Algebra

A mathematical science of studying the symbols is called algebra.

Algebra is a mathematical science, introduced by a Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī in 9th century.

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Introduction

The concept of algebra is mainly used in three different cases. In other words, it is used to represent standard constant values, variables, and also used to find unknown quantities with the help of known quantities in mathematics. You can understand how exactly algebra is used in mathematics as well as in other scientific topics.

1. Representing Constant Values

We know that the total time for completing a day is $24$ hours. It is a constant value. So, I would like to represent it by a letter or alphabet. Therefore, I have chosen alphabet $t$ to represent the total time of a day.

$t=24$

Actually, $t$ is a letter but $24$ is an arithmetic quantity and they never be equal in value. However, we are assumed that they both are equal algebraically. Therefore, the value of letter $t$ is now equal to $24$.

Similarly, the concept of algebra is also used in almost all scientific topics. For example, there are several universal physical constant quantities in science but some of the most reputed physical quantities are denoted by letters or alphabets. Here is an example, which understands you how the value of speed of light in vacuum (in meter per second (m/s)) is denoted by $c$.

$c=3×{10}^{8}$

As explained here, you can represent a constant physical quantity by any letter or alphabet according to the concept of algebra.

2. Representing Variables

Algebra is also used to represent variables. It means, a letter or alphabet can represent various values and you understand here how it is possible.

My current age is $32$. So, I would like to represent it by a letter $a$. Therefore, it is written in mathematical language as follows according to the concept of algebra.

$a=32$

Now, the value of letter $a$ is equal to my age. Actually, age is not a constant factor and it changes every year. Next year, my age becomes $33$. So, the letter $a$ should also represent every value.

$a=33$

Similarly, my age will be $34$ at year after next year. So, it can be written as follows.

$a=34$

Only one single alphabet $a$ now represents $32,33,34$ and it also represents many more values as my age is increased.

$a=\left\{32,33,34,\dots \right\}$

Therefore, a letter or alphabet is used to represent various values of an element in algebra and it is known as a variable algebraically.

3. Finding Unknown Quantities

The concept of algebra is also used to evaluate unknown quantities. The following example understands you how alphabets are used to find the unknown quantities by using the values of known quantities.

For example, assume my age is represented by an alphabet $a$ and my sister’s age is represented by another alphabet $s$. My sister is $4$ years elder than me. Logically, adding number $4$ to my age evaluates my sister’s age. So, it can be written as follows.

My sister age $=$ My age

As per our assumption, it can be written as follows mathematically.

$s=a+4$

This mathematical expression is called as an algebraic expression. It can be used to find the age of my elder sister. You know, my current age is $32$. Restore the value of $a$ to get my sister age.

$⇒s=32+4$

$⇒s=36$

The value of alphabet $s$ is $36$ but we know that $s$ is age of my elder sister. Therefore, age of my elder sister is $36$.

As per this method, you can find values of unknown quantities and this mathematical approach is widely used to develop expressions between two or more elements. The same principle concept is also applied to other mathematical branches to develop mathematical expressions.

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