Why it is important in mathematical Order of Operations? How to solve BODMAS questions in math? Easy tricks to learn the Formula and Meaning with Sample Questions. In math, Operations is a mathematical process that is used to solve a problem. If we do not use the order, then it’s possible that we could get all get different answers. So, Order of Operations becomes very important in solving mathematics. Through Exampitara, you can learn the easy trick to understand the concept of the BODMAS rule and how it works in simplifying expressions with standard rules.
Introduction to BODMAS Rule
Mathematics is a field that depends on logic and some standard rules that make the calculation easier. So, BODMAS is an order of operations used to solve mathematical equations. BODMAS is an acronym that stands for B-Brackets (always solve the number inside the bracket), O-Order of power or roots, D-Division, M-Multiplication, A-Addition, and S-Subtraction.
According to the BODMAS rule, for solving an expression, we need to start with brackets, then with exponents, division, multiplication, addition, and at last, subtraction. We must need to remember the order while solving the mathematical operations, otherwise we can get the wrong answer for the expression.
What is the rule of BODMAS in mathematics?
In arithmetic expression, the BODMAS equation contain two components-
- Numbers
A number is a mathematical value that presents a specific quantity and is basically used in counting and calculations. Different symbols are used to present particular numbers and can be divided into the following parts-
- Whole Numbers
- Natural Numbers
- Rational Numbers
- Irrational Numbers
- Real Numbers
- Complex Numbers
- Imaginary Numbers
- Integers
- Operators or Operations:
Order of Operations involves characters that connect two numbers, creating an equation. However, the common operators used in mathematics are-
- Division (÷)
- Multiplication (x)
- Subtraction (-)
- Addition (+)
Why BODMAS rule is important in mathematics?
Numbers are everywhere and choosing the correct method of mathematical rule helps in gaining the right answer. Learning BODMAS is an important part of mathematics and that’s not only clear your basics but also helps in solving many mathematical problems. Whenever you see any expression, you get confused about which math operation needs to perform first, so when you know the basics of the BODMAS rule, you can easily determine whether to proceed with addition, subtraction, multiplication, or division. BODMAS rule was invented to help students alleviate the confusion and remember the correct order in which calculations should be performed.
Who invented BODMAS?
BODMAS was invented by mathematician Achilles Reselfelt. He has created the mnemonic so that we can remember easy way to calculate the expression containing more than one mathematical operation.
Meaning of BODMAS: Easy Way to Learn the Formula Step by Step
| 1. | B | [{( )}] | Open the bracket first | Calculate the mathematical operation inside the bracket |
| 2. | O | x² | Order of Powers, Exponent, Indices or Roots | Solve the maths equation containing power or roots |
| 3. | D | ÷ | Division | Calculate the number containing division operation |
| 4. | M | × | Multiplication | Solve out the number containing multiplication operation |
| 5. | A | + | Addition | Calculate the number containing subtraction operation |
| 6. | S | – | Subtraction | Calculate the number containing addition operation |
Rules and Conditions for BODMAS
There are some basic rules and conditions that are necessary to keep in mind while solving problems related to BODMAS equation:
| Condition | Rules |
| a + ( b + c ) ⇒ a + b + c | First, open the bracket and then add all the terms. |
| a – ( b + c ) ⇒ a – b- c | First, open the bracket and then multiply the negative sign with each term present inside the bracket. (Note: All the positive terms will be change to negative and negative terms will be change to positive). |
| a ( b + c ) ⇒ ab + ac | First multiply the term outside the bracket with each term present inside the bracket. |
How to solve BODMAS Questions? Step by Step Method to solve the Mathematical Order of Operations
Let’s take some example to understand the steps for solving a BODMAS equation-
Example 1: 36 ÷ 6 X 3 + 22 – (3 + 5) = ?
Step 1– First, calculate the numbers inside the brackets.
3 + 5 = 8
Now, the equation is 36 ÷ 6 X 3 + 22 – 8
Step 2– Solve out the square (Orders)
22 = 4
After that, the equation is 36 ÷ 6 X 3 + 4 – 8
Step 3- Calculate the division part
36 ÷ 6 = 6
The equation will be 6 X 3 + 4 – 8
Step 4- After that, we need solve out the multiplication part
i.e. 6 X 3 = 18
Our equation now becomes 18 + 4 – 8
Step 5- Solve out the addition part first, and then subtraction
18 + 4 = 22 (addition)
22-8 = 14 (subtraction)
Answer= 14
Example 2: 20 – (10 – 3 + 2)
Step 1- Firstly, open the bracket and multiply the negative sign with each term present inside the bracket.
i.e. 20 – 10 + 3 – 2
Step 2- Add the positive terms and negative terms separately
20 + 3 = 23
And, – 10 – 2 = – 12
The equation now becomes, 23 – 12
Step 3- Subtract the terms
23 – 12 = 11
Answer = 11
Example 3: 5 + [6{5 – 4 + 1}]
Step 1- At first, calculate the term present inside the curly bracket.
i.e. {5 – 4 + 1}
5 + 1 = 6
{6- 4}
{2}
Now, the equation is: 5 + [6 {2}]
Step 2- Multiply the term outside the bracket with term present inside the curly bracket.
i.e [6 X 2] = [12]
Now, the equation become: 5 + [12]
Step 3- Open the bracket and add the terms
5 + 12 = 17
Answer = 17
How to Solve BODMAS Questions without Brackets?
Sometimes, some mathematical expressions do not contain brackets and we get confused if we need to apply the BODMAS rule here or not. In these kinds of situations, we still need to apply the BODMAS rule to solve the expressions. Start solving the question in order followed by division, multiplication, addition, and subtraction. Let’s take an example to understand the concepts more clearly-
Example: 10 + 10 X 10 ÷ 10
As per BODMAS rule, we need to start with division part
Division: 10+10X10÷10 (10 ÷ 10 = 1)
Multiplication: 10+10X1 (10 X 1 = 10)
Addition: 10+10 (10 + 10 = 20)
= 20
Common Mistakes occur while using BODMAS Rule
While applying the BODMAS rule to solve an equation, we can make some common mistakes that end up with the wrong answer. These mistakes can be as follows-
- Due to a lack of proper understanding of the addition and subtraction of integers, the error can occur while adding or subtracting positive or negative terms.
- Multiple brackets in an equation can create confusion.
- Confusion between vinculum and brackets. (Vinculum comes under the VBODMAS rule which specifies that firstly we need to solve the mathematical operation under the bar and then go for removing brackets).
Example: 5- [7-{13-(11-(8-6) ̅)}] = ?
Firstly, simplify the value under bar
(8-6) ̅ = 2
Now, the equation is: 5-[7-{13-(11-2)}]
Then, remove the smaller bracket
5-[7-{13-9}]
Now, remove the middle bracket
5-[7-4]
At last, remove the larger bracket
5-3=2.
Answer= 2
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Frequently Asked Questions on the Concept of BODMAS
- Why do we need to use BODMAS in mathematical expressions?
When we solve a mathematical expression, there are many operations present simultaneously in the expression and we get confused, about which operation we need to solve first. In this situation, BODMAS helps in solving the equation in the correct order so that we get a correct answer for the problem.
- What is the full form of BODMAS in mathematics?
BODMAS stands for B- Bracket, O- Order, D- Division, M- Multiplication, A- Addition and S-Subtraction.
- What does O stands for in BODMAS rule?
O stands for Order of Powers, Exponent, Indices or Roots in BODMAS rule. It means we need to solve the maths equation containing power or roots during O order of operation.
- Can we use BODMAS rule if there is no bracket present in the mathematical expression?
Yes, we can apply the BODMAS rule if there is no bracket present. In this condition, we need to solve the expression by starting the order with O i.e. Order of Powers, Exponent, Indices, or Roots.
- Do we need to subtract first or divide first?
We need to divide first. As per the BODMAS rule, we need to solve divide first and then perform subtraction in mathematical order of operation.
BODMAS or PEMDAS. Which is correct in mathematical order of operation?
Both the order are correct to use. BODMAS stands for B- Bracket, O- Order, D- Division, M- Multiplication, A- Addition, and S-Subtraction while PEMDAS stands for P- Parentheses, E- Exponents, M-Multiplication, and D-Division, A-Addition and S- Subtraction. As “brackets” and “parentheses” are the same and “orders” and “exponents” are the same. Also, we can see that the “M” and the “D” are mentioned in the reversed form in PEMDAS but in the English version, multiplication and division are at the same level. In United State, people use PEMDAS and in countries like India, Bangladesh, and Australia, we use the BODMAS rule.
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