Algebra

In simplest way Algebra is a generalized form of Arithmetic.

In Arithmetic we only deal with numbers. There we include different operations on numbers which have one single definite value.

But in the algebra we not only deal with numbers, we deal with some letters also which represent different numbers. These letters may have any value we choose to assign to them. There is no restriction to the numerical values a letter may represent.

Suppose for example, let 'x = 1', that does not mean that x must always have the value 1, but only for this example we can consider x = 1.

For Example:

5x, 2x + 5, 2a + 2, y - 2x, x + 10y, x + 2y - 3z, etc.

Suppose, we consider three circles of radii 7 cm, 8 cm and 9 cm.

We can say here that are three circles of radius r cm, where, ‘r’ represents different numbers.

The letters used in Algebra are called Variables or literal number or simply literals.

Generally in algebra we operate letters or symbols without assigning any particular numerical value at all.

According to the definition of algebra, premising that the signs +, -, × and ÷ are used with the same meaning as in Arithmetic.

Also, the following sign and symbols are frequently used in algebra and have the same meanings as they have in any other branch of Mathematics.

= means, "is equal to"

≠ means, "is not equal to"

< means, "is less than"

> means, "is greater than"

≮ means, "is not less than"

≯ means, "is not greater than"

∴ means, "therefore"