Page 136 - ICSE Math 7

12 Algebraic Expressions

Key Concepts

• Constants, Variables and Terms • Value of an Algebraic Expression
• Algebraic Expressions
• Addition, Subtraction, Multiplication
and Division of Algebraic Expressions

Rahul wants to buy pens. The cost of a pen is ` 15. To buy three such pens he needs ` 15 × 3 = ` 45,
whereas to buy five such pens he needs ` 15 × 5 = ` 75 and so on. Clearly, the amount increases as
the number of pens increases. We can find the cost of ‘n’ pens in the following way.
Total cost of ‘n’ pens = Cost of 1 pen × Number of pens (n)
= ` 15n

Here the value of ‘n’ which is not fixed.
In this chapter, we shall begin with the study of Algebra. It is a branch of Mathematics that generalize the
facts of Arithmetic. In Algebra, we use numerals, basic operations (+, –, × and ÷) and letters of English
or Greek alphabet. These letters are used to represent some unknown terms or to generalize a result.

Constants and Variables
A quantity whose numerical value is fixed is known as a constant, whereas a quantity whose numerical
1
value is not fixed is known as a variable. For example, 3, –4 and 11 are constants, and letters like
6
x, y, z, a, b and c are variables.
Variables are also known as literals or literal numbers. As literals are also numbers, therefore all the
rules for addition, subtraction, multiplication and division of numbers hold true for them.

Points to remember
• A combination of two or more constants is a constant.

• A combination of two or more variables is a variable.
• A combination of one or more constant(s) and variable(s) is a variable.

Terms
A term is a constant or a variable or a combination of both connected by multiplication or division.

For example, 6, 13ab and 8a are terms. If a term does not contain a variable, then it is known as
xy
a constant term. In a term, constant is known as the numerical factor and variables are known as
the literal factors. For example, in the term 8ab, 8 is the numerical factor and a, b and ab are literal
factors. There are two types of terms: like terms and unlike terms.

Like terms

The terms having the same literal factors are known as like terms. Example:
2
2
(a) 8ab and –11ab (b) 5x y and 15x y
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