**Category : **5th Class

**LEARNING OBJECTIVES **

This lesson will help you to-

- learn about the concept of BO&MAS.
- study about the application of BO&MAS in
- study about the importance of BO&MAS rule while solving mathematical problems.

**Real – Life Example**

- The rules of BODMAS are very important in daily accounting and calculations and are used frequently by bankers, accountants, students and even housewives.

** **

**Amazing Fact**

- As in India we often hear about BODMAS in USA the acronym PEMDAS in used. The full form of PEMDAS is ‘Parentheses, Exponents, Multiplication, Division, Addition and Subtraction.

**QUICK CONCEPT REVIEW **

Lesson in a Nutshell

**BODMAS:** BODMAS is the sequence for working out and constructing mathematical equations and formulas containing more than one calculation. This methodology is commonly referred to as the order of mathematical operations.

**Operations:** "Operations" in mathematics refer to addition, subtraction, multiplication, division, etc. If it isn't a number it is probably an operation.

B RACKETS ( ) [ ] { }

O RDER POWER OF \[\sqrt{{}}{{\left( {} \right)}^{2}}\]

D IVIDE \[/\div \]

M ULTIPLY \[*\times \]

A DDITTION +

S UBTRACTION ____

- Divide and Multiply rank equally (and go left to right).
- Add and Subtract rank equally (and go left to right).

** **

**Historical preview**

- Since the introduction of modern algebraic notation, multiplication has taken precedence over addition Thus \[3+4\times 5=4\times 5+3=23.\] When exponents were first introduce in the 16 th and 17 th centuries, exponents took precedence over both addition and multiplication and could b3e placed only as a superscript to the right of their base. Thus 3 + 52 = 28 and \[3\times 52=75.\] To change the order of operations, o9riginally a vinculum (an over line or underline) was used. Today, parentheses or brackets are used to explicitly denote precedence by grouping parts of an expression that should be evaluated first.

- After you have done ‘’B’’ and ‘’O’’, Just go from left to right doing and ‘’D’’ or ‘’M’’ as you find them.
- Then go from left to right doing any ‘’A’’ or ‘’S’’ as you find them.

Steps to simplify the order of operation using BODMAS rule:

- First part of an equation is start solving inside the ‘Brackets’’

**For Example :** \[\left( 6+4 \right)\times 5\]

First solve inside ‘brackets’ 6 + 4 = 10, then \[10\times 5=50.\]

- Next solve the mathematical ‘Of’

**For Example :** 3 of 4 +n 9

First solve ‘of’ \[3\times 4=12,\] then 12 + 9 = 21.

- Next, the part of the equation is to calculate ‘Division’ and Multiplication’.

We know that, when division and multiplication follow one another, then their order in that part of the equation is solved from left side to right side.

**For Example: \[15\div 3\times 1\div 5\]**

‘Multiplication’ and ‘Division’ perform equally, so calculate from left to right side. First solve \[15\div 3=5,\] then \[5\times 1=5,\] then \[5\div 5=1.\]

- In the last part of the equation is to calculate ‘Addition’ and Subtraction’.

We know that, when addition and subtraction follow one another, then their order in that part of the equation is solved from left side to right side.

**For Example:** 7 + 19 – 11 + 13

‘Addition and ‘Subtraction’ perform equally, so calculate from left to right side. First solve 7 + 19 = 26, then 26 – 11 = 15 and then 15 + 13 = 28.

**Misconcept/ Concept **

**Misconcept:** Some question, for example are written as \[6\div 2\left( 1+2 \right).\] There is no sign between 2 and (. This is often misinterpreted as division.

**Concept:** The absence of sign indicates a multiplication So, this expression is actually \[-6\div {{2}^{*}}\left( 1+2 \right).\] The BODMAS rule says –

**First Brackets**

Then Of

Then Division and Multiplication in the order they appear from left to right.

Then Addition and Subtraction in the order they appear from left to right.

Thus note that BODMAS rule does not say that division comes before multiplication. It also does not say that Addition comes before subtraction.

In the above example, first we will solve the brackets: 1 + 2 = 3. So now the equation gets converted to \[6\div {{2}^{*}}3.\] Now the division AND multiplication will be evaluated from left to right. So \[6\div 2=3\] and \[{{3}^{*}}3=9.\] The correct answer is 9.

These are simple rules need to be followed for simplifying or calculating using BODMAS rule.

Rules of BODMAN are same with integers, decimals and fractions.

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