IMPORTANT FACTS AND FORMULAE

I..Numeral : In Hindu Arabic system, we use ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 called digits to represent any number.

 A group of digits, denoting a number is called a numeral.

 We represent a number, say 689745132 as shown below :

We read it as : 'Sixty-eight crores, ninety-seven lacs, forty-five thousand, one hundred and thirty-two'. 

01 NUMBERS SOLVED EXAMPLES

IMPORTANT FACTS AND FORMULAE

I.  Factors and Multiples : If a number a divides another number b exactly, we say that a is a factor of b. In this case, b is called a multiple of a.

II. Highest Common Factor (H.C.F.) or Greatest Common Measure (G.C.M.) or Greatest Common Divisor (G.C.D.): The H.C.F. of two or more than two numbers is the greatest number that divides each of them exactly.

   There are two methods of finding the H.C.F. of a given set of numbers :

1.  Factorization Method : Express each one of the given numbers as the product of prime factors.The product of least powers of common prime factors gives H.C.F.

2.  Division Method: Suppose we have to find the H.C.F. of two given numbers. Divide the larger   number by the smaller one. Now, divide the divisor by the remainder. Repeat the process of dividing the preceding number by the remainder last obtained till zero is obtained as remainder. The last divisor is the required H.C.F. 

Finding the H.C.F. of more than two numbers : Suppose we have to find the H.C.F. of three numbers. Then, H.C.F. of [(H.C.F. of any two) and (the third number)] gives the H.C.F. of three given numbers.

Similarly, the H.C.F. of more than three numbers may be obtained. 

02 HCF and LCM Solved Examples

IMPORTANT FACTS AND FORMULAE

I.    Decimal Fractions : Fractions in which denominators are powers of 10 are known as decimal  fractions.  

                   Thus ,1/10=1 tenth=.1;1/100=1 hundredth =.01;

                    99/100=99 hundreths=.99;7/1000=7 thousandths=.007,etc

03 DECIMAL FRACTIONS SOLVED EXAMPLES

I. ’BODMAS’Rule: This rule depicts the correct sequence in which the operations are to be executed,so as to find out the value of a given expression.

Here, ‘B’ stands for ’bracket’ ,’O’for ‘of’ , ‘D’ for’  division’  and ‘M’ for ‘multiplication’, ‘A’ for ‘addition’ and ‘S’ for ‘subtraction’.

Thus, in simplifying an expression, first of all the brackets must be removed, strictly in the order(), {} and [].

04 SIMPLIFICATION SOLVED EXAMPLES

IMPORTANT FACTS AND FORMULAE

Square Root: If x² = y, we say that the square root of y is x and we write, √y = x.

Thus, √4 = 2, √9 = 3, √196 = 14.

05 SQUARE ROOTS AND CUBE ROOTS EXAMPLES

06 AVERAGE

In this section, questions involving a set of numbers are put in the form of a puzzle. You have to analyze the given conditions, assume the unknown numbers and form equations accordingly, which on solving yield the unknown numbers.

PROBLEMS ON AGES

09 SURDS and INDICES

1.      Concept of Percentage : By a certain percent ,we mean that many hundredths. Thus x percent means x hundredths, written as x%.