"The pure mathematician, like the musician, is a free creator of his world of ordered beauty." -Bertrand Russell
Mathematics is an essential academic discipline that has many different topics worthy of studying such as geometry, trigonometry, and algebra.
In today's article, we will examine a lot of necessary information about algebra and try to encourage secondary school students to thoroughly enjoy their learning experience.
The Foundations of Algebra
People's opinions about algebra are quite divided. On one side of the spectrum are those who greatly appreciate the logical expressions and efficiency of algebra, whereas, on the other hand, there are individuals who despise algebra's many rules and complexity.
Nevertheless, it is important to state that algebra is an essential academic discipline taught in school's worldwide; there isn't any way to escape so it's better to enjoy it thoroughly!
Algebra can easily be defined as a vital part of mathematics in which letters and symbols are utilised to represent numbers or quantities in formulae and equations; it's the way equations describe relationships between variables.
Algebra was originally invented by scholars to make mathematics more simple to all types of people.
While many people have been credited with advancing different aspects of algebra, the term algebra stems from the Arabic word "al-jabr" that was initially found in Muhammad ibn Musa al-Khwarizmi’s 9th-century manuscript that when translated means “The Compendious Book on Calculation by Completion and Balancing.”
Al-Khwarizmi’s book was a masterpiece that highlighted facts such as land distribution, rules on inheritance, and distributing salaries equally.
It is important to note that while Al-Khwarizmi is credited for originated algebraic expressions and terms, it was until the European Renaissance that mathematicians introduced symbolic algebra that is practised today.
There are many branches of algebra with one of them being linear algebra: linear equations that are about linear combinations. Linear algebra is used in almost all areas of mathematics that involve geometry, sciences, and engineering.
Since it is not uncommon to come across algebraic expressions that are extremely complex, algebra needs to be simplified to become more cognitive and straightforward.
How is it done?
Algebra can be simplified by combining like terms, eliminating the parentheses, minus signs such as subtraction and negatives, and by following the BEDMAS or PEMDAS order of operations.
After discovering the origins and precise definitions of algebra, it is of the utmost importance to remember the benefits of studying algebra such as more efficient mathematics skills, improvement of logical thinking, and overall usefulness outside of school in daily life.
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Where to Find an Algebra Tutor
After implementing many distinct techniques such as learning shortcuts, joining study groups, and asking your parents for your help, are you still struggling to grasp the essential concepts of algebra?
Have no fear, Superprof tutors are here to save the day!
Hiring a qualified tutor is the perfect solution to remedying any maths issues that you may face. Also, personal instructors specialising in any domain are highly recommended since they instil confidence in the student, provide personalised assistance, and are available at a time and place that best suits your needs.
When shopping around for a new algebra tutor, it is crucial to look for qualities that should be evident in the best academic instructors such as patience, communication skills, and teaching ability.
While there are many tutoring sites to consult on the internet available for citizens of the UK, the hands-down best option is Superprof.
With maths tutors offering sessions at competitive prices to improve algebra all over the United Kingdom, Superprof has a selection of tutors that will suit the needs of any person.
Whether the pupil wants to learn online or in-person, there is the option of finding tutors that will accommodate your wishes. Check out the Supeprof website to find a professional maths tutor near you. Also, want to know the best part about Superprof tutors? The first lesson is entirely free! That means there is no pressure to stay with the same tutor you choose from the outset if you are not enjoying your classes.
Hire a Superprof private educator today to remedy all your algebra woes; you won't regret it, we promise! Find a mathematics tutor Toronto here.
Introduction to Variables in Algebra
Since algebra is such a layered academic discipline with many concepts, it is sometimes necessary to analyse each concept separately to acquire a further understanding of the entire subject.
What shall we examine now?
Variables. Becoming familiar with variables is necessary before solving, translating, or evaluating an algebraic expression; they are an essential aspect of algebra that cannot be ignored.
But what is a variable?
A variable can be defined as a letter that is used to replace a number. For example, the most commonly used variables that can be observed in algebraic expressions include the letters x, y, z, a, b, c, m, and n. Some letters such as i or e are not used as variables since they have other values in algebra. Also, it is important to mention that the letter o is never used since it might be mistaken for the number 0.
Considering the number of letters that potentially can be used as variables, there is one sign that should be avoided at all costs. Which is that? The multiplication symbol. The variable of x is used quite often for variables; therefore, to use the multiplication sign could be an issue and cause unnecessary confusion for the student.
Variables are used to change verbal expressions into algebraic expressions.
The following are specific terms used also, subtraction, multiplication, and division that can translate words into letters and numbers:
- Addition: sum, greater than increase.
- Subtraction: minus, less than decrease.
- Multiplication: times, product, multiplied by.
- Division: halve, divided by, ratio.
The previously mentioned terms are frequently observed when tackling algebraic expressions and determining variables.
To learn more about variables and practise them, consult the Khan Academy Algebra I section about variables to watch videos about examples containing one or multiple variables.
Algebra Resources Online
Since we are living in the information or technology age, there is more information directly provided to us than ever before; long gone are the days of researching topics at the library!
Thanks to the developments of modern technology such as the internet, there are so many instructional sites worthy of consideration. Nevertheless, a wealth of information does not always mean that everything provided is trustworthy.
At times there seems to be more trash than treasure.
With that being said, it is important to consult reputable sources, like Superprof, as to which algebra websites are the most highly recommended. Without further ado, we will analyse the best websites and podcasts to learn more about algebra.
Reputable Algebra Websites
The following are the best online resources to learn more about algebra:
- Khan Academy: priding themselves on offering free world-class education to all, Khan Academy is a fantastic and trustworthy site to consider the basic and more complex concepts of algebra. Some of the sections available for study on the Algebra I topic include algebra foundations, solving equations and inequalities, working with units, linear equations and graphs, and forms of linear equations.
- Mathplanet: although the study programmes offered on Mathplanet are intended for an American audience, the vital aspects of algebra that are examined are universal; that means even for UK students! Important categories include discovering expressions, equations, and functions, exploring real numbers, and how to solve linear equations. Also, each section includes theory, examples, and video lessons to improve comprehension of algebra.
The previously mentioned websites are brilliantly organised, engaging, and 100% trustworthy resources to learn more about algebra. After visiting these sites, you might not even need to look for anything more.
Highly Recommended Podcasts
Podcasts are digital audio files that have been made available on the internet for downloading to a computer or cellular phone, they usually include a series about specific information which you can subscribe to completely free of charge.
Podcasts are fantastic for those who have little time but enjoy learning new academic disciplines on the go.
The following is a highly recommended podcast that touches on the fundamentals of algebra:
- Philosophy and Fun of Algebra by Mary Everest Boole: recommended by Player FM and updated only a day ago, the philosophy and fun of algebra podcast are meant for children but also enjoyed by adolescents who want to learn the basics of algebra engagingly. The conversational tone is exceptional and past podcasts include topics such as The Great x of the World, Square Root of Minus One, The Makings of Algebra, From Arithmetic to Algebra. This podcast can be downloaded on Google Play, Apple Store, or Player FM.
Learning algebra by using online resources has never been so much fun!
Basic Algebra Rules, Equations, and Examples
Algebra, just like most things in today's society, is governed by rules and regulations. The rules experienced in algebra keep things organised and structured. There are various rules in algebra covering the topics of arithmetic, exponents, and radicals.
Algebra rules of arithmetic include the distributive property of multiplication and guidelines for adding, subtracting, multiplying, and dividing fractions among many others. The following list provides basic information about the previously mentioned algebra rules and how to obey them:
- Distributive Property of Multiplication: based on the fact that you're multiplying something by with a sum of two or more distinct terms.
- Multiplying a Fraction: if you have the purpose of multiplying a fraction, times the numerator to achieve your goal.
- Dividing a Fraction: dividing a fraction is quite similar to that of multiplication except the denominator needs to be divided and then it will have the same effect as multiplying the numerator.
- Rules of Adding and Subtracting Fractions: the denominators must be identical and the numerators must be attached. Also, their sums must be placed over the common denominator.
Exponents are a quantity that represents the power to which a number or expression is to be raised, usually expressed as a raised symbol beside the name or phrase in algebra. The following are algebra rules for exponents:
- Zero-Exponent Rule: can be seen as a0 = 1 in equations and means that anything raised to the zero power is 1.
- Product Rule: the product of two powers with the same base is equal to the base raised to the sum of the two exponents. This rule can be effectively used by writing out the exponents as multiplications.
Another aspect that has a distinct set of rules is radicals.
What are radicals?
While there are many definitions for the word radical, in mathematics it means a quantity forming or expressed as the root of another. The following is an algebra rule for radicals:
The algebraic expression pictured above fits with the critical exponent rule of am ∙ an = am + n.
Before mentioning essential information about algebraic equations, it is important to define what an equation is: an equation can be understood as two expressions on either side of a sign that indicates their relationship. The relationship in an equation can have the same value, be less than, be greater than, or both.
Algebraic equations have terms and components that represent different things. For example, if a term includes letters and numbers, the messages are known as variables, and the numbers are the coefficients. Also, another rule of equations is that if the words have precisely the same variable, they become known as like terms and they can be added, subtracted, divided, and multiplied as if they were simple numbers.
Also, it is important to state that to solve equations at times the expression needs to be rearranged and the x needs to be isolated.
Many algebra examples can be found on reputable sources such as Study.com and Mathplanet.
In conclusion, by analysing many distinct aspects of algebra students become familiar with an important section of mathematics before, during, or after secondary school.
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