**Simplification and Approximation forms an important part of all Banking exams as 3-5 questions are expected from this chapter alone. In Simplification, we have to simplify & calculate the given expressions whereas, in Approximation, we take the approximate values & give the answers accordingly.**

**Basic Rules of Simplification**

**BODMAS Rule**

**It defines the correct sequence in which operations are to be performed in a given mathematical expression to find the correct value. This means that to simplify an ****expression, the following order must be followed –**

**B = Bracket,**

**O = Order (Powers, Square Roots, etc.)**

**D = Division**

**M = Multiplication**

**A = Addition**

**S = Subtraction**

**1. Hence, to solve simplification questions correctly, you must apply the operations of brackets first. Further, in solving for brackets, the order – (), {} and [] – should be stricly followed.**

**2. Next you should evaluate exponents (for instance powers, roots etc.)**

**3. Next, you should perform division and multiplication, working from left to right. (division and multiplication rank equally and are done left to right).**

**4. Finally, you should perform addition and subtraction, working from left to right. (addition and subtraction rank equally and are done left to right).**

**EXAMPLE 1**:

**Solve** 12 + 22 ÷ 11 × (18 ÷

3)^2 – 10

= 12 + 22 ÷ 11 × 6^2 – 10 (Brackets first)

= 12 + 22 ÷ 11 × 36 – 10 (Exponents)

= 12 + 2 × 36 – 10 = 12 + 72 – 10 (Division and

multiplication, left to right)

= 84 – 10 = 74 (Addition and Subtraction, left to

right)

**EXAMPLE 2**:

**Solve** 4 + 10 – 3 × 6 / 3 + 4

= 4 + 10 – 18/3 + 4 = 4 + 10 – 6 + 4 (Division and

multiplication, left to right)

= 14 – 6 + 4 = 8 + 4 = 12 (Addition and Subtraction,

left to right)

**To Solve Modulus of a Real Number**

**The Modulus (or the absolute value) of x is always either positive or zero, but never negative. For any real number x, the absolute value or modulus of x is denoted by |x| and is defined as**

**|x|= x {if x ≥ 0} and −x {if x < 0}**

**EXAMPLE 1:**

**Solve** |8|

|8| = |-8| = 8

#### Tips to Crack Approximation

**Conversion of decimal numbers to nearest number To solve such questions, first convert the decimal to nearest value. Then simplify the given equation using the new values that you have obtained.**

**EXAMPLE 1:**

**Solve** 4433.764 – 2211.993 – 1133.667 + 3377.442

Here,

4433.764 = 4434

2211.993 = 2212

1133.667 = 1134

3377.442 = 3377

Now simplify, 4434 – 2212 – 1134 + 3377 =

4466

**EXAMPLE 2:**

**Solve** 530 x 20.3% + 225 x16.8%

Here, 20.3% becomes 20% and 16.8% becomes 17%

Now, simplify 530 x 20% + 225 x 17%

= 106 + 38.25 = 144.25

#### Approximation of Square Roots

**1. To simplify a square root, you can follow these steps:**

**2. Factor the number inside the square root sign.**

**3. If a factor appears twice, cross out both and write the factor one time to the left of the square root sign. If the factor appears three times, cross out two of the factors and write the factor outside the sign, and leave the third factor inside the sign. Note: If a factor appears 4, 6, 8, etc. times, this counts as 2, 3, and 4 pairs, respectively.**

**4. Multiply the numbers outside the sign.**

**5. Multiply the numbers left inside the sign.**

**6. To simplify the square root of a fraction, simplify the numerator and simplify the denominator.**

**How to calculate Square Root?**

**Perfect Square**

**If the square ends in 1 The number would end in – 1,9****If the square ends in 4 The number would end in – 2,8****If the square ends in 5 The number would end in – 5****If the square ends in 6 The number would end in – 4,6****If the square ends in 9 The number would end in – 3,7****If the square ends in 0 The number would end in – 0**

When a number is given, split it in two parts, in such a way that 2nd part has last two digits of number and first part will have remaining digits.

**Ex 1: Square root of 3481**

Split number in two parts i.e. 34 and 81(last two digits)

We know that square of number ends in 1, so square root ends either in 1 or 9.

Check, 34 lies between 25 (square of 5) and 36 (square of 6). Take smaller number.

So, our answer is either 51 or 59.

but we know 50² = 2500 and 60² = 3600, 3481

is nearest to 3600. So the answer is 59.

or 34 is more close to 36 than 25, so the answer

is 59.

**Ex 2: Square root of 76176**

Split: 761 76

Number will end in either 4 or 6,

729(272) < 761 < 784 (282), So the answer

may be 274 or 276. 761 is more close to 784,

so the answer is 276.

**Ex 3: square root of 75076**

Split: 750 76

Number will end in either 4 or 6

729(272) < 750 < 784 (282), So the answer may

be 274 or 276. 750 is more close to 729 than

784, so the answer is 274.

**Non-Perfect Square: This gives approximate value not an exact value.**

**Ex4: Square root of 1000**

961(312) < 1000 < 1024(322)

Now, 1000 is nearest to 1024

So, 32 – ((1024-1000)/(2× 32))

32 – (24/64)

32-.375 = 31.625

or 31+((1000-961)/(2× 31))

31 + (39/62)

31+.629 ≈ 31.63