Variable in Math

Introduction to variable in math:

In mathematics, the term “variable” is used in algebra. Variable is nothing but the letter which represents the some numerical value. For example consider the algebraic expression 4x. Here 4 is the constant and x is the variable.

Discuss:

(a)   Consider x + y = 10.

The variable x and y are variables and they has some numerical values that makes the above statement true.

Examples:

1. P = 4s    2. x + 5 = 10

Here

4, 5, 10 are constants.

P, s, x are variables.

Note:

The numbers are constants.

To denote variable in math we use the alphabets A to Z or a to z.

Let us see some example problems.


Variable in math - Example problems:


1. Pick out the constants in the following:

8, a, x, y, – 25, 0, z, 35, 2.7,

Solution:

The constants are 8, – 25, 0, 35, 2.7 and

2. Pick out the variables in the following:

63, x, 27, m, p, q, 10, 0, y

Solution:

The variables are x, m, p, q and y

2. Pick out the variables and constants: A, – 15, q, l, 22.3, 73

Solution:

The variables are A, q and l

The constants are – 15, 22.3 and 73.

Practice problems:

1) Pick out the variables in the following:

6, c, – 12, h, k, 16, m, n, – 22, p, s, 30

2) Write any five variables:



Power of the variable in math:


In math, the product of 18 and a is 18 × a and it is written as 18a .Similarly the product of two literals a and b is a × b = ab

Now let us see how the repeated product of a literal with itself is written in math.

Multiply a with a. We get a × a and is denoted by a2.

We read a2 as a to the power of 2. Similarly d × d × d = d3, which is read as m to the

Power of 3

In a2, 2 is the power and a is the base.

In d3, 3 is the power and d is the base.

Example problems using the variables:

a + 5 = 10. Find the value of a.

Solution:

To find the value of a, we have to move the like terms in one side

For that, subtract 5 on both sides

a + 5 – 5 = 10 – 5

Simplify,

a + 0 = 5

a = 5.