# Basic Rules Of Simplification With Examples

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
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,

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