Truth be told that Algebra is all about equations and, outrightly, based on unknown values called variables. Thus, to perform arithmetic operations, there are various sets of rules that need to get followed. Algebra is a cardinal life skill that is worth understanding as it embraces the journey from basic mathematics to statistics and calculus. Algebra is divided into different branches: elementary algebra, advanced algebra, abstract algebra, linear algebra, and commutative algebra.

• • • Elementary algebra: Elementary algebra is one of the fundamental mathematics fields that talks about the properties of numbers and their relations. It helps in building good knowledge about the understanding of arithmetic. Various civilisations like Babylonian, Greek, Indian, Chinese, and Islamic have contributed to advancing elementary algebra. Elementary algebra’s basic knowledge helps in the apprehensions of other subjects like statistics, computer science, economics, and business.

   

  • • Advanced algebra: It is one of the cardinal branches of algebra that emphasised intermediate-level algebra expressions. It includes the topic related to Equations with inequalities, matrices, solving systems of linear equations, graphing of functions and linear equations, conic sections, polynomial equations, quadratic functions with inequalities, rational expressions, and trigonometry. It prepares students to solve high-level algebraic equations with ease.

   

  • • Abstract algebra: Abstract algebra encompasses abstract algebraic structures, preferably than the usual number systems. It is related to algebraic expressions independent of the distinct nature. Abstract algebra explains advanced algebra topics and ensures an in-depth understanding of commutative algebra, representation theory, and homological algebra that is a part of abstract algebra. This branch of mathematics is called abstract algebra.

   

  • • Linear algebra: It is the branch of mathematics dealing with linear equations. Today, linear algebra is a central locus apex of all facets of mathematics that works on the modern portrayal of geometry, lines, planes, and rotations. In a nutshell, it deals with the application of linear algebra to spaces of functions.

   

  • Commutative algebra: It analyses commutative rings, their ideals, and modules of those rings. Commutative algebra is a part of algebraic geometry and algebraic number theory. With the help of commutative algebra, various other disciplines of mathematics can get derived swiftly. It is one of the pivotal components of modern pure mathematics.

There are 5 properties of Inequalities.

1. Addition property: It states that if any inequality subsists when adding any same number on both sides will not change the discrepancy in that number.
2. Subtraction property- It states that if any inequality subsists when subtracting any same number on both sides, inequality will still exist.
3. Multiplication property: It affirms that if one side of the inequality can multiply by any number, then another side of the inequality can multiply by the same number.
4. Division property: It insists that if one side of the inequality can get divided by any number, then another side of the inequality can get divided by the same number.
5. Transitive property: It states that for any real numbers a, b, c. If a ≤ b and b ≤ c, then a ≤ c.

In the case of multiplication and division of algebraic expression, you need not consider whether the variable is the same or not; you need to multiply/divide every expression simultaneously to get the results.

Factorisation refers to any entity’s cleavage, such as a number, a matrix, or a polynomial. It converts that entity into a product of another object. This concept is mostly taught in secondary classes from 6 to 8. For example- -12, -6, -2, -1, 1, 2, 6, and 12 are called factors because their reminder is always 12. It is sometimes referred to as algebra factorisation.

The linear equations in one variable refer to an equation that gets manifested in ax+b = 0, where a and b are two integers, x is a variable with only one solution.

The first step of solving linear equations in one variable is to simplify and use add or subtract properties to move the variable term to one side and all other terms to the other side.

The true virtue of algebra is that it is the basic language that can get used to describe various real-world phenomena in no time. From measuring gravity to finding the value of an unknown object, Algebra can be used to solve any mathematical problem.

1. What are the basics of algebra?
   The basics of algebra include:
   • Addition and subtraction of algebraic expressions
   • Multiplications and division of algebraic expression
   • Verbal Problems
   • Literal equations
     
2. Which category of math can be termed algebra?
   Algebra refers to the branch of mathematics that talks about various symbols, and dominions used manipulating symbols and signs. The symbols you see written in Latin and Greek letters are variables, such as “x” or “y.”
   
   
3. Is algebra easy to learn?
   Algebra is never hard to learn, but all you need is a better understanding of the subject matter and in-depth apprehension of concepts. Many students study the mechanics of algebra than focussing on its face value. It helps them to get a better idea about the core approach of algebra before its implication.
   
   
4. What is the usage of algebra?
   The primary usage of algebra is to build a mathematical relationship and its equation with the help of symbols, alphabet, and letters. With the help of algebra, you can supersede values and explain the equations for the unfamiliar quantities.