Mathematics with Prof. S.R. Naidu

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. ...

Roots Similarly ,in   Thus the square root of a number is that number the square of which is equal to the original number. The symbol denotes the square root.       Thus the cube root of a number is that number whose cube is equal to the original number.The symbol denotes the cube root.Thus                                    

42 =2×3×7 here 2,3,7 are factors of the product 42. 45=3×3×5 here 3,3,5 are factors of the product 45. Similarly in ab ,a and b are the factors of ab. In 7xy, 7,x,y are factors of 7xy.   Thus ,when numbers or letters standing for numbers are multiplied together to form a product ,each of them is called a factor of that product.   When the same factor is repeated in a product we use a different mode of writing the product.         and a×a×a=       is called the fourth power of a and we say it as a to the fourth power.     2 is called as the index or exponent of the power.   Note: If index is unity it is omitted. Thus a stands for     They all have same meaning   a , 1a, a .