When solving an equation, a set of guidelines known as the order of operations must be followed. When we use the word “operations” in math, we refer to the process of evaluating any mathematical expression, which includes arithmetic operations like addition, subtraction, multiplication, and division. In this article, we explain the rules governing the order of operations in detail and provide some examples.
What is the order of operations?
The order of operations is a mathematical principle that dictates that, from left to right, we should evaluate parentheses and brackets first, exponents and orders second, division or multiplication third, and addition or subtraction last.
In arithmetic, evaluating a math expression may require us to perform numerous mathematical operations, and achieve several outcomes by simplifying the answer. For every kind of expression, there can only be one right response.
We use a set of rules to simplify any given mathematical phrase in order to find the correct answer. All of the fundamental mathematical operators are based on these rules: Addition (+), subtraction (-), division (÷), and multiplication (x) are examples of operators.
BIDMAS
BIDMAS is key to the order of operations. It stands for:
- Brackets ( x )
- Indices x2
- Division ÷
- Multiplication x
- Addition +
- Subtraction –
When faced with an equation, start solving from the top (brackets) and working your way down to subtraction.
How to solve a problem in mathematics
Why is the order of operations important?
A mathematical problem’s various components should be solved in a specific order according to the order of operations. Calculation is just another word for operation. Examples of operations include addition, subtraction, multiplication, and division.
The importance of the order of operations stems from the fact that it ensures that everyone can understand and approach a mathematical problem the same way to arrive at the right answer. Formulas for actual calculations in science and finance would be quite worthless without a set order of operations, and it would be challenging to determine whether your response on a math test was correct.
The order of operations in mathematics helps determine the right value for an equation. By way of analogy, the order of events plays a role in daily life as well. For instance, it will be difficult to get dressed if you put on your shoes before your pants. Similarly, if you don’t follow the correct procedure while cooking, the result will be a kitchen disaster.
Ways to Remember Order of Operations
BIDMAS, PEMDAS, and BODMAS are three distinct words that all mean the same thing. You may get mixed up so try remembering them with a pneumonic. For example, the phrase “Please Excuse My Dear Aunt Sally” is a reminder of PEMDAS.
It stands for “Parentheses, Exponents, Multiplication, Division, Addition, Subtraction”. Similarly, by using the word BODMAS, we can recall the sequence of events (Brackets, Orders, Division, Multiplication, Addition, and Subtraction).
Implementing the suggested actions is the simplest approach to learn the order of operations:
- First begin by condensing terms inside the brackets.
- Then put the exponential terms to use.
- Division or multiplication should come next.
- Conclude by counting, deducting, or adding.
How to follow the order of operations in mathematics
Rule 1
Take note of the expression. The first rule is to solve the numbers that are enclosed in brackets or parentheses. We resolve grouping operations from the inside out. There is a certain way to solve the parenthesis, i.e., [ () ], therefore take note of the pattern of brackets that are present in the phrase.
First, solve the round brackets (), then the curly brackets { }, then the box brackets [ ]. What this means is that whatever equation is within the brackets, you solve that first before anything else.
Rule 2
Search for and solve any number that is present in the form of exponents after solving the numbers in the parenthesis.
Rule 3
We are now down to the fundamental four operators. Find the numbers that have been multiplied or divided, and then solve them from left to right.
Rule 4
Finally, search for terms with addition or subtraction and work your way right to left.
Examples of order of operations
To understand the rules used in the order of operations, let’s take a look at some practical examples.
2 + 4 x 12 = ?
Following BIDMAS, we can see that multiplication comes before addition. Therefore, while you may be tempted to solve as you usually do from left to right, you must first tackle 4 x 12.
4 x 12 = 48
Next, we can move on to addition.
2 + 48 = 50
Our answer is 50 but what would have happened if we hadn’t followed the order of operations?
2 + 4 x 12 = 72
72 is the wrong answer, and by a large amount. This shows the importance of following the order of operations.
4 x (5 + 2) = ?
According to BIDMAS, we must first tackle the brackets.
(5 + 2) = 7
Then we can tackle the multiplication.
4 x 7 = 28 is the correct answer.
If we hadn’t followed the order of operations, we would have gotten an answer of 22 which is, again, off target.
3 x 102 = ?
According to BIDMAS, we must first tackle the indices (power).
102 = 100
Then we can multiply.
3 x 100 = 300
2 x (3 x 4) + 42 = ?
This is a complex one so you may be unsure where to begin. Nevertheless, using BIDMAS you will find the right answer.
First, you must tackle the brackets (3 x 4).
(3 x 4) = 12
Now our equation reads 2 x 12 + 42 = ?
According to BIDMAS, we must now tackle the indices (power).
42 = 16
Therefore: 2 x 12 + 16 = ?
Next we do multiplication.
2 x 12 = 24
Therefore: 24 + 16 = ?
And finally, we add.
24 + 16 = 40
As such, 2 x (3 x 4) + 42 = 30
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