Page 130 - ICSE Math 6

11 Fundamental Concepts of

Algebra

Key Concepts

• Constants and Variables • Coefficient
• Matchstick Patterns • Algebraic Expressions
• Use of Variables • Monomials, Binomial and Trinomial
• Terms (Constant, Like, Unlike) • Polynomial

Algebra is a branch of Mathematics which uses numerals (0 to 9),
signs of basic operations (+, –, × and ÷), letters of the English alphabet Maths Info
(a to z) and letters of the Greek alphabet (a, p, f etc.) to represent The word algebra is derived
some unknown terms or to generalize a result or pattern. Use of letters from the title of the book
allows us to form rules and formulae in general. ‘Aljebar w’al almugabalah’.
Let’s look at the following examples to understand how patterns are generalized.
(a) On her birthday, Sana wants to distribute 4 toffees to each student of her class.

For two students, she needs 4 × 2 = 8 toffees, whereas for three
students she needs 4 × 3 = 12 toffees and so on. Clearly, the number
of toffees increases as the number of students increases. We can Number of Number of
see a pattern in the table given alongside and generalize it to find students toffees
the subsequent terms as follows:

Number of toffees required = Number of toffees for each student 1 4 × 1 = 4
4 × 2 = 8
2
× Number of students = 4n, where n represents the number of 3 4 × 3 = 12
students. . . . . . .
The expression 4n is the general expression for the number of
toffees required when 4 toffees are given to each student.

(b) Consider the pattern,
1 + 3 = 4 = 2 2

1 + 3 + 5 = 9 = 3 2
1 + 3 + 5 + 7 = 16 = 4 2
.
.
.
So, sum of first n odd numbers = n 2

Constants and Variables

A quantity whose numerical value is fixed is known as a constant
whereas a quantity whose numerical value changes is known as a Maths Info
3
variable. For example, 2, –5, 10 , etc., are constants and x, y, z, 6a, A combination of constants
7 and variables is a variable.
7b, etc., are variables. Variables are also known as literal numbers or

114