The Idea of a Variable:

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

• Its value is not fixed; it can take any value 1, 2, 3, 4,...

• n is an example of a variable.

• One may use any letter as m, l, p, x, y, z, etc. to show a variable.

• Remember, a variable is a number that does not have a fixed value. For example, The length of a square can have any value. It is a variable. But 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.

Understanding Use of Variable:

Let us take one more example. For the Republic Day celebration in the school, children are going to perform mass drill in the presence of the chief guest. They stand 10 in a row. How many children can there be in the drill?

The number of children will depend on the number of rows. If there is 1 row, there will be 10 children. If there are 2 rows, there will be 2 × 10 or 20 children and so on. If there are r rows, there will be 10r children in the drill; here, r is a variable which stands for the number of rows and so takes on values 1, 2, 3, 4, ....

In the above examples, the variable was multiplied by a number. There can be different situations as well in which numbers are added to or subtracted from the variable as seen below.

1. Sarita says that she has 10 more marbles in her collection than Ameena. If Ameena has 20 marbles, then Sarita has 30. If Ameena has 30 marbles, then Sarita has 40 and so on.
   We do not know exactly how many marbles Ameena has. She may have any number of marbles. But we know that, Sarita's marbles = Ameena's marbles + 10. We shall denote Ameena’s marbles by the letter x. Here, x is a variable, which can take any value 1, 2, 3, 4,... ,10,... ,20,... ,30,... . Using x, we write Sarita's marbles = x + 10. The expression (x + 10) is read as ‘x plus ten’. It means 10 added to x. If x is 20, (x + 10) is 30. If x is 30, (x + 10) is 40 and so on.
   
   
2. Raju and Balu are brothers. Balu is younger than Rajuby 3 years. When Raju is 12 years old, Balu is 9 years old. When Raju is 15 years old, Balu is 12 years old.
   We do not know Raju’s age exactly. It may have any value. Let x denote Raju’s age in years, x is a variable. If Raju’s age in years is x, then Balu’s age in years is (x – 3). The expression (x – 3) is read as x minus three. As you would expect, when x is 12,(x – 3) is 9 and when x is 15, (x – 3) is 12.