Undersanding Algebra-rainism

Introduction to undersanding algebra: Algebra is a branch of Mathematics. An Arab Mathematician, Mohammed ibn AlKhowarizmi about 825 A.D. Wrote the first book on Algebra, called Aljebar W"al Muquabalah. Later it was called Algebra in English. In Algebra, the unknown values or the values to be found out are represented by symbols and letters. In Algebra we study not only about numbers but also other important concepts that are used in Science and Engineering. In this chapter we are going to study some basics of Algebra Mathematical statements Place holders Literals Constants and Variables Power (or Exponent or Index) of a variable Coefficients Terms Addition and Subtraction of terms In Arithmetic we make statements with numbers having definite value. In Algebra, besides numerals we use symbols and literals in place of unknown numbers to make a statement. Hence. Algebra may be regarded as an extension of Arithmetic. Algebra is a branch of Mathematics consisting of both numerals and literals Mathematical statements : A statement is the meaningful .bination of words. In addition, if we use numbers to make a statement, it is called as Mathematical statement. Place holders : You know that mathematical statements involves unknown numbers. We use different symbols to represent those unknown numbers. Such symbols are known as place holders, because they hold the places. Literals : So far we have learnt, how to use place holders to represent unknown numbers. Instead of place holders, we can use letters like a, b, c, x, y etc. to represent the unknown numbers. These letters, which are used to represent numbers, are called Literals. Constants and Variables: Product of two numbers is 20. This can be written as l b = 20 Here 20 is a numeral and its value is fixed. But "l" and "b" are literals (literal numbers) and the values of "l" and "b" are not fixed. Power (or Exponent or Index ) of a variable : We have learnt that the product of 16 and x is 16 x and it is shortly written as 16x. Similarly the product of two literals x and y is x y = xy. Now let us see how the repeated product of a literal with itself is written. Multiply x with itself. We get x x and is denoted by x2. Coefficients : The number (constant) connected to a variable or product of variables by means of multiplication (or Division) is called the coefficient. Terms : The .bination of constant and variables .bined by means of multiplication (or division) is called a term. Like Terms : Two or more terms which have the same variable or same product of variables or same division of variables are called like terms. Unlike Terms : Two terms which have different variables or different product of variables or different division of variables are called Unlike Terms. Addition and Subtraction of terms : Since the literals are used to represent numbers in algebra, they must obey the fundamental Operations. In this section we are going to learn some basic concepts of addition and subtraction in Algebra. In algebra, we classify the terms as like terms and unlike terms. Algebraic Expressions: In this branch of mathematics, we use letters like a, b, x and y to denote numbers. Performing addition, subtraction, multiplication, division or extraction of roots on these symbols and real numbers, we obtain what are called algebraic expressions. The word algebra is derived from the Arabic word al""jab. In Arabic language, "al" means "the" and "jabr" means "reunion of broken parts". The usage of the word can be understood by a simple example. In the equation x + 5 = 9, the left hand side is the addition (sum) of two parts x and 5. If we add (unite) (""5) to each side of the equation, we get (x + 5) + (""5) = 9 + (""5) or x + [5 + (""5)] = 9 "" 5 or x + 0 = 4 or x = 4. Here 9 and -5 are reunited to get 4. This type of mathematics is called algebra. Indian mathematicians like Aryabhatta, Brahmagupta, Mahavir, Sridhara, Bhaskara II have developed this subject very much. The Greek mathematician Diophantus has developed this subject to a great extent and hence we call him the father of Algebra. Symbols in an algebraic expression are called variables of the expression. For example, in ax + b, if a and b are specific numbers and x is not specified, then x is the variable of ax + b. In 2x^2 + 3xy + y^2, x and y are variables. If the variables in an algebraic expression are replaced with specific numbers, then the expression yields a number and this number is called a value of the expression. For example, 2x^2 + y is an algebraic expression and x and y are variables of the expression. Polynomial Expression: In this branch of mathematics, we use letters like a, b, x and y to denote numbers. Performing addition, subtraction, multiplication, division or extraction of roots on these symbols and real numbers, we obtain what are called algebraic expressions. The word algebra is derived from the Arabic word al""jab. In Arabic language, "al" means "the" and "jabr" means "reunion of broken parts". The usage of the word can be understood by a simple example. In the equation x + 5 = 9, the left hand side is the addition (sum) of two parts x and 5. If we add (unite) (""5) to each side of the equation, we get (x + 5) + (""5) = 9 + (""5) or x + [5 + (""5)] = 9 "" 5 or x + 0 = 4 or x = 4. Here 9 and -5 are reunited to get 4. This type of mathematics is called algebra. Indian mathematicians like Aryabhatta, Brahmagupta, Mahavir, Sridhara, Bhaskara II have developed this subject very much. The Greek mathematician Diophantus has developed this subject to a great extent and hence we call him the father of Algebra. Symbols in an algebraic expression are called variables of the expression. For example, in ax + b, if a and b are specific numbers and x is not specified, then x is the variable of ax + b. In 2x^2 + 3xy + y^2, x and y are variables. If the variables in an algebraic expression are replaced with specific numbers, then the expression yields a number and this number is called a value of the expression. For example, 2x^2 + y is an algebraic expression and x and y are variables of the expression. 相关的主题文章: