BODMAS Rule In Maths with Sign Replacement: Check Out Simplification Tricks Here

The number series in the aptitude section is a very important topic for competitive exams. This topic is divided into several small topics and one such topic is a simplification. In this topic the questions asked is related to the BODMAS rule. This rule is very common in mathematics. It stands for Bracket Of Division Multiplication Addition and Subtraction. Thus, today we are going to cover simplification on BODMAS rule. Though this area may have less of direct questions appearing in most of the competitive exams, but its indirect application makes this topic very relevant from the Quant section point of view. Simplification or simplify fractions means to simplify a complicated mathematical expression to get a single or direct answer.

Now our basic understanding of mathematical operations is strong. We know how to add, subtract, multiply and divide even large numbers. But how do we solve a question that involves all of these operations? Come let us find out using the BODMAS rule.

We have shown here 2 tricks to solve the Simplification Question:

Trick 1: Sign Replacement

  • Multiply replace with subtraction: * => –
  • Addition replace with division: + => /
  • Division replace with addition: / => +
  • Subtraction replace with addition: – =>+

Trick 1:  BODMAS Rule

  • Bracket (Brackets are solved in order of (), {} and [] respectively.
  • Orders (i.e. power and square root)
  • Division and Multiplication (Left to right)
  • Addition and Subtraction (Left to right)

Steps to solve BODMAS Question

Step 1: Always remember to solve the expressions that are in the bracket first. Also, while solving these brackets you need to apply the BODMAS rule first.

Step 2: After solving the brackets, you need to solve the mathematical operators ‘order’ and ‘of’ next. Here, ‘of’ means a part of and it is solved by replacing it with a multiplication sign. While ‘order’ is similar to an exponent. After the brackets are solved, powers are solved. This also includes the roots.

Step 3: In the next step, the equations that have multiplication and division sign in it is solved left to right. You need to calculate this after completing the above 2 steps.

Step 4: At the end, you need to solve the equations left to right that contain ‘subtraction’ and ‘addition’. Here you can notice that these steps also followed the BODMAS rule.

Example 1: 15+2/800+80×100 =?

  • Replace all sign using the trick 1 (i.e. 15/2+800/80-100).
  • After that apply BODMAS rule left to right (i.e. 7.5 + 800/80-100)
  • Then divide 800 to 80 (i.e. 7.5 + 10 -100)
  • Solve left to right (i.e. 17.5-100)
  • Answer is -82.5

Example 2: 36+18/12-44×30 =?

  • Replace all sign using the trick 1 (i.e. 36/18*12+44-30).
  • After that apply BODMAS rule left to right (i.e. 2*12+44-30 )
  • Then multiply 2 to 12 (i.e. 24+44-30 )
  • Solve left to right (i.e. 68-30 )
  • Answer is 38

Simplifying the Brackets

The expansion of brackets is known as the simplification of the brackets. To remove the brackets from an expression, you need to expand them by multiplying them. Also, for this step, you can use the distributive law. It is written as

a(b + c) = ab + bc

For brackets also there is a rule that you need to follow while simplifying them. You need to follow the order of (), {}, [ ] for solving the brackets. This means that you solve the equations in the () bracket first and then the other two.

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