Understanding Algebra

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One key to being successful in algebra is performing inverse functions. Inverse functions are a way of undoing or untangling a problem. If a chosen problem, for example, contains multiplication, you will use division, which is the inverse of multiplication, to solve the problem.

The Basics

The inverse of subtraction is addition. The inverse of multiplication is division. The inverse of division is multiplication. The inverse of an exponent is a root square root, cube root, etc. Focus on isolating the variable. You will do this with a series of inverse operations. This will keep the equation balanced and still equal. Cancel addition by using subtraction and vice versa. Individual terms in an equation are linked by a combination of plus and minus signs.

Remember that you must do everything equally to both sides of the equation. So you will get: Cancel multiplication by using division and vice versa. In the same way, you can perform inverse operations on multiplication and division. To get the variable alone, you will divide.

Example #1

Remember that for an equation, you must divide both sides of the equation equally. Since this is a multiplication problem, you will solve it with division: Divide both sides equally by 3. Instead, show division by writing the terms as a fraction. As problems become more complicated, you may have to perform multiple operations to get to a solution. You will usually use addition and subtraction first, to isolate the variable with its coefficient.

Then you will use multiplication or division to find the solution. In algebra, you can almost always find out if you have done the problem correctly by checking your answer. Take the solution that you found, and insert it back in the original problem in place of the variable. Then simplify the problem, and if you reach a true statement, you solution was correct.

Learn the basic math facts. Algebra is a system of manipulating numbers and operations to try to solve problems. When you learn algebra, you will learn the rules to follow for solving problems. But to help make that easier, you need to have a strong understanding of basic math facts. You should know basic addition, subtraction, multiplication and division facts and be able to work with them easily. In particular, you should be able to do the following: Being able to work with two-digit numbers is even more helpful.

Know your multiplication tables from 1 through Know division and factors for numbers up through 12x Practice the rules of fractions. Algebra uses the rules of fractions as much as any other numbering system. You need to be comfortable with finding common denominators, adding and subtracting fractions, multiplying and dividing fractions.

When you learn algebra, you will expand this knowledge into working with unknown variables, but you need a strong understanding of the basics first. You need to know the concept of reciprocal numbers. The short definition of a reciprocal is that it is a fraction turned upside down. You use reciprocals as an alternative to division, when the problem is complicated. Instead of dividing by one fraction, you can multiply by its reciprocal. Know how to use negative numbers. You will often be using negative numbers or variables.

You should review how to add, subtract, multiply, and divide negatives before starting to learn algebra. Here are some basic rules for working with negatives. On a number line , a negative number is the same distance from zero as the positive, but in the opposite direction. A negative plus a negative will also be negative. Adding two negative numbers together makes the number more negative. Two negative signs together cancel each other out. Subtracting a negative number is the same as adding a positive number. Multiplying or dividing two negative numbers gives a positive answer.

Multiplying or dividing one positive number and one negative number gives a negative answer. Why do you have to reorder some algebraic questions before you can answer them, and not others? It was discovered long ago that algebraic equations are most easily solved by following certain steps in a particular order. Not Helpful 4 Helpful 8.

I am starting college in the future. What is the easiest and fastest way to learn algebra? I have been out of high school 40 years. The easiest way is to read an algebra textbook and understand each concept as it's presented. You could also hire a tutor. Not Helpful 8 Helpful I absolutely suck at math; I don't understand a word the teacher is saying. It's hard for me to fully understand websites like this. Any advice on how I can improve? It sounds like you could definitely use the services of a good tutor.

A "good" tutor is one who can sense that a student is not grasping a concept and is adept at adjusting an explanation until the student does understand. If you don't want to pay for such a service, perhaps you could find a friend or relative who understands algebra and who's willing to spend some time helping you.

Not Helpful 0 Helpful 1. Ask your teacher things you don't get, or ask classmate or friend for help. Maybe even stay at lunch or after school with your teacher so you can fully understand it. You could always find Khan Academy videos that are helpful. Likewise, the upper "3" means the variable "a" is cubed or itself times itself times itself or "a" to the third power.

Notice how some of the variables in the above formulas are directly adjacent to each other. This is the standard used to indicate the variables are multiplied. Yes, the slash in the sphere and cylinder formulas means divide by that lower number, 6 and 4 respectively. What you have been and are doing is just simplifying, a. The mathematicians are no more able to look at an equation and instantly come up with the answer any better than the rest of us can.

They just solve and proceed from line to line, trusting they solved the previous line s correctly. This time there is more than one set of parentheses. When that happens, the rule is to do the innermost ones first. Another example would be This results in a number 5 less than zero, so we say negative 5 or The 8 is called a positive number, just as the 1 is called a negative number. Adding a positive number to a negative number is really just subtracting the negative number from the positive number. For the sake of completeness, the next section is about what else you should know about negative numbers.

Numbers plus negative numbers result in lesser numbers. Keep in mind is a lesser number than -5, etc. Numbers minus negative numbers result in larger numbers. In other words, minus minus results in a positive increase a. Minus a minus is exactly the same as plus a plus, e.

Book Contents

This is a good time to mention that in mathematics, two negatives equal a positive when applied to minus a minus subtraction, or any multiplication, or any division. Spreadsheet software or applications will happily do the arithmetic and sort out the negatives versus the positives for you once you have replaced all the variables. It even knows to do the innermost before the outermost, etc. As an example, suppose you have simplified an equation to the following mess:. The spreadsheet will immediately solve the equation and give back the answer of If you have the software or Google Drive access, go ahead and try it.

If you are really good at spreadsheet calculations, you can, of course, do equations with the variables still in place; substituting the variables with cell locations or range names. At this point the equation becomes invalid. An equation immediately becomes invalid when a divide-by-zero scenario occurs. Software applications are designed to recognize this when it happens. Plugging whatever-divided-by-zero into a spreadsheet used to give interesting results, before applications were modified to detect this.

The basic concept of algebra is just plugging the numbers into the variables, and then doing the arithmetic. One merely keeps simplifying the equation until it is solved. You now have a full understanding of that concept. Yes, you have been using variables since the first paragraph. Here is the last example. It is presented in a different format.

The question, however, remains the same. You already know everything needed to solve this equation.


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Other examples would be: Whenever you change the actual value on one side of the equation; you must do the same on the other side of the equation. The same rule applies for addition, multiplication, and division. So we multiply both sides of the equation by 8. To find out, we go back to the original equation and replace X with We then simplify reduce the equation as before to its simplest form.

There is a lot more a very lot more to algebra, but it is really only an expansion of what you have already learned. Algebra is the basis of all other mathematics; including geometry, trigonometry, calculus, and so on. A good understanding of algebra is required to succeed at the other mathematics.

Mathematics, itself, is the foundation of most other disciplines.

How to Learn Algebra Fast—Rules, Equations, Solutions

This foundation is not just necessary for the sciences such as physics, electronics , chemistry, biology, astronomy, and so on. A mathematical foundation is necessary for many careers; including marketing, economics, architecture, and many, many others. Sign in or sign up and post using a HubPages Network account. Comments are not for promoting your articles or other sites. I ma closer now than ever. I tried and tried and tried to 'get' algebra. Took it in high school, didn't get it; dropped the class because I didn't want an "F" on my transcript.

Tried again as an adult in community college. Monopolized the teacher's office hours; became well-known in the learning center; hired a private tutor. I still couldn't grasp it. It seems so arbitrary. Your explanations make the very basics of addition and subtraction clearer, but I still am flummoxed by the division and multiplication. I suck at basic math in the first place.

I understand in English grammar, how a double negative negates the statement, for instance, "She doesn't have no sugar," ends up meaning she does have sugar.

How to Understand Algebra (with Pictures) - wikiHow

But, in my mind, it just doesn't seem to translate across to numbers, and make sense. That's where I always thought it seemed arbitrary, and why I fall flat on my face every time; because I'm trying to make sense of it, and I can't. That, and each new problem looks so different that I can't seem to apply the formula, becuase it isn't parsed English grammar term; don't know if it applies to math , just like the example problem s.

Geometry was invented first!!! I was always bad in math especially algebra , this really helps, but my question is , is there a book I can buy using these symbols? I did 5 line papers with this and I hope my mom is proud when she sees all the work I did. Im so thankful for all the help an support,i have a big test coming up,was so worried,but now ,i feel so secure,thanks for ur help.

Math was always a weak subject for me. This would be helpful and useful for anyone who's struggling with it. Voted up for useful! Where were you when I was struggling with Algebra in 7th grade? And you even have pictures. I tried so hard, I used to stay after school for extra help.

Finally the teacher agreed to pass me with a D if I would stop coming. I thought it was a good deal, although I was an A student in other subjects, I just couldn't grasp it. My son is now a teacher, and tells me she was a failure as a teacher for not trying harder! I could have sworn I've been to this website before but after browsing through some of the post I realized it's new to me. Anyways, I'm definitely delighted I found it and I'll be bookmarking and checking back frequently!

Hope this was helpful. Good hub on algebra, I hate it though, I speak like 5 languages but can never do math. Have a lot of respect for people in the science field.

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