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PERCENTAGES CONCEPTS,FORMULAS,DEFINITIONS,EXAMPLES,TRICKS

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    PERCENTAGES is very important chapter for all  competitive  exam and everything is included in it like all Problems on percentages,  fractions and percentages, price change,result and population,results on depreciation,comparison of percentages,successive increase and decrease etc. Percentages The Percentage is a fraction whose denominator is always 100. The percentage sign is %. Example -   7% can be converted to a fraction as 7/100 = 0.07   If, we want to calculate P% of Q, then    Percentage Formula:-      P% of Q =  Q× P/100 Qes.  If 30% of x = 60, then find the value of P. Soln .      x × 30/100 = 60 ⇒ x = 60 × 100/30 ⇒ x = 200. Fractions and Percentages To express Y % as a fraction,    Y% = Y/100   As -  30% = 30/100 = 3/10          98% = 98/100 = 49/50 To Express X/Y as a percentage we can say,   X/Y = (X/Y × 100) % ...
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SIMPLIFICATION AND APPROXIMATION,CONCEPTS,FORMULAS,DEFINITIONS,EXAMPLES,TRICKS

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SIMPLIFICATION AND APPROXIMATION is very important chapter for all competitive exam and everything is included in it like all simplication and approximation,simplication,fraction,decimal,surds and indices etc.





SIMPLIFICATION AND APPROXIMATION



SIMPLIFICATION:


 It means reducing the expression in simpler form using various functions.

The function used to simplify follows a fixed order known as BODMAS


Where,


B = Bracket


O = of


D = Division


M = Multiplication


 A = Addition


S = Subtraction



Brackets: 


There are three types of brackets:-


1) Round brackets ()


 2) Curly brackets {}


3) Box brackets []


1st we shall use the bracket () {} and [] .

OF means multiplication but it is used before division.

then we can use addition and substraction.




APPROXIMATION :


 It is simplifying(clarify) the mathematical expression to its nearest value but not exactly correct.  

when we find out the approximate value, we have to round off the digits in the expression to the nearest value and simplify the expression using BODMAS


Fraction:


 it is defined as the part of a whole thing.  we define function in two-portion. 1st portion is top and 2nd portion is lower. name of the top is numerator and name of the lower is denominator.


The fractions are expressed in the form of P ∕ Q



Types of fraction: -


1. Proper fraction:   In a fraction numerator(top) value is less than the denominator(lower) value is called proper fraction.


Example:     4/5, 9/13 etc.


2. Improper fraction:  The fractions, where the numerator(top) is bigger than the denominator(lower) are called improper fractions.


 Example:        9/5 , 6/11 etc.


3. Mixed Fractions:   A mixed fraction has a combination of a whole and a part.


(Quotient) whole Remainder / Divisor


   Example:     3 whole 4 / 5 ,   2 whole 6/7 etc.


4. Unit fraction:   In a fraction, the numerator value is always ONE(1). The fraction is called a unit fraction.



Decimal



Decimal is the fraction which is represented by the decimal point followed by the number of zeroes of its tenth,hundredth etc .

Example

62.8= 628/10 , 6.28= 628/100 , 0.628= 628/1000



When dividing a number by 10, 100 or 1000, the digits of the number and the quotient are same but the decimal point in the quotient shifts to the left by as many places as there are zeros over 1.



Recurring Decimal 


 the remainder never becomes zero.


In this concept the remainders repeat after a certain stage forcing the decimal expansion to go on for ever



Example


10/3 = 3.3(recurring on three at right side)



Qes: compare 5/4 and 7/6.



soln:  lcm of 4 and 6 = 12

5/4 × 12 = 15

7/6 × 12 = 14

15 > 14 

So,

5/4 > 7/6


2nd METHOD

 5/4 and 7/6 

6 × 5 = 30

4 × 7 = 28

30 > 28

So,

5/4 > 7/6



Surds and Indices (pic)

A surd is an irrational number that will be expressed with roots.

As - √14 , ∛14





Pic of Indices














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