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Numbers and Symbols Interchange

We are all familiar with the symbols used for indicating mathematical operations such as addition, subtraction, multiplication, division, etc. When more than one symbol is used in a mathematical expression, we are not supposed to carryout the operations at our discretion. There is a rule as to which operation is to be carried out first known as BODMAS rule. Each letter of the word BODMAS represents a mathematical operation and the order of the letters indicate the order in which the operations are to be carried out. The operations indicated by the letters in BODMAS are given below:
B Brackets Removal of bracket (After simplifying the terms therein).
O Order (exponents) Conversion of exponents to normal form.
D Division  
M Multiplication  
A Addition Addition of numbers with like signs.
S Subtraction Subtraction of numbers with opposite signs.
BODMAS rule should be applied for simplifying the terms inside the bracket also.

Though we are familiar with the BODMAS rule, one example is given below, so as to recollect the concept. Consider the following expression.
x = (2 + 3)2 + 2 × 3 + (4 ÷ 6) ÷ 5 - 3
The above expression can be simplified by using BODMAS rule in the following order.
Step 1: Remove the brackets.
x = 52 + 2 × 3 + 10 ÷ 5 – 3
Step 2: Convert the exponent to normal form.
x = 25 + 2 × 3 + 10 ÷ 5 - 3
Step 3: Carryout division.
x = 25 + 2 × 3 + 2 – 3
Step 4: Carryout multiplication.
x = 25 + 6 + 2 – 3
Step 5: Carryout addition.
x = 33 – 3
Step 6: Carryout subtraction.
x = 30
  • The operations Division and Multiplication can be performed simultaneously. Similarly, the operations Addition and Subtraction can be performed simultaneously.
    After removing Brackets and converting the exponents to normal form, just proceed from left to right performing Division or Multiplication as you find them. Then again go from left to right performing Addition or Subtraction as you find them.
  • In some books, it is given that the letter ‘O’ of BODMAS stands for the operation ‘Of’, which is nothing but multiplication.
    For example, Description: 50932.png of 12, means  × 12 = 4.

In this chapter, we deal with the numbers given in the form of mathematical expressions (or equations). We are asked to interchange the numbers or symbols or both in the given mathematical expression. Four options are normally given for each problem, out of which only one holds good. We have to interchange the numbers or symbols or both as suggested in the problem and simplify the expression to find out which option is correct.

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