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Example 1: Study the pattern of matchsticks used to make triangles. Complete the given table.

Number of Triangle(s) Formed 1 2 3 .......... 5 ..........
Number of Matchsticks Required 3 .......... 9 12 .......... 18

Solution: From the given matchstick pattern for triangle, the number of matchsticks required
= 3 × Number of ∆s.

If we take letter n for the number of ∆s, where n can be any natural number 1, 2, 3, …
Therefore, the number of matchsticks required = 3 × n
If n = 1, the number of matchsticks required = 3 × 1 = 3
Maths Talk
If n = 2, the number of matchsticks required = 3 × 2 = 6
As we write the rules for the patterns
If n = 3, the number of matchsticks required = 3 × 3 = 9 of letters L and C. Some letters of

If n = 4, the number of matchsticks required = 3 × 4 = 12 English alphabet give us the same
If n = 5, the number of matchsticks required = 3 × 5 = 15 rules as given by L and C. Which are
these? Why does this happen?
If n = 6, the number of matchsticks required = 3 × 6 = 18

Number of Triangle(s) Formed 1 2 3 4 5 6

Number of Matchsticks Required 3 6 9 12 15 18

The Idea of a Variable

In the above example, we found a rule to give the number of matchsticks required to make a
pattern of ∆s. The rule was:
Number of matchsticks required = 3n, where, n is the number of ∆s in the pattern, and n takes
values 1, 2, 3, 4, ...

Here, the value of n keeps changing (increasing). As a result, the number of matchsticks required
also keeps changing (increasing).
Hence, n is an example of a variable. Its value is not fixed; it can take any value 1, 2, 3, 4, ...

The word ‘variable’ means something that can vary, i.e., change.

Thus, the letter which represents an unknown quantity is called a variable. One may use any letter
as m, l, p, x, y, z, etc. to show a variable.

These letters are used to find the value of unknown quantities in certain circumstances.
They obey all the fundamental rules of mathematics such as addition, subtraction, multiplication
and division.
Suppose, Ruhi has some stamps and her younger brother Rohan has 5 more stamps than Ruhi.

How much stamps do Rohan have?
Clearly, Rohan’s stamps = Ruhi’s stamps + 5

101 Introduction to Algebra