Mathematics with Prof. S.R. Naidu

Express using symbols 1. y subtracted from x x-y 2.5 multiplied by k 5 k 3.n added to m m + n 4. a divided by 3 a/3 5. p multiplied by r pr 6. x divided by a x/a 7.Thee sum of a,m and x a+ x+m 8. The product of a, b, x a b x 9 The difference between 8 and 5 is 3 8-5=3 10.The sum of 8 and 3 is equal to the sum of 5 and 6 8 + 3 = 5 + 6

Zero Zero may be defined for the present,as the absence of any magnitude.It is obtained by subtracting a number from another which is exactly equal to itself.4-4=0. IMPORTANT PROPERTIES OF ZERO  1. 0+0 =0 ;  x+ 0 =x ; -x+0= -x 2.0-0=0 ; x-0=x ; -x-0=-x we understand that x+ 0 = x- 0 ∴ +0 = - 0 3. 0 x 0 = 0 ; x x 0= 0 ; 0 x x = 0 . 4 . 0➗ x = 0 5. x➗ 0 is infinite when xキ0 ( i.e. x is not equal to zero ) and 0 ➗ 0 is an indeterminate result. 6. 0 square = 0 x 0 =0  Thus zero raised to any power is equal to zero and consequently any root of zero is equal to zero. integral numbers divisible by 2 are called even numbers integral numbers not divisible by 2 are called odd numbers in working examples the positive root is usually taken.

POSITIVE AND NEGATIVE NUMBERS When no sign precedes a term,the sign + is always understood. The use of the signs + and - is so constant and so important .The magnitude of a quantity considered apart from its sign is called its absolute magnitude.Thus a gain of Rs 5 and a loss of Rs 5 ,are equal in magnitude though opposite in sign. Addition: If two positive numbers are added together the sum is positive and if two negative numbers are added together the sum is negative ,but if a positive number and a negative number are added together the result will be positive or negative according as the positive or negative number has greater numerical absolute value. +4+ (+3)=+7 +7+ (-4)=+3 5+ (-8)= -3 (-3) + (-4) = -7 In adding up numbers it is immaterial in what order we take them,provided that each number has its own sign placed before it. Subtraction: To subtract a positive number means to add the corresponding negative number and if the number to be subtracted is negative,change it into a pos...

BRACKETS   The terms enclosed in brackets are to be treated as a single number. Thus a+(b-c) means that we have first to subtract c from b and then add the result to a. a x (b + c) means that the sum of b and c is to be multiplied by a. Removal of brackets Brackets are more   changing the value of the expressions enclosed in them. The value of an expression containing brackets remains unaltered even if we remove the brackets ,provided that these brackets are preceded by the positive sign.   In case of subtraction we can remove brackets preceded by the negative sign by changing the sign of every term in the brackets i.e. changing + into – and – into +. Consider the four cases in general 1.a + ( b + c) =a+ b+ c        2. a + ( b – c) = a+ b – c 3. a – ( b + c ) =a- b – c 4. a – ( b – c ) = a – b + c These results are always true for all values of a, b and c. Again , just as we can remove brackets , we can also en...

PROBLEMS AND EQUATIONS     A has five times as many rupees as B and Rs.7 More.If A has in all Rs 67,how many rupees has B. Rs. 5 x + Rs 7 = Rs 67 5 x + 7   = 67 This algebraical statement of the equality of two expressions is called an equation.The expression on the left hand side of the sign of equality is called the left –hand- side ( L.H.S.) of the equation while the expression on the right hand side of the sign of equality is called the right –hand-side (R.H.S) of the equation. In an equation the unknown number is denoted by a letter. The process of finding out the value of this letter so found is called the root of the equation.   Let solve 5 x+ 7= 67 5 x= 67-7 5 x= 60 X=60 / 5 X= 12 Thus B has Rs 12. The solution of an equation is mainly based on following four rules 1.If equals be added to equals , the sums are equal. 2.If equals be subtracted from equals ,the remainders are equal. 3.If equals be multiplied by equals, th...

The sign and letters denoting numbers are known as algebarical Symbols and collection of such symbols is called an algebraical expression or simply an expression. In an expression the parts connected by the signs    A term may be the product of two or more factors. For instance 5xy is the product of three factors 5,x and y.The numerical factor is called the numerical coefficient of the product.Here In 5xy,5 is the numerical co efficient of the product.   If we consider y as the term then the coefficient is 5x.A coefficient involving letters is called a literal coefficient.   The coefficient 1 is always omitted so that x means 1x.   Terms that consist of the same letter or same combination of letters are called like terms. E.g.   5a and 4a,3xy and 4xy. Terms that do not consist of the same letter or same combination of letters are called unlike terms. E.g. 5m and 4n ,7xy and 8mn.   Expressions are either simple or compound. ...