Algebraic Expressions to Algebraic Equations

If you are reading all my articles on algebra then you should have gained good understanding of algebraic relations. Also, you know that how they originate from the word phrases in our daily lives.

Algebraic Expressions to Algebraic Equations

In this article I will explain the difference between algebraic expressions and algebraic equations. You will learn that why algebra doesn't stop at algebraic expressions? Why do we need algebraic equations?

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Algebraic Expressions to Algebraic Equations

In my previous articles on algebra, while explaining algebraic relations, I anonymously introduced you with algebraic equations. But, in this article you will find out the clear difference between algebraic expressions and equations.

Algebraic Expressions to Algebraic Equations

Algebraic Expressions to Algebraic Equations

To understand the difference, let's review the following word phrases or sentences;

1. added to 25 times the number of lawns mowed by Arthur.

2. Arthur's earnings are added to 25 times number of lawns mowed by him.

3. Five times a number added to twenty.

4. Five times a number added to twenty is fifty.

Word phrases (sentences) number (1) and (2) are from my previous article. In word phrase number (1), "the added to 25 times number of lawns mowed by Arthur" there is only one variable which is, "number of lawns mowed". Consider we represent this variable by the letter "n"

So, the algebraic relation becomes, "60 + 25n"

In number (2) word phrase, there are two variables, earnings and number of lawns. Represent earnings by letter "e" and number of lawns by letter "n" again. The algebraic relation becomes,

e = 60 + 25n

Notice the difference between both the relations. One of them has equal sign used in it, and we call it an equation instead calling it algebraic expression as "equal" to "equate" and it becomes "equation."

The hint in the word phrase for the equation: The use of words "is" or "are" in word phrases give the indication of equations instead the algebraic expressions.

Now the solution to word phrases number (3) and (4) are given below;

3. Consider the number in the phrase is represented by letter "m", our unknown in the phrase and hence variable. The relation is given as;

5m + 20

No use of words "is" or "are" in the word phrase number (3), therefore no equal sign used in the relation. Hence, the relation is an algebraic expression.

4. In number four the relation is given below;

5m + 20 = 50

As the word "is" used in this word phrase, therefore equal is used in the relation. Hence the relation is an equation.

Equations are like a balance, having both sides equal to one another. Focus your mind to keep the balance of an equation all the times you work on them.

I hope that above explanation is enough to make all my readers understand the difference between algebraic expressions and equations.

In other words, it can be said that when there are variables involved in a relation but no equal sign is used the relation is algebraic expression and if an equal sign is used, the relation is an equation.

From here, we'll take two paths to explore algebra further. One path is exploring equations and the other is exploration of polynomials. So, stay tuned as more algebra is on its way.

Algebraic Expressions to Algebraic Equations

Understanding Algebraic Concepts

When a student declares that he does not like mathematics, probably what he meant was that he is finding the teaching of algebra difficult. In schools and colleges, algebra is the core of mathematics manipulation. Any student that has a good grip in mathematics will tell you that the secret to doing well in mathematics is having a good understanding of algebraic concepts.

Understanding Algebraic Concepts

Understanding Algebraic Concepts

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Understanding Algebraic Concepts

Understanding Algebraic Concepts

If you are a student or perhaps your child is finding mathematics difficult, the tips below could make understanding algebraic concepts a little easy. The words that are most associated with algebraic problems are: to solve, simplify and re-arrange equations and expressions.

Solving algebraic equations

This simply requires a student to obtain a value for a variable. Ideally you have to ensure that the single variable in question is made to stay on one side of the equation. The reason for this action is to make sure that numbers are collected together separately on one side while letters or variables are collected together on the other side to avoid things been mixed up. This is the first step to solving any algebraic equations.

Checking the signs

The next important thing is to check the signs associated to the numbers and variables. You have to Watch the 'equal' sign separating the expressions. Preferably it makes sense to have all the numbers on the right hand side of the 'equality' sign while the numbers containing the unknown variables or letters tidied up on the left hand side. Now carefully ensure that signs swapped as the numbers and variables swapped sides. For example if a negative variable is swapping side to the other side of the 'equality sign', it would become a positive variable instantly.

This approach is simply the fundaMental for understanding algebraic concepts and manipulation. I would rather suggest that you spend the time mastering this art of algebraic moves in order to be competent dealing with any future algebraic problems.

Simplifying algebraic expressions

This is one of the easy problems in algebra. Here attention is needed to collect same variables together. In mathematics collecting variables of the same kind is known as 'like terms'

It is crucial to look at the variables carefully for example quadratic variables are not the same as linear variables. In order words they are not like terms. Once you have identified the like terms, the next sTAGe is to check if the expression can be simplified any further.

There are cases where you have to factorise the expressions before simplifying. In such situation, try not to mix things up. Keep is tidy at all times. Let the beauty of mathematics stands out.

Re-arranging and manipulating algebraic expressions

This is the sTAGe to display your understanding of algebraic concepts. With your knowledge of signs checking and variable swapping, you will begin to enjoy the work of your hand. You will begin to make different variables subjects of formulae. At this sTAGe your competent in mathematics will begin to show.

You have got to open your mind and believe that you can truly do mathematics before you can go the extra mile in the subject. Patience is crucial in understanding mathematics. Don't settle for a quick fix. Trial and improveMent is the best approach. Don't quit just because you found it difficult first time. Mathematics is for the patient, wise and knowledgeable.

Understanding Algebraic Concepts

SAT Essay - 8 Ways To Write A Great Introduction

You can't afford to have writer's block since you only have 25 minutes to write your SAT Essay. So to help my students put pen to paper Faster I created these 8 techniques for creating a compelling introduction quickly. Try them and they'll help you too.

SAT Essay - 8 Ways To Write A Great Introduction

SAT Essay - 8 Ways To Write A Great Introduction

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SAT Essay - 8 Ways To Write A Great Introduction

SAT Essay - 8 Ways To Write A Great Introduction

1. Understand the prompt first

The number one thing you must do to write a great introduction is to make sure you know what you are writing about first. The biggest mistake I've seen in scoring SAT Essays is that many students misread the prompt. To avoid this I have my students underline or circle important words and phrases to make sure they have truly digested the prompt. I suggest you do the same.

2. Use an analogy or metaphor

Analogies require creativity. A trait that SAT Essay graders love to reward. For an essay in which the prompt was "Is it true that to make progress people must make sacrifices?" A student created the following analogy,

"To climb a mountain a person must struggle and strain. And this is the case with any worthwhile goal..."

3. Tell a brief anecdote

You can create an engaging introduction by telling a brief (1-2 sentence anecdote) such as the following.

When I trained for my first marathon it was difficult and often painful. But I wanted to have the accomplishMent of running 26.2 miles so I did it anyway. To make progress in life requires sacrifice.

4. Use a quote that was not used in the prompt

It is useful to memorize quotes that you love. You never know when they can come in handy on the test. For example for the essay topic "Do mistakes lead to growth?" one of my students wrote

Someone once asked Edison, "how can you feel good about your work, having failed nine-hundred and ninety-nine times to make a light bulb?" To this Edison replied, "I have not failed so many times, I have merely learned nine-hundred and ninety-nine ways not to make a light bulb. Why did Edison react this way? Because he knew that mistakes are always experiences that lead to learning and growth."

This was a great quote to begin his essay with and would definitely impress SAT Essay graders.

5. Mention a topic in the news

SAT Essay Experts will often say to stay away from news in the body of your essay. And they are right. However, in the introduction it can be very useful IF you have the facts straight AND it's even better if it is a news story that isn't well covered. If you use this idea make sure it clearly fits the topic.

6. Make up an anecdote using very specific details

I don't recomMend this as you don't need a creative introduction badly enough to take the trouble to make one up. I had a student insist on trying this and his were so bad at first anyone could guess they were fictional. Finally, however he started to put details that were so specific that I couldn't tell if it was real or not. So you can fool graders if you want to but I don't recommend it.

7. Use a cliche in an inventive way

Most books and articles on writing say to stay away from cliches however, it's a secret of professional writers that if you change a cliche it captures people's attention.

One student used the following cliche to make a great introduction for the topic "Which is a better indicator of a person's true character, their actions or their words?"

"A picture tells a thousand words" is a saying that applies to the newspaper industry but which also applies to people. The picture created by a person's actions tells us a thousand words about him or her and goes much farther than words do in telling us about a person's true thoughts and feelings. Several examples from literature and history demonstrate this point.

Using the cliche "A picture tells a thousand words" to make the point that actions speak louder than words is very unique and very powerful.

8. When all else fails just do a quick summary of what you will cover in your essay

Make sure you clearly state your thesis and state which categories of information your examples are from

For example, "Examples from history, literature and science will prove that people care far too much about what others think of them."

Most of all remember, you do not need to write an impressive introduction so badly that you sacrifice the rest of your essay. In fact I taught my students to write great body paragraphs first as these are just as important. Then when they could write them quickly I taught them how to write great introductions and powerful conclusions.

SAT Essay - 8 Ways To Write A Great Introduction