Calculating the value of an expression that comprises numbers is an essential part of working with numbers.
The “BODMAS rule” defines which operation takes precedence over the others in terms of simplification when an equation contains the operations addition (+), subtraction (-), multiplication (x), division (/), bracket (), and Of (of). To fully grasp the BODMAS rule, we must first define it and understand it with BODMAS rule examples.
What is the BODMAS formula?
To make complex arithmetic equations like multiplication and division simpler to grasp, this mathematical rule or order is used. To solve an issue involving several operators, you must first figure out the correct sequence they should be applied to. We may use the BODMAS rule to tackle this problem.
Explanation of the BODMAS Rule:
It illustrates the sequence of operations that must be carried out when a given statement is solved.
Following the BODMAS rule, when an expression contains brackets ((), []), we must first solve or simplify the bracket, then ‘order’ (which includes powers and roots, among other things), followed by division, multiplication, and addition and subtraction from left to right, and finally removal from left to right. If you try to solve the issue in the incorrect sequence, you will get an erroneous solution.
Note: The letter “O” in the BODMAS complete form is also known as “Order,” It refers to the numbers that include powers, square roots, and other such operations. Check out the examples provided below to understand better how to use the BODMAS rule in practice.
BODMAS Rule in its entirety:
For those unfamiliar with BODMAS, the full name of the acronym stands for Brackets Orders Division Multiplication Subtraction (BODMAS). When implementing the BODMAS rule, it is essential to remember the sequence of these operations.
| B | Brackets | ( ), { }, [ ] |
| O | Order of | Square roots, indices, exponents and powers |
| D | Division | ÷, / |
| M | Multiplication | ×, * |
| A | Addition | + |
| S | Subtraction | – |
To get correct results, it is necessary to follow this procedure.
BODMAS is abbreviated as follows:
Brackets are used to hold things together (Parts of a calculation inside the bracket always come first).
The following is the order of precedence for brackets: [(bar)]
- Orders are placed (powers and square roots)
- Division
- Multiplication
- Addition
- Subtraction
Each letter of the word corresponds to the initial letter of a particular operating system. When an expression has two or more comparable operators in sequence, the order of precedence is left to right. Using BODMAS, we can evaluate an expression in the correct order of importance, avoiding confusion.
Everything inside the bracket is completed first. Then look for any abilities or roots that may exist. Do any division or multiplication in an expression starting from the left and working your way to the right, followed by addition and subtraction beginning from the left and working your way to the right.
In this case, division and multiplication are given equal priority, and addition and subtraction are equally important.
In mathematics, what is the BODMAS Rule?
Mathematics is a subject that is founded on reasoning. In arithmetic, an expression or an equation consists of two components, which are as follows:
Calculations and counting are both made possible by using numbers, which are mathematical values used to represent specific quantities. A numeral is a symbol that is used to indicate a specific number. According to the property, numbers may be grouped into the following categories:
- Natural Numbers are a kind of number that you may find in nature.
- Integers
- Numbers that make sense
- Irrational numbers
- Accurate numbers.
- Numbers that be difficult to understand
- Imaginary Number.
Operators or operations are defined as follows: An operator is a character that joins two integers together to form an expression or equation in mathematics. The following are the most often encountered operators in mathematics:
(+) is used to indicate an addition.
Subtraction is a mathematical operation (-)
Multiplication is a term used to refer to the act of multiplying two numbers together (x)
Division () is a mathematical concept.
The BODMAS rule, which governs the sequence of operations or the precedence of operators in mathematics, is defined as follows: A bar is a symbol used to group the values. Symbols that are grouped are considered as a single statement.
Solved Examples.
The following BODMAS rule examples problems using integers and decimals values.
Question 1: What is the definition of neologism?
Solution:
Calculate the value of 2[2+239-2(17+2)] by multiplying it by two.
The solution is as follows:
Given the situation, 2[2+239-2(17+2)]
By using the BODMAS Rule,
First, make the value between the brackets as simple as possible ()
=2[2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2]
= 2[2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2]
subtraction of the value contained between the brackets
2[2+2] = 2[2+2]
Fill in the blanks between the brackets with the value you want to use.
=2[4]
Finally, combine both numbers to get an answer of 8.
As a result, the value of 2[2+239-2(17+2)] is equal to 8.
Question number two:
Question 2. Find the value of 4.5 – [2 + 0.5 of (2.1 – 1.3 x 1.01)] + [2 + 0.5 of (2.1 – 1.3 x 1.01)].
Solution:
If we consider the following equation: 4.5– [2 + 0.5 of (2.1– 1.31 x 1.01)]
By using the BODMAS Rule,
To begin, simplify the value contained inside the brackets ()
equals [2 + 0.5 of (2.1 – 1.3 x 1.01)] divided by 4.5 “Multiply 1.3 by 1.01” is a mathematical formula.
= 4.5 – [2 + 0.5 of 0] = 4.5 – [2 + 0.5 of 0] .787] “Subtract 1.313 from the sum of 2.1”
Reduce the complexity of the value contained between the brackets []
= 4.5 minus [2 + 1] .4435] “Multiply 0.5 by 0.787” is a mathematical expression.
= 4.5 – 3.4435 = 3.4435 “Insert two values between the square brackets []”
Last but not least, subtract the values.
1.0565 = 1.0565
In this case, the answer is 1.0565 since 4.5 – [2 + 0.5 of (2.1 – 1.3 x 1.01)] is 1.0565.
Conclusion:
Register with Vedantu to answer additional problems involving arithmetic operations utilising the BODMAS rule and other rules that simplify the equations.