Amazing Algebra Facts To Make You Better At Problem Solving

Sridevi Tolety
Jan 06, 2023 By Sridevi Tolety
Originally Published on Feb 02, 2022
Edited by Naomi Carr
Fact-checked by Shruti Thapa
One of the most basic branches of mathematics is Algebra.
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Age: 3-18
Read time: 7.1 Min

The majority of math is just trying to solve, and provide reasoning for, different properties that abstract notions have.

These abstract notions can be with the use of lines or natural numbers. They can also be entities that are defined by properties that are basically known as axioms.

Mathematics is a word with Greek roots meaning study, knowledge, and learning. Math includes various different topics such as number theory, arithmetic, formulas, algebra, spaces and shapes (known as geometry), and calculus.

In general, there is no specific consensus that defines the epistemological status or exact scope. If you enjoy reading about the fun of solving and learning algebra, read on to learn more about some basic formulas, history, and more about math!

The History Of Algebra

Algebra is a part of mathematics that concerns the study of relation, quantity, and structure. It can be said that algebra is almost like learning another language.

Learning just simple and basic algebra can enable us to learn and solve the problems of the modern world by understanding them better. Such problems cannot be solved by using simple arithmetic, instead, algebra uses symbols and words to make statements.

The familiar concept of real-life word problems can be transformed into mathematical equations for us to find the correct answer!

We can trace back the origin of algebra to the ancient colony of Babylonians. They had developed a system of arithmetic called Babylonian mathematics, which helped them to calculate and make algorithms to solve problems.

These systems that they had developed were very advanced.

The Babylonians were able to solve complex problems that we can today solve by using quadratic equations, linear equations, and indeterminate linear equations. The Greeks, Chinese, and Egyptians in the 1st millennium BC were solving mathematic equations including rhetorical algebra, abstract algebra, or advanced mathematics concepts.

They would do this with the use of different methods, which can be seen described in Euclid's 'Elements', 'The Nine Chapters', and the 'Rhind Mathematical Papyrus and on the Mathematical Art'.

It is said that Muhammad ibn Musa al-Khwarizmi who was a mathematician, was the first to invent the word algebra. He is known today as the father of algebra.

The Basics Of Algebra

Various different areas and fields of specialization like engineering, natural science, finance, medicine, and social sciences need to use basic arithmetic operations and mathematics for systematic exploration. Some mathematical applications have been developed into different fields, and people have made careers out of it, for example, statistics and game theory!

These parts of mathematics are often known as the field of applied mathematics.

Some mathematics is not specifically derived due to its application or need for a solution, such math is known as pure math. This is independent of any applications.

However, much of the time, practical applications are found in or used in many cases once they are discovered. One of the most famously known examples of this is the factorization of integers. This goes back to the mathematician, Euclid.

Factorization did not have any practical applications immediately after its discovery. In fact, it was rarely used before we found it had a major application in computer networks!

Algebra uses many symbols in arithmetical operations where operators are used. Algebra is a very interesting topic and a subject we use in our day-to-day life unconsciously! For example, we do calculations in grocery stores while buying produce.

Algebra is also a basic skill we need to further our knowledge in calculus or statistics. We can also make a career in it. Students might find algebra equations difficult as they require logical analysis and complex thinking, but with practice, anyone can become good at algebra!

What are the different algebra theorems?

Before the period known as Renaissance in the middle ages, the field of math was divided into two different parts; one part was arithmetic. Arithmetic was basically the usage of numbers, number systems, and its manipulation to solve linear algebra, algebraic expressions, or advanced algebra, which we even use today in modern algebra.

The second part was geometry which is the study of different geometric shapes giving rise to geometric methods.

Some other fields, such as astrology and numerology, were also studied during that time. However, they were not properly differentiated from the remaining mathematics.

Some of the most common and well-known algebra theorems in linear algebra include the Hawkins–Simon condition, the fundamental theorem of linear algebra, rank–nullity theorem, Rouché–Capelli theorem, and Cramer's rule. Some famous theorems in abstract algebra for abstract structure are Cartan's theorem, primitive element theorem, Eckmann–Hilton argument, and fundamental lemma (also called Langlands program).

Basic Algebra is taught to someone with just Arithmetic skills.

What are the different algebra formulas?

Applied mathematics is a branch of math that deals with methods commonly used in engineering, science, and industry as well as business.

Hence it can be said that applied math is just mathematical science that contains really concentrated knowledge. This term of applied math can be explained as a specialization for professional mathematicians so they can work on solving real-life problems.

This might then lead to a career that is primarily focused on solving practical problems, especially using the study, formulation, and usage of math models in the fields of engineering and science or other fields where math is used.

The basic properties of algebra can be seen in the form of algebraic equations, symbolic algebra (symbolic language), word algebra equations, algebraic structures, and mathematical symbols.

It can also be seen in the use of a simple equation with the use of general concepts like binary operations, linear equation, elementary equation, equals sign, negative numbers to calculate solutions.

Some of the common properties are the commutative property where a + b = b + a, which means that you can change the sequence of numbers with signs, and the answer will remain the same.

Another property is the commutative property of a multiplication operation, which is simply a × b = b × a.

Associate property of addition says that a + (b + c) = (a + b) + c, whereas the associative property of multiplication can be explained as a × (b × c) = (a × b) × c. The distributive property is known as a × (b + c) = a × b + b × c or a × (bc) = a × b - a × c which will give the same solution of each side.

Some basic and commonly used algebraic properties are the reciprocal property where a = 1/a or 1/b= b(a, b are the inverse elements), the multiplicative identity of a × 1 = 1 × a = a, the additive identity in algebra where a + 0 = 0 + a = a and the additive inverse where a + (-a) = 0.

Here we can see the three rules of algebra which the commutative, associative, and distributive laws!

Fun Facts About Algebra

Sometimes mathematics is utilized because of curiosity in a specific area or the will to solve complex problems. Such mathematics might only be relevant in the field that used it, but it is also usually applied in solving and providing solutions for other problems which are similar to those areas.

Math which started becoming useful in solving problems in specific areas became a part of the general concepts of math.

Often people distinguish between applied math and pure math. But pure math often has many real-world applications, such as the usage of number theory in the field of cryptography.

Elementary algebra is one of the most commonly known and learned forms of basic algebra. This basic mathematics is taught from the very beginning to students who possess almost zero knowledge of math except for the arithmetic functions. Arithmetic is the area where only the basic operations, which are -, +, ÷, x, and numbers, are used.

Variables are symbols in algebra that are used to hold a place.

Variables can be defined as any terms such as a, z, x, y.

This is very useful due to the fact that it allows us to formulate the general and basic laws of arithmetic like a + b = b + a, which eventually leads us the formulate the general and basic laws of arithmetic for all values of b or an in the properties of the number systems which are real.

Having variables also allows us to use numbers that are essentially unknown.

This is very useful when we have equations where we know all the numbers except one. For example, we can solve the value of variable x in the equation 2x -4 = 10.

Hence it becomes easy to break down the equation into smaller parts without changing its meaning and keeping the variable intact.

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Written by Sridevi Tolety

Bachelor of Science specializing in Botany, Master of Science specializing in Clinical Research and Regulatory Affairs

Sridevi Tolety picture

Sridevi ToletyBachelor of Science specializing in Botany, Master of Science specializing in Clinical Research and Regulatory Affairs

With a Master's degree in clinical research from Manipal University and a PG Diploma in journalism from Bharatiya Vidya Bhavan, Sridevi has cultivated her passion for writing across various domains. She has authored a wide range of articles, blogs, travelogues, creative content, and short stories that have been published in leading magazines, newspapers, and websites. Sridevi is fluent in four languages and enjoys spending her spare time with loved ones. Her hobbies include reading, traveling, cooking, painting, and listening to music.

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Fact-checked by Shruti Thapa

Bachelor of Arts specializing in English

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Shruti ThapaBachelor of Arts specializing in English

With a passion for American, British, and children's literature, Shruti is currently pursuing a Bachelor's degree at Garden City University, Bengaluru. Her fluency in Nepali, Hindi, and Mandarin demonstrates her linguistic abilities and global perspective. In addition to her literary pursuits, she has a keen interest in non-fiction literature, aesthetics, early childhood education, and Egyptian history. Shruti's research paper 'Bringing Art Illustrations In Education And Pop Culture' showcases her proficiency in these areas and her dedication to academic excellence.

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