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Algebra

We know that there are infinitely many numbers. However, there are only 26 alphabets in the English language.

Can we represent numbers with the help of letters?
Yes, we can represent the numbers with the help of alphabets(letters).
Alphabets like a, b, c, x, y, z, l, m, n, etc. are used in Mathematics to denote variables.


Let us take an example.
In a class, the number of boys are 20 more than the number of girls. How many boys are there in the class?
The number of boys in the class varies with the number of girls.
If there are 10 girls in the class, then the number of boys = 10 + 20 = 30
If there are 55 girls in the class, then the number of boys = 55 + 20 = 75

Therefore, we can write a rule to find the number of boys as follows:
Number of boys = Number of girls + 20

Here, number of girls in the class can vary, and can take different values. On the other hand, number of boys in the class varies according to the number of girls in the class.
If we replace the number of boys and girls in the class with letters m and n respectively, then we get following expression:
m = n + 20
Here, n can take any value such as 0, 1, 2, 3... etc.,  and the value of m will change accordingly. Since the values of m and n can vary, these are known as variables. 

A variable is something that does not have a fixed value. The value of a variable varies.

Also, a symbol with a fixed numeric value is known as a constant.

For example, 2, –4, , –3.4, etc., are constants as each of them have a fixed numeric value.  

A combination of variables, numbers, and operators (+, –, ×, and ÷) is known as an algebraic expression.

For example,

  1. x + 7
  2. 2 – y
  3. (5 × y) + 9
  4. 11xyz + ab2 2p4q3 +
  5.  + 2p5 1.5z

Let us try to form few simple mathematical expressions by applying the four operations on numbers.

  1. 42 is added to 58 and then the result is divided by 25 =
  1. The product of 24 and 15 is subtracted from the product of 30 and 43 = (30 × 43) – (24 ×15)

In the same way, we can form algebraic expressions by applying the four operations on variables.

  1. z divided by 5 and 5 added to the result =
  2. x multiplied by 6 and 4 added to the product = 6x + 4
  3. 39 subtracted from 5m = 5m – 39
  4. 5 added to 6m and the result is subtracted from 8n = 8n – (6m + 5)
  5. 16 subtracted from 7x and the result is subtracted from –2y = –2y – (7x – 16)

To understand the concept better, look at the following video.

In this way, we can represent a given real-life situation by using variables.
Let us now solve some more examples to understand the concept better.

Example 1:
Write down...

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