Variables

The branch of mathematics where letters are used along with numbers is called * Algebra*.

This Topic gives you an overview of;

- Variable
- Concept of variables- Matchstick Patterns
- More Examples on match sticks patterns
- Difference in Variables and fixed numbers

An unknown quantity can be represented by a **variable**. Usually, a variable is any letter from the English alphabet that represents an unknown quantity. The relation between the unknown quantity and other quantities can be expressed with the help of the variable. The value of the variable varies with the given condition on the variable.

Concept of Variables- Matchsticks Patterns

Matchstick patterns help us to understand the basic concept of variable. Here is an example of students forming matchstick patterns; the goal is to find how many matchstick do they need to form the L shape patterns.

A Student picks two sticks, forms letter L similarly another student forms picks 4 sticks and forms 2 L shape pattern similarly for 3, she picks 6 sticks and it goes on . We will tabulate the number of Ls formed and number of matchsticks needed to form the pattern.

While writing the table, the number of matchsticks required is twice the number of Ls formed.

Number of matchsticks required = 2 × number of Ls.

For convenience, let us write the letter n for the number of Ls. If one L is made, n = 1; if two Ls are made, n = 2 and so on; thus, n can be any natural number 1, 2, 3, 4, 5..., etc.

We then write,

Number of matchsticks required = * 2 × n*.

Instead of writing Number of matchsticks required = 2 × n, we write** m=2n.**

Here m and n are variables.These m and n represent numbers; while representing as number it can represent any values its value is not fixed.

Thus, for n = 1, m = 2 × 1 = 2,

For n = 2, m= 2 × 2 = 4,

For n = 3, m = 2 × 3 = 6 etc.

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

Let us find the rule for pattern “C” formed below:

Tabulate the number of matchsticks and number of c pattern formed.

From the table we come to know that the number of matchsticks required is thrice the number of Cs formed.

We then write,

Number of matchsticks required = 3 × n.

Shortly we write, **m=3n.**

Similarly to make a ”F” pattern, we require 4 match sticks.

Hence the rule is m= * 4 X n = 4n*.

Difference in Variables and Fixed Numbers

We may use any letter as m, l, p, x, y, z etc. to represent a variable. Remember, a variable is a number which does not have a fixed value.

For example, the number 5 or the number 100 or any other given number is not a variable. They have fixed values. Similarly, the number of angles of a triangle has a fixed value i.e. 3. It is not a variable. The number of corners of a quadrilateral (4) is fixed; it is also not a variable.

But n in the examples we have looked is a variable. It takes on various values 1, 2, 3, 4....,etc.

Summary

- We learnt that an unknown quantity can be represented by a variable.
- We looked at patterns of making letters and other shapes using matchsticks.
- We learnt how to write the general relation between the numbers of matchsticks required for repeating a given shape.
- The number of times a given shape is repeated varies; it takes on values 1,2,3,....,etc. It is a variable, denoted by some letter like n.
- A variable takes on different values; its value is not fixed. The length of a square can have any value. It is a variable. But the number of angles of a triangle has a fixed value. It is not a variable.
- We may use any letter n, l, m, p, x, y, z, etc. to show a variable.

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