Simplification problems with solutions
Introduction
Simplification problems is one of the important topic given in Nithra Jobs site which will be helpfull for interview process and also in competitive exams. Nithra Jobs acknowledges the importance of simplification skills in the modern professional landscape. By solving this you can evaluating your mathematical proficiency, logical reasoning, and problem-solving abilities. Simplification questions ans answers questions are designed to test the candidates' aptitude for numerical reasoning, mental calculation, and their ability to arrive at accurate solutions within limited time.
Formulas1. 'BODMAS' Rule:
This rule depicts the correct sequence in which the operations are to be executed, so as to find out the value of given expression.
Here B - Bracket,
O - of,
D - Division,
M - Multiplication,
A - Addition and
S - Subtraction
Thus, in simplifying an expression, first of all the brackets must be removed, strictly in the order (),{} and ||.
After removing the brackets, we must use the following operations strictly in the order:
(i) of (ii) Division (iii) Multiplication (iv) Addition (v) Subtraction.
2. Modulus of a Real Number:
Modulus of a real number a is defined as
|a| = {a, if a > 0}
{-a, if a < 0}
Thus, |5| = 5 and |-5| = -(-5) = 5.
3. Virnaculum (or Bar):
When an expression contains Virnaculum, before applying the 'BODMAS' rule, we simplify the expression under the Virnaculum.
Solved Problems
1. Find the value of 1 / ( 3 + 1 / ( 3 + 1 / ( 3 - 1 / 3 )))?
Answer: 27 / 89
Explanation:
Let the value be x
x = 1 / [ 3 + 1 / ( 3 + 1 / ( 3 - 1 / 3 )))]
⇒ x = 1 / [ 3 + 1 / ( 3 + 1 / ( 8 / 3 ))]
⇒ x = 1 / [ 3 + 1 / ( 3 + 3 / 8)]
⇒ x = 1 / [ 3 + 1 / ( 24 + 3 ) / 8]
⇒ x = 1 / [ 3 + 8 / 27 ]
⇒ x = 1 / ( 89/27)
⇒ x = 27 / 89
The value is 27 / 89
2. Find the value of 6/9 + 7/9 + 9/9 + 69/99.
Answer: 3.141414
Explanation:
Let the value be x
x = ( 6 / 9 ) + ( 7 / 9 ) + ( 9 / 9 ) + ( 69 / 99 )
x = ( 2 / 3 ) + ( 7 / 9 ) + 1 + ( 69 / 99 )
x = ( 66 + 77 + 99 + 69 ) / 99
x = ( 311 / 99 )
x = 3.141414
The value is 3.141414.
3. 64% of 2650 + 40% of 320 =?
Answer: 1824.
Explanation:
Let the value be x
x = 64% of 2650 + 40% of 320
x = ( 64 / 100 ) * 2650 + ( 40 / 100 ) * 320
x = ( 0.64 * 2650 ) + ( 0.4 * 320 )
x = 1696 + 128
x = 1824
The value is 1824.
4. What will come in place of the question mark (?) in the following questions? (202 + 302) / 3900 =?
Answer: 1 / 3
Explanation:
=( 202 + 302) / 3900
= ( 400 + 900 ) / 3900
= 1300 / 3900
= 1 / 3
The value of ( 202 + 302 ) / 3900 = 1 / 3
5. What will come in place of the question mark (?) in the following questions? 8 % of 450 - 7 % of 300 =?
Answer: 15
Explanation:
= 8 % of 450 - 7 % of 300
= ( 8 / 100 ) * 450 - ( 7 / 100 ) * 300
= ( 8 / 2 ) * 9 - ( 3 * 7 )
= ( 4 * 9 ) - 21
= 36 - 21
= 15
The value of 8 % of 450 - 7 % of 300 is 15
Conclusion
Nithra Jobs recognizes the importance of simplification questions for competitive exams and encourages candidates to develop these abilities to develop in their careers. Job seekers preparing for interviews and competitive exams should dedicate time to practice the simplification tricks and improve their simplification skills. It will be easier to solve if you are thorough at simplification formulas.
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