# Algebraic Expression

Algebra is a branch of Mathematics in which we use letters of English alphabet to represent some values. As letters do not have any numeric value of their own, they can be assigned any value which is not fixed. Thus, these letters has varying values unlike numbers & is called variables.

Thus, we study numbers & letters with mathematical operations in algebra. When these numbers called constants and the variables get bonded with the help of the operations of mathematics, we get algebraic expressions.

Now, what is an algebraic expression? Before we know algebraic expressions, let us recall that expression in mathematics, rather arithmetic, means that the numbers are related to each other by different mathematical operations of + , - , * & / . For example : 2 + 7 , 3 * 9 , 15 / 6 , 24 – 8 are expressions in arithmetic.

In algebra, since our numbers and values get extended to letters as well, so we can define an  algebraic expression as an expression involving mathematical operations between the fixed and the variable values in algebra. Thus, 2*a + b , 4 – 7*y , 5 / 6y are the examples of algebraic expressions.

Till now, in-spite of being unfamiliar with algebraic expressions, we have done many of them in the form of generalised formulae. For example, we give the formula for the perimeter of a Rectangle by: Perimeter of Rectangle = 2 * ( l + b ), what l and b stand for here. These are the values which we assign to the length & breadth of a particular rectangle. Thus, this is also an algebraic expression. Similarly we have learnt many other formulae in which we use English letters to denote some values. They are all examples of algebraic expressions.

Let us now learn writing algebraic expressions.

To write algebraic expressions, we must try to understand the relation between different values being expressed in the statements. We will be able to understand this with the help of examples.

Statement                    Mathematical relation                           algebraic expressions

1. 24 decreased by x                                 subtract                                                     24 – x
2. 4 times a                                               multiply                                                       4 * a
3. 15 more than z                                      add                                                               z + 15
4. b reduced by 13                                    subtract                                                         b – 13
5. 3 times k increased by 7                      multiply & add                                               3*k + 7
6. Sum of p & q divided by 4                    add & divide                                               (p+q)/4

Thus, we see that it is very easy to write algebraic expressions provided we understand the bonding operation between the values & express them properly in the order expressed in the statement.

## Algebraic Expressions and Identities

Algebraic expressions are formed from variables and constants. The expression 3y + 5 is formed from variable ‘y’ and constants 3 and 5. The value of variable can vary. Therefore the value of expression...Read More

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