Order of Operations
In logic-oriented subjects like mathematics, the order of operations is a set of standard rules that reflect conventions about which process to perform first to evaluate a given numerical expression. With a basic summation that just has two numbers and one single operation, or sign, it's easy to calculate the result. Either you perform addition, subtraction, multiplication, or division.
BODMAS can be defined as the set of operations that have to be performed first and the conventions that have to be followed. Failing this would lead to a wrong answer. So it is very important to practice and remember BODMAS and follow it whenever it is required.
If you calculate in the wrong order you will get the answer wrong. So learn the order systematically. The bracket comes first, next is the exponents, division multiplication, addition, and then the subtraction.
What exactly is BODMAS?
BODMAS is a set of rules or an order to perform an arithmetic expression so that evaluation becomes easier. Mathematics is all about logic and certain rules are mandatory to be followed. BODMAS is one of them which if not followed the whole answer can go wrong and end up in losing the marks unnecessarily.
BODMAS can be further defined as standard rules for simplifying the expression having multiple operators.
Athematic expressions have mainly two components that are Numbers and operators:
Numbers
Numbers are the values for making calculations and representing the quantities. There are natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, complex numbers.
Operators
The Operators is the combination of two characters that form an expression or the equation. The most common are addition, multiplication. Division and subtraction. Any expression having just one operator, the solving becomes easy but when there are multiple operators it becomes a little tough.
According to BODMAS when we have to solve an expression we have to first solve the expression with brackets then with the exponents, division, multiplication, addition, and subtraction. The order has to be remembered while solving the equations. If you just do without following this rule you will get the answer wrong.
For example:
See the equation (3+4)5+6-2
According to BODMAS:
The first step is to add the numerical that is in the bracket that is 3+4=7
The next step is to multiply 7 with 5=7x5=35
The next step is to add 35+6=41
Then subtract 2 that is 41-2=39
Whenever an equation is involved with bracket, addition, subtraction BODMAS has to be followed. This acronym is created so that it is easier to remember.
FAQs on Bodmas Rule
1. Why do we use Bodmas?
The BODMAS rule helps students by an acronym to remember the proper order of mathematical operations – a correct and proper order in which to solve maths problems. Some children use it as a mnemonic (like Richard Of York Gave Battle In Vain is used to remember colours). When a student completes a mathematical number sentence which involves various different methods of operations, then BODMAS helps them to know a proper order which is to be followed to complete them in.
Anything inside the Brackets should be completed or solved first, then the orders, followed by any of the division or multiplication mentioned and which is finally followed by addition or subtraction. They are very useful for making difficult expressions easier to understand. Unlike the original mathematical rules, such as associativity of addition or distributivity of multiplication over addition, they are not hard and fast rules.
2. What are Bodmas rule examples?
Let us consider, 3 x (2 + 4) + 52. Here, the BODMAS rule states we should calculate operations which is mentioned inside the Brackets first (2 + 4 = 6), then the Orders (52 = 25), then any Multiplication or Division (3 x 6 (the answer to the brackets) = 18), and finally any Addition or Subtraction (18 + 25 = 43). It is highly possible that students can get the answer wrong of 35 by working from left to right.
As per the Bodmas rule, if an expression comprises brackets ((), {}, []) we must first solve or simplify the bracket followed by of (powers and roots etc.), then multiplication, division, subtraction and addition from left to right. Solving the question in the wrong order shall always result in a wrong answer.
3. How is Bodmas calculated?
According to BODMAS rule, the brackets have to be solved first followed by powers or roots (i.e. of), then Division, Multiplication, Addition and at the end Subtraction. Solving any expression is considered correct only if the BODMAS rule or the PEMDAS rule is followed to solve it.
When you finish a mathematical sentence of numbers that are involving various different operations here is when BODMAS helps you to know which order to be followed to complete the questions. Anything which is inside Brackets should be completed first, then the orders, which is followed by any multiplication or division and at last by subtraction or addition. When you complete a mathematical number sentence which involves various different operations then BODMAS ease you to know the proper order to complete them the solution.
4. How does Bodmas rule work?
It explains the order of operations to solve an expression. According to Bodmas rule, if an expression consists of brackets ((), {}, []) we must first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition, and subtraction from left to right.
The order of operations is as follows: 1) simplify terms inside parentheses or brackets, 2) simplify exponents and roots, 3) perform multiplication and division, 4) perform addition and subtraction. Division and multiplications are both given equal priority, as are addition and subtraction. Solving the given solution in the wrong method or order shall results in the wrong answer ultimately.
5. When to use BODMAS?
BODMAS has to be used when there are multiple operations involved in the mathematical calculation. This rule has to be followed so that you get an accurate answer. The rules have to be followed according to BODMAS, that is the calculations in the brackets first then the exponents if any then comes division, multiplication, addition, and then subtraction. This rule has to be remembered so that there is no calculation error while solving any problems.
6. What is the easy way to remember the BODMAS?
The simple rules that have to be followed are that the first the brackets have to be simplified then comes the exponential terms. Once these calculations are done then the calculations with division.multiplication, addition and then subtraction. Division and multiplication have to be performed from left to right and also addition and subtraction to be performed from left to right. If these rules are remembered and followed many mistakes can be avoided. So students should not forget these basic rules of BODMAS.
7. What are the common errors that often happen while using BODMAS?
Usually, when there are multiple brackets the students often get confused. So when there are many brackets one can simplify the similar brackets simultaneously. There might also be an error when there is the involvement of addition and subtraction. Students have to be very careful and take care of the signs so that they get the answers accurately. When there is division and multiplication involved or when there is addition and subtraction one has to perform the calculations always from left to right.
8. What are the conditions for BODMAS?
If there is any bracket involved in the equation then first the bracket has to be opened and then the addition and subtraction has to be performed. If there is a negative sign then open the bracket and multiply the negative sign with each term. If there is any term outside the bracket then multiply the term that is outside with each term in the bracket. The expression or the equation can be simplified easily without any mistakes if these rules are followed.
9. Will the BODMAS rules be applied always?
Yes, even if there are no brackets involved there will be other operations and you have to follow the same set of rules. If there are no brackets involved then the nest simplification should be done with powers and roots the tobe followed by division, multiplication then addition and subtraction. Remembering these rules and applying them will always be beneficial and silly errors can be avoided. Students should always remember and do the simplification. These are simple rules but should be remembered always.
