Algebraic Expressions Algebraic Expressions ALGEBRA IS A METHOD OF WRITTEN CALCULATIONS that help us reason about numbers. At the very outset, the student should realize that algebra is a skill. And like any skill -- driving a car, baking cookies, playing the guitar -- it requires practice. A lot of practice. Written practice. That said, let us begin. The first thing to note is that in algebra we use letters as well as numbers. But the letters represent numbers. We imitate the rules of arithmetic with letters, because we mean that the rule will be true for any numbers. The letters a and b mean Whatever numbers are in the numerators. The letter c means Whatever number is in the denominator. The rule means: "Whatever those numbers are, add the numerators and write their sum over the common denominator." Algebra is telling us how to do any problem that looks like that. That is one reason why we use letters. (The symbols for numbers, after all, are nothing but written marks. And so are letters As the student will see, algebra depends only on the patterns that the symbols make.) The numbers are the numerical symbols, while the letters are called literal symbols.
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In mathematics, an algebraic expression is an expression built op from constants, variables, and a finite number of algebraic operations (addition, subtraction, multiplication, division and exponentiation to a power that is a rational number). For example, is an algebraic expression. (Note that taking the square root is the same as raising to the power .) A rational algebraic expression (or rational expression) is an algebraic expression that can be written as a quotient of polynomials, such as x2 + 2x + 4. An irrational algebraic expression is one that is not rational, such as √x + 4. Some but not all polynomial equations with rational coefficients have a solution that is an algebraic expression with a finite number of operations involving just those coefficients (that is, can be solved algebraically). This can be done for all such equations of degree one, two, three, or four; but for degree five or more it can only be done for some equations but not for all. Problem:- Jeanne has $17 in her piggy bank. How much money does she need to buy a game that costs $68? Solution:- Let x represent the amount of money Jeanne needs. Then the following equation can represent this problem: 17 + x = 68 We can subtract 17 from both sides of the equation to find the value of x. 68 - 17 = x Answer:-: x = 51, so Jeanne needs $51 to buy the game. 1. Letters used as symbols for numbers: In the algebraic expression 2x, the letter x stands as a symbol for any number.One can choose any number to write for x .
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So, x holds a place for any number. One can write 3, 10, 100 or any other number as required for x . Since x changes or varies based on what is to be written for it, it is therefore called Variable. What varies is a variable. Other variables in the above examples for algebraic expression are p, q and y 2. Symbols used to denote Multiplication 1. Now consider 2x. What does it mean? It means multiplication of 2 and x, i.e., 2 × x. 2 × x is also called product of 2 and x. Product refers to multiplication. In 2x we know x is the variable and we also know it stands as a symbol to write any number for it. In other words, it holds a place to write any number for it. Then let us see what will 2x become, when numbers like 3, 10, 100 are written for x 2x means product (multiplication) of 2 and x. So, we get 2 × 3 = 6, 2 × 10 =20, 2×100 =200 2. Again consider 2x It may also be written as 2.x standing for multiplication (product) of 2 and x. so, we have 2.x = 2.3 = 6 or 2.10 = 20 or 2.100 = 200, depending on what number is written for x. In algebraic expressions, dot indicates multiplication 3. Consider 2x once again. It can also be written as 2(x) standing for multiplication of 2 and x So, we have 2(3) = 6 or 2(10) = 20 or 2(100) =200, based on what number we choose to write for x
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