Many people think that algebra and geometry are two boring and complex sciences. In fact, any precise science causes more problems for students of all ages. While students study at elementary or middle school, they treat math and arithmetic as fun. So, why do students hate to learn algebra when it comes to the high school? Why do high school and especially college subjects look much more boring?
From the first sight, one may say that the basic problems become more complicated. When students move to the high school level, they face cases which are more difficult to solve. It is caused by the next reasons:
- Lack of fun
- Lack of visual elements
- Stricter requirements
- Urgent deadlines
- More complex content
After all, your teacher doesn’t help you the same way he or she did before. Young children get more assistance with their homework assignments. Their works are not treated too harshly. Finally, while arithmetic equation usually involves up to 3 elements or only one unknown number (X), high school and college algebra implies dealing with longer equations with a lot of unknown numbers. That is why this subject is difficult to master.
How to Solve Algebra Problems: Basic Rules
If you want to learn algebra, it is important to begin with simple things like the equation above. You should know the answer to the problems like that one from your arithmetic course. Simply counting the numbers is not a hard task.
Arithmetic is pretty easy by its nature. When it comes to learning algebra, a lot of new features appear. The first problems students have to solve look this way:
x-3=4
The answer is obviously 7. By the way, when you start to study algebra, you may notice that this science is using letters as well as many other signs. The letter x, for instance, stands for the unknown component, also called a variable. The equation of such type is easy to solve. Students have already learned all possible answers from their arithmetic course. Thus, we can say that algebra is nothing more than substituting letters for figures.
To learn algebra faster, students have to view it as a puzzle starting with stuff like “x – 5 = 2” and ending up with something like “x = 7.” The same things work with addition, multiplication, and division.
It looks pretty much easy, but there are two sides of the coin. To solve the problem, it’s not enough to write down the answer. Learning algebra is also about learning how to interpret the received number/result. A step-by-step mini-guide should help:
- Understand what has to be removed to get “x = …”
- Adding the opposite of subtracting. Use this golden rule to solve your algebra equation.
- Apply the principle to the both sides.
Once you master at least these basic stages, you’ll be able to pass various tests associated with algebra like SAT. Here are more tips for writing SAT exam.
Learning Algebra: Exploring Examples of Problems
You should practice first to understand. Check out the example:
A student wants to
remove the "-5." |
It means doing the opposite. In our example,
add 5: |
Apply the given method to both sides: | Solved! |
Guess why we added 2 to both sides of the given equation. Well, you have to learn that algebra is the science of creating a balance. Make a balance out of any equation – and you’ll get the right answer!
Some students start using online writing services to solve too much difficult algebra assignments. When you’re overloaded with the work or simply don’t know how to solve a large case, this solution is really wise.
Another example might be as follows: 4 + 5 = 9
We can pretend that the letter A means 4, i.e.:A = 4
And
The letter B stands for 5, i.e.:
B = 1
Thus, the solution would be A plus B is 9, i.e.:
A + B = 4
It is the opposite side of the coin, meaning how to compose equations.
Most Effective Ways to Learn Algebra
To learn math or any of its branches, one has to make a lot of efforts. It’s not enough to memorize things only like you do when you study English literature or history. Students need to turn on their analytical and critical thinking too.
What may really help on the way to mastering the art of algebra is the variety of online applications created specifically for the students of the math classes. Computer algebra systems were also created to atomize the system of solving complex math problems and large cases. You will probably agree with the fact that it is much easier to solve various equations and use formulas in Excel instead of doing everything manually on the separate sheet of paper.
So-called self-directed learning is the nice method to study basically any discipline.
If you want to learn math quickly and solve equations easily, the basic secret is to practice all the time. There are a lot of free examples online. Free algebra equations and tutorials are also available online.
Before getting started (if you prefer studying on your own without advanced help), you should check the most prestigious educational institutions regarding their academic materials. Various colleges and universities have different requirements for the papers. The most advanced materials are usually suggested by the Ivy League (US) and Russell Group (UK) universities, so we recommend downloading algebra information from the official websites. The boards of these groups introduce topics at the undergraduate level mostly.
Let’s discuss how to solve practical problems. The choice of the disciplines then is influenced by the type of practical problems you are keen on. Mind that such sort of cases demands particular basic skills and awareness of the generic instruments of math, such as algebra, geometry, calculus, combinatorics, probability, and statistics. Just like a group of languages (Slovenian, Scandinavian), each of the courses is related to another one.
Another time-tested method is to download free books or buy useful guides online. Online libraries often have free previews, so you can decide which ebook suits your needs best. With the help of math, you can improve a set of various skills: from analytical and critical thinking to research skills. Even amateur mathematics can help you to learn many basics. You should absorb lessons from both technical and non-technical books when learning algebra. These books can define which area of math suits your interest best of all. Different online tests on your personality can also give a hint.
Popular science market is opened for all students who have a pure interest in everything new and unexplored. It is not necessary to read chapter by chapter – find only pieces of information which you consider interesting and useful for your goals. As an example, you may have a look at Fermat’s last theorem book. Many general survey books on algebra and other related fields can solve all your problems and remove any doubts. This literature is easy to read unlike many of your textbooks. Many distinguished teachers and professors recommend the books by famous British mathematician Prof. Ian Stewart. The man writes in a very clear and entertaining style. The scientist brings his topics alive for the reader.
Students have to understand they can not read an algebra book the way they read fiction or non-fiction literature. It’s something rather different. The process of using such book must be both active and interactive. It cannot be a passive experience. The basic thing is to realize that while reading algebra book, one has to obey the specific arguments and, in addition, complicated and subtle lines of reasoning. Go on answering questions which the content presents to you. The best way to check your knowledge and skills is through reproducing calculations/results for yourself. Try to make notes either on the paper or your laptop when reading the selected book.
That is a simple way to define which fields of math students wish to learn as well as how to answer the most common questions. Do you want to become a mathematician or someone else? How can you connect your life with this science? It is also important to define which level of proficiency would be enough for your requirements.
The basic principle of learning algebra can be discovered through plugging the numbers into the variables before doing the actual calculation. Another way is to keep simplifying the equation until it is solved. It is often asked to interpret the results. The learning process is impossible without this step. Now you have a full understanding of the concept, so you can be using variables freely.
There is one more good example of algebra problem. It has a bit different format. The question is still about the unknown variable X. As a reader, you know every detail needed to solve this equation.
A=1, B=2, C=3, D=4, E=5
T=-1, U=-2, V=-3
(6X/8)+(2T+4)=((CD/2)-AD)+V
Note that 6X means 6*X; and AD means the same as A*D.
We plug in the variables, and the equation appears to be:
(6X/8)+((2*-1)+4)=((3*4)/2)-(1*4)+-3
Some simplifying arithmetic gives us:
(6X/8)+-2+4=(12/2)-4+-3
The Importance of the Subject
Arithmetic is the first class in your life to learn fractions and decimals. Algebra consists of the many similar elements. On the whole, math is a sort of independent language. So, another good practice used to learn algebra and other sub-languages of mathematics is to give the meaning to this language. In other words, consider the next factors:
- Potential benefits for your further development and, perhaps, career. In which fields can the language be used? Will it make a value during various journeys or life challenges? Remember that math is a universal language which is understood by every nationality even better than English.
- Are there any good aesthetic qualities? It does not necessarily have to please your ear, but it may be still good from other sides.
- The academic level of difficulty.
Math is a wide and all-time expanding subject. It may be called both science and language, so it possesses both humnatirain and precise science values. It is one of those tools that we use almost every life but rarely pay attention.
The following disciplines require a deep knowledge of algebra and other related sciences. Here is the list of such courses:
- Management
- Marketing
- Economics
- Macroeconomics and microeconomics
- Accounting
- Finances
- Statistics
- Computer science/information technologies
In fact, many other fields may require solid math skills, even history and geography. So, it’s impossible to ignore its role in all aspects of our life. Only when you understand the meaning and value of the certain phenomenon, you realize why it is important to learn it. That is another thing we want to prove in our article.
Some of the basic rules of algebra can be explored on the various websites like this one. Now, it is time to have a closer look at the different sides of the discussed subject. You all know that algebra is about numbers. However, you should be more specific in terms of defining its basic features.
These are likely to include the following topics in the course of standard high school/college algebra:
- Set Theory
- Group Theory
- Algebra (linear, abstract, etc.)
- Calculus of a single variable
- Calculus of more than one variables
- Common differential equations
- Partial differential equations
- Real Analysis
- Complex Analysis
- Topology
- Discrete mathematics (combinatorics, graph theory, etc.)
- Number Theory
- Geometry
- Trigonometry
- Probability theory
- Statistics
By living in the age of modern technologies, it is better to solve all the problems on your PC or laptop. Using Excel might save more time than using an ordinary calculator. At the same time, you have to learn how to work with your calculator really fast as you will be limited by the time during your algebra or statistics exam. Moreover, always bring a handy calculator with you. Students are not allowed to use laptop, notebook, or smartphone calculators on their tests – only special devices are allowed!
Conclusions
The book-based method is the basic method preferred by most of the mathematicians. If you want to learn algebra perfectly, be ready to invest a lot of time in watching an educational video and reading corresponding literature. And don’t forget to order free examples or cheap problems solutions from the trusted academic writers!