Introduction to Algebra: The Basics
Algebra is the study of mathematical symbols and various algebraic rules to manipulate these symbols. These symbols are known as variables, and with the knowledge of algebra, you can solve specific kinds of mathematical problems quickly. Algebra requires an in-depth understanding of mathematics along with the knowledge of basic operations like addition, subtraction, multiplication, and division.
Algebra, along with its sister branches like trigonometry and arithmetic, has a wide variety of applications in real-life situations and professions like architecture, engineering, construction, and medical science. This makes algebra an exciting subject to learn. This article provides some of the basic rules that can be applied to learn algebra without much difficulty.
Essential points to keep in mind while learning Algebra
- Get yourself acquainted with the concept of negative numbers. Always remember that in case of negative numbers, the higher the magnitude, the smaller is the number.
- Always use a new line for a new stage while solving the algebraic equation. This will avoid a lot of confusion.
- While solving the algebraic equation, use the mathematical operations according to a specific priority order given by the acronym: PEMDAS, where,P: Parenthesis, E: Exponents, M: Multiplication, D: Division, A: Addition,S: Subtraction.
To understand the importance of this priority order, let’s solve a problem:Solve: 9+4×5
If you try to add 9 to 4 before the multiplication process, you’ll get an answer as 65, which is the incorrect answer. By using PEMDAS acronym, multiplication should be done before addition, so the correct answer to this problem is 29. So, this means it is essential to use the priority order to find a proper answer while solving arithmetic or algebraic equation.
How to Use Negative numbers?
A negative analogy of a number is at the same distance from 0 as the positive analogy but in the opposite direction. So, to simplify the concept of negative numbers, imagine that number on a number line. While dealing with negative numbers, some essential points should always be kept in mind like:
- If you add two negative numbers together, the result will be a more negative number.
- If you multiply or divide two negative numbers, it will always lead to a positive answer.
- If you multiply or divide a positive and a negative number, it will lead to a negative answer.
- Subtracting a negative number is the same as adding a positive number.
Understanding what variables are and how to work with them
In the algebraic problems, some mathematical figures are used to interpret unknown numbers, which have to be found out, using a correct formula and approach. These unknown figures, whose values you have to determine, are known as variables. These variables are usually represented by English alphabets (a, b, c, x, y, z) or using Greek letters like theta (?) or beta (?).
In algebraic problems, you have to just try to obtain the value of a variable. As discussed earlier, algebraic equations may have numbers, variables, or both on either side of the equation. If you have to solve: x + 6 = 4*3, keep all the variables on one side (here just a single variable, i.e., x) and try to obtain a unique numerical value on the other side by applying mathematical operations. In this case, to do so, it is important to take the “+ 6” value on the other side after multiplying 4 with 3. The multiplication of 4 and 3 gives you 12. Now subtract 6 from 12, you’ll stay with x = 6. So as earlier discussed, a student should always stick with the generally accepted order of algebraic operations and multiply before subtracting. So, the answer is x = 6.
It is, in fact, very easy!
How to solve Complex Equations
Every algebraic equation (involving one variable, here x) can be solved using the same method as discussed above; however, you can get the final answer in the form of a positive integer, negative integer, or even in decimals as well.
Example: x+15= 6x + 101
Bringing all the variables on the right-hand side performing a mathematical operation of subtraction will give:
Step 1: 15-101 = 6x-x (Note: Due to the movement on the other side sign changes as discussed before)
Step 2: -86 = 5x (Performing simple mathematical operation of subtraction)
Step 3: : -86/5 = x (When the coefficient of the variable is shifted to the other side, it acts as the denominator on the other side)
Step 4: : -17.2 (When -86 is divided by 5 we obtain the final value of our variable)
It is also important to note that in algebra, the variable can be on either side of the equals sign. There is no rule which states that the ‘x’ (variable) must be on the left-hand side.
Some more tips to strengthen your skills
It is a proven fact that our mind perceives visual concepts in a better way as compared to plain concepts. The same is the case with algebra as well. If you need to acquire a deeper understanding of algebra, you should use various visual elements to remember the details in a better way. You may add images to explain everything from formula to equation. Instead of pictures, some teachers also use a collection of physical objects during their lessons for a better understanding. These visualizations may be in the form of objects like blocks and coins. So, you can try both of these approaches and choose the best-suited approach according to your understanding.
Algebra offers tools for writing formulas and solving equations that are much clearer and simpler than the traditional method of writing everything out in words. And as discussed earlier, this branch of mathematics has a wide variety of applications in various real-life situations in the field of technology, sports, financial management, and even health and fitness. So, algebraic problems are introduced in the school curriculum, various aptitude examinations and in some of the college curriculum as well. However, just learning algebra is not enough; a student must be able to apply the gained-skills for a better understanding of this subject. Solving real-life issues, where algebra skills are required, is one of the best ways to practice algebra.
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