Simplification

## Simplification

### VBODMAS Rule

• When an expression involves the + and – signs, the order of operation is from left to right

### .

• Thus 20 – 15 + 2 – 4 means that 15 is to be subtracted from 20 then 2 is to be added to the result and then 4 is to be subtracted from the result.
• When an expression involves x and ÷ signs, the order of operation is from left to right. Thus 55 ÷ 5 x 3 means that 55 is to be divided by 5 and the result is to be multiplied by 3.
• 45 x 5 ÷ 3 means that 45 is to be multiplied by 5/3.
• When an expression involves all the signs (i.e. +, –, x, ÷) then division and multiplication must be performed before addition and subtraction.

### Brackets

• The expressions within brackets are to be treated as a single identity thus 6 x (3 – 2) means that 6 is to be multiplied by the difference of 3 and 2.
• So 6 x (3 – 2) = 6 x 1 = 6

Note: Operations within the bracket are to be carried first.

Brackets are of 4 types.

• Bar bracket or Vinculum
• Circular bracket ( )
• Curly bracket { }
• Square bracket [ ]

### Removal of a bracket

• 5 + (9 + 2) is equal to 5 + 11 = 16
• 5 + (9 – 2) is equal to 5 + 7 = 12
• The rule is that when a bracket is preceded by a + sign, the bracket may be removed without making any change in the expression.
• Now consider the expressions when the bracket is preceded by a ‘–’ sign
•  20 – (8 + 3) = 20 – 11 = 9 also 20 – (8 + 3) = 20 – 8 – 3 = 9
• 20 – (8 – 3) = 20 – 5 = 15 also 20 – (8 – 3) = 20 – 8 + 3 = 12 + 3 = 15
• The rule is that if a bracket is preceded by a negative (–) sign, the bracket can be removed by changing the sign of every term within the bracket.

### Bracket within a bracket

• Let us take an example
• Supposing we want to simplify

• We will first remove the bar bracket then circular bracket, then curly bracket and at the last stage we remove the square bracket.
• So the expression given above is

= 24 – [12 – {8 – (9 – 2 – 3)}]

= 24 – [12 – {8 – 4}]

= 24 – [12 – 4]

= 24 – 8

= 16

• The rule of VBODMAS gives us the arrangement according to which an expression is to be simplified. VBODMAS stands for vinculum, brackets, of, division, multiplication, addition and subtraction respectively.
• Algebraic Identities: The algebraic identities noted below are used as expression formulae:

## General Rules For Solving Problems In Arithmetic

• (a+b) (a-b) = a2 - b2
• (a+b)2 = a2 + b2 + 2ab
• (a – b) 2 = a2 + b2 – 2ab
• (a + b)3 = a3 + b3 + 3ab (a+b)
• (a – b)3 = a3 – b3 – 3ab (a–b)
• a2 + b2  =  (a + b)2   – 2ab
• a3 + b3 = (a+b) (a2 + b2 – ab) = (a+b)3 – 3ab (a+b)
• a3 - b3  =  (a – b) ( a2 + b2 + ab) =  (a–b)+ 3ab (a-b)
• a3 + b3 + c3 = (a + b + c) (a2 + b2 + c2 – ab – bc – ca) + 3abc If a + b + c = 0, then a3 + b3 + c3 = 3abc
• (a+b+c)2 = a2+b2+c2+2ab+2bc+2ca
• (a+b+c)3 = a3+b3+c3+3a2 (b+c) + 3b2(a+b)+3c2(a+b)+6abc [remember there are ten terms]
• To find the sum of a and b, given their difference and product:
a + b =
• To find the difference of a and b, given their sum and product: a – b =

### Questions on Simplification

• Generally the types of questions which can be asked for simplification are of the following types.

### Type 1

• Questions involving expressions in which the items / numbers are either to be added or subtracted. The numbers may be integers or decimals.

### Type – II

• The numbers to be added or subtracted are fractions. The fractions may be pure or mixed fractions.

### Type – III

• The numbers or items in the expression are connected with the signs of multiplication or division e.g.

i) 1.6 x 20 x 12 + 30 x 2

ii) 2.21 ÷ 0.7 = ? + 5.5

iii) 4545 ÷ 50 ÷ 5 = ?

### Type – IV

• These questions contain signs of multiplication, division, percentage, of, etc and also fraction e.g.

i) 35% of 495 + ? = 250

ii)

iii) 30% 150 + ? of 300 = 40 % of 450

### Type V

• Square – roots and cube roots along with fractions etc. are there in this type of questions on simplification like.

### Type VI

• This type of questions may relate to surds and / or indices like

i) (19.7)5 ÷ (19.7)4 =?

ii) 2310.5 x 235.1 ÷ 231.2 = 23?

### Type VII

• Type VII may relate to inequalities or equalities with signs of (<, =, >)
The document Simplification | General Test Preparation for CUET is a part of the CUET Course General Test Preparation for CUET.
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## FAQs on Simplification - General Test Preparation for CUET

 1. What are the general rules for solving problems in arithmetic simplification?
Ans. The general rules for solving problems in arithmetic simplification include performing operations inside parentheses first, followed by multiplication and division from left to right, and finally addition and subtraction from left to right.
 2. How do I simplify arithmetic expressions involving parentheses?
Ans. To simplify arithmetic expressions involving parentheses, you should start by performing operations inside the innermost set of parentheses first. Repeat this process for any remaining sets of parentheses until all parentheses have been removed.
 3. What is the order of operations in arithmetic simplification?
Ans. The order of operations in arithmetic simplification, also known as PEMDAS, is as follows: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
 4. Can you provide an example of simplifying an arithmetic expression using the order of operations?
Ans. Certainly! Let's simplify the expression: 3 + 4 * (2 - 5). First, we evaluate the expression inside the parentheses: 2 - 5 = -3. Then, we multiply 4 by -3: 4 * (-3) = -12. Finally, we add 3 to -12: 3 + (-12) = -9. Therefore, the simplified expression is -9.
 5. Are there any exceptions to the order of operations in arithmetic simplification?
Ans. Yes, there are exceptions to the order of operations in arithmetic simplification. For example, if there are multiple operations with the same precedence (e.g., multiplication and division), you should perform them from left to right. Additionally, if there are nested parentheses, you should start with the innermost set and work your way outwards.

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