

What is the order of operations?

It is the order in which operations are carried out in an exercise.

Which operation has the highest priority?

The powers and roots. Parentheses are not really operations, but rather symbols that help us group operations together.

Which is solved first when there are no parentheses, addition or multiplication?

examples with solutions for order of arithmetic operations

Exercise #1

Solve:

$-5+4+1-3$

Video Solution

Step-by-Step Solution

According to the order of operations, addition and subtraction are on the same level and, therefore, must be resolved from left to right.

However, in the exercise we can use the substitution property to make solving simpler.

-5+4+1-3

4+1-5-3

5-5-3

0-3

-3

Answer

$-3$

Exercise #2

$3+4-1+40=$

Video Solution

Step-by-Step Solution

According to the rules of the order of arithmetic operations, we solve the exercise from left to right since it only has addition and subtraction operations:

$3+4=7$

$7-1=6$

$6+40=46$

Answer

$46$

Exercise #3

$-7+5+2+1=$

Video Solution

Step-by-Step Solution

According to the rules of the order of arithmetic operations, we solve the exercise from left to right since it only has addition and subtraction operations:

$-7+5=-2$

$-2+2=0$

$0+1=1$

Answer

$1$

Exercise #4

$9+3-1=$

Video Solution

Step-by-Step Solution

According to the rules of the order of arithmetic operations, we will work to solve the exercise from left to right:

9+3=11

11-1=10

ย

And this is the solution!

Answer

$11$

Exercise #5

Solve:

$9-3+4-2$

Video Solution

Step-by-Step Solution

According to the rules of the order of operations, we will solve the exercise from left to right since it only has addition and subtraction operations: