Every table is an expression!

Every table is an expression!

Yesterday we looked at Algebraic expressions. We saw at the beginning that Mathematics is all about numbers. The Indian Math system provides a lot of exercises for numbers. That is why our early education system emphasized memorization of tables. That mental sum is also necessary for practicing math.

You will be surprised to know that we can learn whole mathematics by using tables. So I hear you ask, can we further understand this algebraic expression by putting it into tables?

You are right to ask. Take the second tables for example. Every table is an arithmetic equation. If we take away its equal sign, it is arithmetical expressions. Now look at the second table.

Does it start with 1 ×2 = 2? It is an arithmetic equation. If we take the equation of this and stop it as 1 × 2, it becomes an arithmetic expression. I think now you have got a better understanding of expression and equation.

Well, now the question is let's express this second table as an algebraic expression. How to say it? What changes in the second table? See what doesn't change. As we saw yesterday, Algebraic expression is made up of variables and constants. That means creating variables and constants.

In the second table, 2 is not going to change. But at each step the numbers multiplied by two keep changing as 1, 2, 3, 4, 5, …. Then we can say 2x as the algebraic expression of the second table by keeping 2 as a constant and changing numbers as x as variable. Why not say x2 then let's say that. But we will say 2x as it is customary to denote the constant first and the variable second. Now this 2x is the algebraic expression for the second table. Equating this expression to a number such as 2x = 8 is an equation.

As soon as you say 2x = 8, you will tell yourself that 2 × 4 = 8. So here you will say the value of x is 4. I think you now have a very good understanding of algebra and algebraic equations. So if you tell me the algebraic expression for the third table, you will close your eyes and say 3x. 3x should be called 3n also. We are going to define the variables ourselves. It's like naming a pet. You can keep your favorite pet name.

Everything is fine. You ask me, when will start the lesson on perimeter and area.

We must say that we have almost started. Now let us tell you the algebraic expression for the fourth table. I know you will say answer as 4x.

Did you know that 4x is the formula for a perimeter? What, wondering if the algebraic expression for the fourth table is the formula for the perimeter? Do not doubt. It is the formula for perimeter. What do you mean the formula for perimeter? The formula for the perimeter of a square is 4x.

Not familiar with the square? All four sides are equal. If you multiply one side by four than you can find the perimeter by adding four equal sides, then you can calculate the perimeter very easily. That is, multiplication is the abbreviation of addition.

Now what is the perimeter of a square with side 1 unit 4 × 1 = 4?

What is the perimeter of a square with 2 unit side 4 × 2 = 8?

What is the perimeter of a square with 3 unit side 4 × 3 = 12?

What do you mean by the fourth table? This is what I said before.

So you're right to say the fourth table, you're right to say the algebraic expression for the fourth term is related to the perimeter of the square.

Can you realize that the perimeter of the square is hidden inside the fourth table? That's why I said that you can learn the entire math by keeping only the tables in mind.

We took the perimeter of the square to be 4x, right? But you know that you can define a variable and change it.

Now let's find the perimeter of the square if the side of the square is a unit. What sir, do you not even know this, you are saying 4a. Very well. Generally speaking, the side of the square is taken as a, so we will refer to the perimeter of the square with the variable a.

That's not possible, you may say, I'll just use x, so there's nothing wrong with that either. Note before starting the calculation that you have taken the side of the square as x. This is the definition of variable. You know that very well. Now you want to explain about other formula? Surely I will explain tomorrow one by one.

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