Before you take algebra, you have to learn the basics of addition, subtraction, multiplication and division. Those forms of mathematics seem concrete and make sense. Then, algebra comes along and you have to deal with exponents, parenthesis and hypothetical numbers. You are probably wondering why and how can this be logical? Simplifying algebraic expressions may change your mind. Check out Beginning Algebra: Building a Foundation to understand algebra the right way.
Algebra can be and has been frustrating for many people of all walks of life. Nonetheless, it is crucial to remember that the most successful individuals are those who can solve complex problems, effortlessly. Algebra is one of the first steps on that path to learning how to conquer difficult obstacles.
With algebra, you must define the problem, think of ways to solve it, look for a solution and analyze your results. Since algebra is very abstract, it causes your brain to think in new patterns. Have you heard of the phrase “use it or lose it”? Well, your brain is a muscle, and that phrase can be applied here, as well. If you do not work your brain, it might start to lose its sharpness.
Envision a week that ends in chaos. How would you pick up the pieces? Where would you start? Also, if you had people and your budget going out in multiple directions, how would you control that? Think of algebra as an approach to organizing a multitude of diverse situations.
The first and most important step to solving an algebra problem is to clarify its expression. Using simplification techniques, you can easily calculate the expressions and complete them, instantaneously. It is good to know that the order always remains the same whether it is a small expression or a long question. The process of simplification always starts with the parentheses.
Parentheses and More
Solving the parentheses is a mathematical principle that has to be executed in order to solve an expression. There are several ways to figure out an algebraic expression to ensure you get the same results. On the other hand, if you do not follow the order of operations, according to the mathematical principles, then you will more than likely get the wrong answers. In order to simplify an expression, you have to learn the basic rules so that you can competently solve any expression and come up with the right answer.
Some options for solving algebraic expressions are explained below. The methods are easy to learn and convenient to implement. The most critical thing to note, regarding simplifying algebraic expressions, is that you have a higher probability of getting the same answer, no matter which method do you use.
Play with the “Like Term” Method
“Like terms” refers to the terms that might have different variables, but have the same power. In these cases, the order to the variables does not matter. You only solve the expression using powers. To illustrate, x2 and x is the same variable, but they have different powers. You can find out the value of the variables by taking it to either side of the “=” sign. In order to solve your expression using this method, you have to find the “like terms” and then solve the problem. The next step is to combine the like terms to make it a unique term.
Try the Factorization Method
Factorization is the process of division in which the number is divided into multiple numbers. For an example, “12” is a number, and 1, 2, 3, 4, 6 are all its factors. The most important thing to learn in this process is that you have to know the divisible of each and every factor.
In order to write the divisible of a number, you can use different methods. The first method would look like this, 4 x 5. Another method is to write divisible of 20 is 4 (5). Prime numbers are the numbers that are only divisible by two; that is 1 and itself. Similar to the “like term” method, the factorization method also comes with the following steps:
- Find the greatest common factor that is available in the expression.
- Divide all the terms in the given expression using the smallest common factor.
- Represent your expression as the multiple of a common factor along with the remaining terms.
Solve Expressions Using the Additional Simplification Method
With this method, you can add like terms that have the same power, and then solve the associated problems. This procedure emphasizes like terms, so it makes solving a much more simple process.
You could memorize problems to help you recall the correct order of operations. However, you can also use the PEMDAS acronyms to help you remember operations much more easily in addition to aiding you in solving expressions. This way, you can come to the correct solution much more quickly. The acronym is quite useful because each letter stands for parentheses, exponents, multiplication, division, addition and subtraction. Not to mention, it is place in the correct order.
Basic algebra is usually taught to students 8th to 9th grade. There can be easy and difficult ways to learn and teach algebra. It depends on the teacher, the goals and how prepared the students are to learn. On the other hand, there are some shortcuts that can be used to make algebra more fun. Even if you do not plan on being a math major, all career paths require knowledge of math. Moreover, the more practice and understanding you have, the better your career and life prospects.
Once you can memorize the order of operations, you should have no issues when it comes to simplifying algebraic expressions. That is just the first step. You should take it further to improve your mathematical competence and confidence. You might even set a goal for algebraic mastery. Learn more by taking these Udemy courses, Algebra 1 Made Easy and Algebra 1: Straight to the Point. If you are preparing for the SAT, you should read this Udemy article, SAT Math Problems: Getting Ready for One Tough Test.