Algebra is a complex high school and college science which requires an in-depth knowledge of mathematics as well as the basic operations (adding, subtracting, multiplying, and dividing). Algebra as well as its "sister" - trigonometry - are involved in numerous real life situations and professions such as engineering, construction and architecture.
Basic Points in Algebra
- Understand and use the order of math operations with respect to the given acronym: PEMDAS.
- Be aware of the negative numbers and know how to manage them. Remember the basic rule: the higher the figure, the further it is from zero.
- Make long problems easier by having them organized. Put down every new stage on a new line.
- Learn variables which cannot be defined as numbers (x, y, and z).
- Solve algebraic equations by excluding the numbers to obtain only the variables.
Let’s go into some details. You may wonder what PEMDAS is in algebra. Well, it is a helpful instrument for memorizing the specific system and order of operations. You may find out how to use the order of operations by reading the corresponding article. In brief, this order refers to:
If you wish to know why the order is so critical in algebra, you must realize that working with operations in the wrong order can influence the response from the negative aspect. For example, in case you deal with the issue like 7 + 3 x 4, if you decide to add 3 to 7 before the multiplication process, you’ll receive 40, which is the incorrect answer. By all mathematical rules, people should conduct multiplication before addition. This way, you’ll obtain 19, which is a correct answer to the given problem. So, mind your order of operations!
Studying Basic Algebra Principles
Check the main math operations. Begin with arithmetic. To learn algebra well, a student has to master arithmetic as the basis. Such functions as adding, subtracting, multiplying and dividing are learned from the elementary school education, so you should not have problems with them. In fact, algebra is completely based on these basic math operations, but it involves more complex formulas, equations, and work with other symbols different from numbers. If you don’t possess the mentioned skills, you still have time to study them on your own on the internet or with the help of the math books. In other words, everything must be studied step-by-step to obtain the necessary knowledge in order to start getting high grades.
If you simply hate working with numbers, you should understand - there is no need to be a professional in the corresponding field to learn algebra on the basic level. In case you would like to work in the field of journalism or law, you may simply learn the basic equations instead of studying all those nasty advanced calculus formulas that are essential when you choose statistics or accounting.
Also, students may buy prepared algebra solutions from the online academic writing services to both improve their skills and gain a sufficient score / grade. Keep in mind students are always allowed to bring their calculator with them in class. You may use various software solutions like Excel to solve big algebra questions times faster and more accurately. The main point is to learn how to work with different devices. That is what an average citizen needs.
At the same time, students are not allowed to bring anything else except for their calculators and pens to their exam. Smartphone or laptop calculators won’t work as these devices are forbidden by any teacher during the examination. Dedicate enough time to learning how to work with your calculator fast enough as far as every exam is limited by time.
How to Use Negative Numbers?
You might probably know that -/- gives + while -/+ still stands for them -. Those are the basics only.
You will frequently meet negative figures in algebra, statistics, economics, accounting, and - some other disciplines which require a knowledge of math. It would be better to have a look at the basic operations like adding, subtracting, multiplying, and dividing before moving to the same operations with the negatives. We will mention some of the major principles and concepts used in algebra in order to proceed with the negative numbers.
- Remember: a negative analogy of a number is the same distance from 0 as the positive analogy is but in the opposite direction. Apply number line to take it easy. A number line makes it easy to define which numbers are greater or lesser. The principles of using it may be explored on the math dedicated website.
- If you try to add 2 negatives together, the number turns even more negative. The digits will become higher, but the meaning will remain with the sign -. Thus, it will be lower in any case.
- Subtracting a negative number means the same as adding a positive number.
- Multiplying or dividing negatives always leads to a positive answer.
- Multiplying or dividing a positive and a negative brings us to a negative figure.
Algebra Problems Have Their Own Structure
Just like an essay or research paper, an algebra problem and its solution have their structures. You should now not only provide the answer, but to describe the process as well as interpret the received results.
You have to remember how to organize lengthy problems. Difficult problems with many possible solutions may take plenty of your time. To avoid mistakes, it is critical to organize the process by beginning with the new number line each time it is possible to take a new step toward a solution. When you work on a two-sided equation, it is recommended to put down each symbol of equality underneath each other. That is a great approach to avoiding mistakes or fixing them later.
E.g. to cope with the equation 10/5 – 1 + 4 x 3, we may structure the entire solution this way:
10/5 – 1 + 4 x 3
10/5 – 1 + 12
2 – 1 + 12
1 + 12
Any algebra problem can be resolved in such a way. A step-by-step method is always effective, so don’t forget about it when learning algebra.
Knowing What Variables Are and How to Work with Them
Algebra plays a great role in passing SAT. It is one of the required sections, so it is better to learn the discussed subject before taking the test. You may find out about SAT scores more. The test results might help on your way to entering college.
Anyway, working with variables is one of the conditions. SAT involves tasks associated with these figures. As we have discussed above, in algebra, students first meet letters and other symbols in addition to the good old numbers. These figures are usually used to interpret unknown numbers which have to be found with the help of correct formula and solution.
These things are also known as variables. Their values are unknown, and sometimes it is pretty hard to discover them. In some cases, you won’t even have to get corresponding numbers. There can be too many unknowns to find specific answers, so students should only show the way to solve the problem.
Here are several ordinary examples of variables in algebra:
- Letters (a, b, c, x, y, and z)
- Greek letters like theta or beta
- Please keep in mind - not all symbols are unknown variables. E.g. pi, or π, is always equal to approximately 3.14159.
Anyway, you should think about these variables as “unknown” numbers to make it easy. Most of the time, the purpose is to reveal the hidden number. The sample of the problem to explore is shown below.
5x + 5 = 15, x is our variable respectively. It means that a certain value corresponds to the given letter. It should make the left side of the equation equal to 15. Because 5 x 2 + 5 = 15, the correct response is x = 2.
An easy method to master variables is to remove them with the question marks. For instance, a student may want to turn the equation 1 + 4 + x = 12 as 1 + 4 +? = 12. The answer is 7, of course.
But what should you do in case the variable pops up more than one time? It is still possible to solve an algebraic problem of the type. Learn to treat variables as ordinary numbers. You can apply any arithmetical operation to the variables that are alike.
To make it easy, x + x = 3x, but x + y has another value (let’s say, 3xy).
To help you understand, there is an equation 1x + 3x = 8. You can add 1x and 3x together to obtain 4x = 8. Since 4 x 2 = 8, you discover that x = 2. It works with the same variables only!
How Does the “Cancelling” Principle Work?
Make an attempt to obtain the variable by itself. Algebra equations have either numbers, variable, or both on two sides. If you must solve x + 4 = 8 x 3, learn to place and analyze the variable all alone. To do so, it is important to delete “+ 4” value. Subtract 4 from the first side. You’ll stay with x = 8 x 3. Still, to get both sides equal, you will have to subtract 4 from the second side. Thus, you’ll get x = 8 x 3 – 4. By sticking to the generally accepted order of algebraic operations, a student should multiply before subtracting. The answer is x = 24 – 4 = 20. It’s just this easy!
You may want to find out how to cancel addition with subtraction. Obtaining the unknown value by itself on the first side refers to replacing the numbers next to it on the other side of the equation. It looks like the opposite operation. On the whole, addition and subtraction are opposites as you could notice from the example below. It is one of the basic rules you should memorize when learning algebra.
The same principle works with multiplication and division. Thus, it becomes simpler to learn algebra even without any free help.
Lessons to Strengthen Your Skills
If you need some more lessons to develop deeper skills in algebra, use various visual elements to better remember the information. You can apply images to illustrate anything from formula to equation. Instead of the pictures, some teachers use a group of physical objects during their lessons to develop student’s knowledge and understanding. These might be blocks and coins.
What about "common sense checks"? It is another great way to learn algebra lessons deeper. Every time you convert a problem written in words into algebraic shape, check the formula by plugging in simple values. Now think whether your equation is meaningful when x equals to zero, 1, and -1?
The answers are not all the time the integers. Algebraic problems do not always require solutions with round and simple figures. These figures can be expressed through decimals, fractions, and irrational numbers. That is why each student really needs to bring a calculator to each lesson. However, the tutor may ask to give the final answer in the exact form.
If you’re already doing great in algebra, check out whether you can deal with factoring. One of the most complicated math skills is factoring. Most of the students who are keen on algebra learn this section sooner or later. It is used to obtain a shortcut in order to get lengthy equations into easy forms. It is considered a semi-advanced algebra section, so you definitely need some help when moving to such chapter.
Solving real-life issues where algebra skills are required is one of the best ways to practice all the time. To learn algebra is not enough – a student has to apply the gained skills. Otherwise, this person may forget even the basics.
You can train when dealing with your finances. You can practice by obtaining a part-time or seasonal job where the math skills are essential. You may start learning new related disciplines like statistics, accounting, economics, geometry, finances, etc. In fact, even computer science demands a solid knowledge of mathematics. As a rule, engineering and construction students have to face various algebra problems regularly.
Finally, you can order free or paid online help in the shape of algebra problem solutions samples or papers written from scratch after turning to the online experts in the field of academic writing!