Algebra is a branch of mathematics that substitutes letters for numbers. An algebraic equation represents a scale where what is done on one side of the scale is also done on the other side of the scale and the numbers act as constants. Algebra can include real numbers, complex numbers, matrices, vectors, and many more forms of mathematical representation.

Simply put, algebra is about finding the unknown or putting real-life variables into equations and then solving them.

Unfortunately, many textbooks go straight to the rules, procedures, and formulas, forgetting that these are real-life problems being solved and skipping the explanation of algebra at its core: using symbols to represent variables and missing factors in equations and manipulating them in such a way to arrive at a solution. Learning algebra can seem intimidating, but getting the hang of it is not that hard!

The field of algebra can be further broken into basic concepts known as elementary algebra or the more abstract study of numbers and equations known as abstract algebra. The former is used in most mathematics, science, economics, medicine, and engineering, while the latter is mostly used only in advanced mathematics. Let's learn more about this fascinating subject!

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Origins of Algebra

Tracing the history of algebra, the first name that comes up is Muhammad ibn Musa al-Khwarizmi, also known as the "Father of algebra." He was a Persian mathematician who wrote a book named Kitab Al Muhtasar fi Hisab Al Gabr Wa I Muqabala in Arabic, later translated into English as "The Compendious Book on Calculation by Completion and Balancing," from which the word algebra was derived. The book provides a systematic solution for linear and quadratic equations. According to Al-Khwarizmi, the word algebra is described as the 'reduction' and 'balancing' of subtracted terms that transposition to other sides of the equation (cancellation of like terms).

Before you learn the concepts of algebra, familiarize yourself with its history. | Image credit: Gerd Altmann on Pixabay

History & Evolution of Algebra

There are three critical developmental stages in "Symbolic Algebra," which are as follows:

  1. Rhetorical Algebra: It was developed by ancient Babylonians where the equation was written in the form of words that remained up to the 16th century.
  2. Syncopated Algebra: Its expression first appeared in Diophantus Arithmetica (3rd century), Brahmagupta's "Brahmagupta's sputa Siddhanta" (9th century), where few symbols were used, and subtraction was used only once in the equation.
  3. Symbolic Algebra: All the symbols were used in algebra at this stage. Many Islamic mathematicians, like Ibn Al-Banna and Al Qalasadi, wrote in their books about Symbolic Algebra. Francois Viete fully developed it in the 16th century. Rene Descartes introduced a modern notation that could solve geometrical problems in terms of algebra known as Cartesian Geometry.

In early algebra, quadratic equations played an important role, where it is said to belong to one among the above three equations. The Greeks and Vedic Indian Mathematicians developed two more stages of algebra which lie between rhetorical and syncopated stages known as Geometric Constructive stages.

Understanding the Variable in Algebra

A variable is a letter representing some unknown; a variable always represents a number, but it carries varying values when written in an expression. By convention, mathematicians usually assign letters(not mandatory) at the end of the alphabet (such as x, y, and z) to be variables.

All algebraic expressions and terms consist of at least one variable. It is the variable that distinguishes an algebraic expression from an arithmetic one. The presence of a variable in a mathematical expression enables infinite possibilities to determine the value of the expression.

A variable is a quantity that can change with the context of a particular mathematical problem or an experiment's context. Generally, we use a single letter or alphabet to represent a variable. The most commonly used symbols to represent a variable are alphabets like x, y, a, b, c, m, n, and z.

The variable is a crucial element of algebraic expressions. | Image source: Math Expression

Types of Variables

  • Dependent Variable: The dependent variables show the effect of manipulating or introducing the independent variables.
  • Independent Variable: The independent variables are those the researcher controls.
  • Quantitative Variable: The numerical variables are called quantitative variables. They always represent a measurable quantity.
  • Categorical Variables: The variables which take on values that are names or labels are considered categorical variables. They are also called qualitative variables.
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List Of Useful Algebra Resources For All

Check out these apps and websites that make algebra learning fun and efficient!

Algebra Learning Websites

Udemy

There are thousands of online courses on algebra listed on the website. One of the main reasons for such a vast library on a particular topic is the broad scope of algebra. Algebra starts with middle school and has such advanced skill levels that universities and colleges offer specializations in the subject.

No matter your level or your goal to learn Algebra, you can find an appropriate course for yourself on this highly dynamic website. You can find courses that range from beginner to advanced levels for academic purposes. You can also access numerous courses designed specifically for individuals working in the field out there.

Coursera

The website offers several online courses, guided projects, and degree programs on algebra that can help you grow your skillset and knowledge and have an accredited degree that will help you with your professional career.

LinkedIn Learning

LinkedIn believes in cutting across geographical boundaries for everyone and making it possible for all to get the right opportunity they deserve based on their abilities and skillset. They are offering a dedicated section that is all about learning online. This section features a wide range of courses on employable skills and other courses that will add value to your career.

These courses cater to the needs of most students who wish to learn online, as they cover the gap that you need to get your next dream job of yours. You can find numerous algebra courses focused on solving equations and getting acquainted with the subject.

Algebra Learning Apps

  • Brainly Homework Help & Solver: Brainly is 100% free, and one can access it anytime.
  • Socratic – Math Answers & Homework Help: This app is powered by AI. It is free, and one can find answers to their problem in a snap.
  • Schoolyourself: Schoolyourself provides free interactive lessons on maths from award-winning Harvard instructors through hundreds of interactive, personalized math lessons and a custom analytics platform.

Important Algebra Rules and Expressions

Learn the basic rules of algebra and never miss a trick to ace the subject and score high on your test!

Commutative Rule of Addition

In algebra, the commutative rule of addition states that when two terms are added, the order of addition does not matter. The equation for the same is written as (a + b) = (b + a). For example, (x3 + 2x) = (2x + x3).

Commutative Rule of Multiplication

The commutative rule of multiplication states that when two terms are multiplied, the order of multiplication does not matter. The equation for the same is written as (a × b) = (b × a). For example,

(x4 - 2x) × 3x = 3x × (x4 - 2x).
LHS = (x4 - 2x) × 3x = (3x5 - 6x2)
RHS = 3x × (x4 - 2x) = (3x5 - 6x2)
Here, LHS = RHS, which proves that their values are equal.

abide by laws
Rules are the guiding principles of algebraic operations. | Source: Gerd Altmann from Pixabay

Associative Rule of Addition

In algebra, the associative rule of addition states that when three or more terms are added, the order of addition does not matter. The equation for the same is written as a + (b + c) = (a + b) + c. For example, x5 + (3x2 + 2) = (x5 + 3x2) + 2.

Associative Rule of Multiplication

Similarly, the associative rule of multiplication states that when three or more terms are multiplied, the order of multiplication does not matter. The equation for the same is written as a × (b × c) = (a × b) × c. For example, x3 × (2x4 × x) = (x3 × 2x4) × x.

Distributive Rule of Multiplication

The distributive rule of multiplication states that when we multiply a number by the sum of two numbers, it results in the same output as the sum of their products with the number individually. This is the distribution of multiplication over addition. The equation for the same is written as a × (b + c) = (a × b) + (a × c). For example, x2 × (2x + 1) = (x2 × 2x) + (x2× 1).

The cardinal rule of algebra itself is balance. An equation has an equals sign, and whatever is on one side of the equals sign must equal what is on the other side of the equals sign. With that in mind, we can do anything we want to an equation - as long as we preserve the balance on both sides of the equals sign.

Need Help For Algebra?

You can find an algebra tutor for both in-person and virtual learning. In-person tutors are hired locally using services such as Superprof or teacher recommendations. If you hire an in-person tutor, you’ll need to set the price range for tutoring sessions and payment methods and transport yourself or your child between home and the algebra lessons.

Alternatively, you can use an online tutoring service to get algebra homework help or learn skills like problem-solving and solving differential equations. Online tutors offer virtual lessons and support for various math classes, including algebra. You can also find math tutors to help with test prep for college entrance exams.

Qualities Of A Good Maths Teacher:

Here are the qualities you should look for in a math tutor.

  • Communication: You and your tutor must be able to communicate well. Find someone quick to respond to emails, phone calls, or texts.
  • Patience: Math can be difficult to learn. If your tutor grows frustrated, you will also be frustrated with the entire process. Find a tutor willing to explain a concept in multiple ways to help you fully understand it.
  • Teaching Aptitude: A tutor must possess the skill level and ability to successfully relay information to teach someone else.
  • Passion for Math and Teaching: Look for a tutor who will be excited to explain everything to you because they truly love and enjoy algebra. Find someone who wants to share his or her passion for derivatives and integration with you!
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Shreyanjana

Shreyanjana is an archaeologist who ironically finds the written word to be the most powerful means of storytelling. A travel buff and a photography enthusiast, she has been writing and sharing stories of all sorts ever since she can remember.