We think (along with many professionals) that mathematics is a language. Just as you can translate a text from English into French (or from any language into any other language) without losing the meaning, you can translate from any language into language of Math and vice versa. For example: Saying (in English) that a basket contains some apples and some oranges, will translate into language of math as z=x+y, where z is the number of fruits in the basket, x is the number of apples in the basket, and y is a number of oranges in the basket. The meaning is exactly the same. However, the expression z=x+y is not in English any more. It is algebraic expression.
So what is Algebra? Algebra is one of fundamental component of mathematics. Without good understanding of Algebra it is going to be impossible to understand more advanced concepts, for example calculus. Algebra should be taken very seriously. Many professions, such as accounting, engineering, architecture, etc. are reliant on math and numbers. But just as many trades, such as electricians, plumbers, masonry, etc. also rely on math-driven proportions, measurements, and quantities to do their jobs well. Products used by us every day could not have been produced in a safe and efficient manner, and made safe and effective without carefully constructed mathematical formulas.
Numbers are an integral part of the world and mathematics helps to make sense of them by ordering them in a way, that makes it easy to manipulate them and understand relationships between them. Mathematics is structured as a succession of blocks leading up from the simple arithmetic to more complex branches, for example trigonometry, calculus, etc. Algebra is not the most complicated part of mathematics, however, it requires certain discipline of the mind to understand and, even enjoy it.
Below you will find some tips to help you with it:
Study the definitions.
Just as every word in the English (or any other language) has a particular meaning, so do the algebraic terms. To understand algebra you need to understand those terms. Use your dictionary (or better still -- encyclopedia) to learn algebraic terms. Just as the meaning of words in the language of your mother tongue is firmly etched in your mind, so must be the algebraic terms. Study and memorize them. This will help you to study and work with formulas and equations. Below you will find definitions of some of the basic algebraic terms. Don't take my word for it. Verify the definitions by independent sudy.
Constant – a non-varying value (for example 3, 25, 124). Letter at the beginning of English alphabet are conventionally used to denote constants (for example a, b, c, etc.). Constants are almost always present in the algebraic formulas or equations, for example y=x+a, where a is a constant and could be any given number.
Variable – a symbol representing some data, which is commonly a number, but may also be any mathematical object such as a vector, a matrix, or even a function. Don't let this confuse you. For the purposes of elementary algebra a variable is a number we don’t know yet. The symbol is conventionally one of the last letters of the English alphabet, such as x, y, or z. For example: x+a=b, where x is variable, a and b are constants.
Expression – In mathematics, an expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Complicated? Don't sweat it. What it means is: numbers, symbols and operators (such as +, ×, etc.) grouped together that show the value of something. For example: a x b is an expression.
Equation – In mathematics, an equation is a formula of the form A = B, where A and B are expressions that may contain one or several variables called unknowns, and "=" denotes the equality binary relation. Although written in the form of proposition, an equation is not a statement that is either true or false, but a problem consisting of finding the values, called solutions, that, when substituted for the unknowns, yield equal values of the expressions A and B. Again, this is not as complicated as it looks. It is just a group of expressions that are located on either sides of an equal sign. An equation says that two things are the same, using mathematical symbols. Fo example: y-x+a, or 10=2+8.
Some of the textbooks do not have glossaries. If yours does not, use your dictionary with it.
How to study?
The best way to understand Algebra, in my opinion, is to follow a process. When presented with a problem, first try to visualize it. If possible, draw a diagram, or a table. Write down what is given (i. e. what values and relations are known). Understand what are asked to find. Think what formula is best used to answer the question and write it down. Carefully note what each letter in the formula means. Analyse the formula to figure out which elements of the formula are known and which are not. Follow the same process for each unknown element, until all elements are fully defined. Substitute unknown elements for their formulas in the formula that answers the final question. Simplify the final formula, then substitute all elements for their values, and finally -- calculate. When substituting for the values, always use the units of measure. The easiest check if the result is correct is the unit of measure of the final answer. If it is correct, it is one of the indicators that the result is also correct. There usually are different ways to arrive at the answer. Compare them and evaluate which method works best. Determine why (and how) method A is more efficient than method B. Asking questions and seeking help from your classroom teacher and your peers will help.
When you need to work things out by yourself, make sure the environment of your study place is quiet and free of distractions. Practice, practice, and then practice some more. Pay attention, and do your work step by step. That way you can check each step you took. Don't try to memorize. Repeat your work and keep track of the elements that are problematic for you. Once you understand, you will remember.
Do not stop when you get a correct answer. Solve the same problem again using different method, if possible, to check your answer. If your answer is not the same, it means you did not understand that problem.
Do not hesitate to call 416.727.4220 or e-mail us at email@example.com if you need help. We will work with you and (and with your permission with your teacher) to determine what help and to what extent is required, and will be glad to help you on the road to quality education.
A math tutor is recommended for students who are having problems following the teacher in class and studying by themselves. Your math tutor can help you to study algebra using methods that are more suitable to individual study. The methods may include, among other things, real-life examples, games, puzzles, illustrations, etc. Remember -- Algebra is never dull and can be a lot of fun.
Be Patient. You will make mistakes. This is part of the learning process. Your mistakes, if you are persistent, will help you understand the material better. Learn from your mistakes, and do not let them stop you. Stick with it. Before you know it, you’ll will ace the Algebra, and may even learn to love it!
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