In easy words, order means the sequence and operations means the tasks and if confined together the term would mean the sequence of doing multiple tasks. Now coming to mathematical terms, the order is a universally accepted sequence and operations refer to the basic operations like addition, subtraction, multiplication, division etc. and when the terms are confined it becomes an order of operations that means an organised way of approaching any mathematical problem which involves multiple operations. Hence, order of operations, i.e., BODMAS has a rule guiding us the correct approach to sort any mathematical or algebraic expression.

This may help anyone to solve any complex expression or equation in a step-by-step and easy way. The rule is generally called BODMAS or PEMDAS (in some countries).

## The basic rule- BODMAS

The rule makes it easy to solve different expressions and their subexpressions in an orderly way avoiding confusion. Each alphabet in the word BODMAS means a particular operation. The order of operations as expressed by the rule can be explained as

- Brackets: Priority is given to brackets and again there is a systematic order of solving brackets. The order of solving brackets is first to come bar bracket-, then stands the round brackets (), third in the line is the curved {}, and then last is the square brackets []. The brackets in any expression or equation are the first to be solved and if it’s the case of multiple brackets then the said order of the same is to be followed.
- Of: Then comes the operation of exponents (of multiplication on account of exponents) to be solved and proceed further.
- Then the order continues with division (÷), multiplication (×), addition (+), and subtraction (-).

## Rules to be followed

These steps represent the actual meaning of the rule. In order to solve any particular problem of operations, the rule of operations is particularly used moving left to right on account of the acronyms. The sequence follows the below-mentioned details:

- First, we start with observing the equation, and then the solution is started in a sequence of solving the operations by grouping them first inside the brackets or the parenthesis from inside to outside. The above-mentioned order of brackets i.e., [{()}] is followed in case of multiple brackets and that is followed by the sequence of operations.
- After getting all the Brackets solved one should look for the number with an exponent in any form. Solving exponents form the second rule of the concept.
- Now, moving left to right we have our four mathematical operators and rule number three makes it mandatory to solve them in order as in starting from division over to multiplication then consider addition, and last but not the least is the subtraction.

The acronyms used are different at some places, namely BODMAS and PEMDAS. Cuemath describes the topic with examples and rules in such a way that it’s tough to make a mistake at any point of the question.

## BODMAS Vs PEMDAS

Recalling BODMAS

- BRACKETS
- O for the Order
- Division
- Multiplication
- Addition

Expanding PEMDAS

- Parenthesis
- Exponents
- Multiplication
- Division
- Addition

With the use of any of the above orders, it becomes very simple to work out even the toughest problem. Let’s understand the concept with a few examples.

Expression: {(4 + 4-1) ÷7} × 2

Solution: Application of BODMAS,

Bracket first we get {7÷7} × 2

Then again solving curved brackets we get 1×2= 2

Thus, solved.

Equation: 2x= 3*(2-1) +3, find x

Solution: Using the rule 2x= 3*1+3 which makes 2x= 3+3 and the result is x=6/2=3.

Solved.

Thus, with the help of order of operations both the expression and equation can be solved with ease. This becomes the perfect sequential approach to any operation. Integers can be positive or negative. Sometimes negative signs create confusion but following the rule carefully lets you out of all troubles. Just be careful while multiplying the signs in the case of integers. In mathematics as well as computer programming, the order of operations is also called the precedence rule.