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Algebra Feedback

by Ron Kurtus

Readers have sent in a total of 66 comments and questions on Algebra issues. They are listed according to date.

You can read them to further your understanding of the subject.

List of next 15 letters




Need skill in solving equations General South Africa
Explain negative term in proof Product of Two Negative Numbers is Positive UK
Number with nine letters Terminology India
Should include completing the square method Quadratic Formula Sri Lanka
Exponent of large number Division with Exponents India
What is linear algebra? General Nigeria
Trying to solve math problem General USA
Multiplying two negative numbers General India
Helping students with Algebra Multiplying Binomial Expressions Sri Lanka
Understanding vectors General Zambia
Difference between linear polynomial and linear equation General India
Geometric representation of linear polynomia General India
Exponential laws Multiplication with Exponents RSA
Where do exponents go in Algebra course? General USA
I have a better theory Square Root Approximation India

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First 15 letters


Need skill in solving equations

December 31, 2014


Can you please give me a best skill of solving algebric cause am struggling.please help

Welcome - South Africa (25676)


The main concept in solving an algebraic equation is to separate the variable for which you are solving from other variables.

A simple example is to solve for y in the equation 3y + 4x = y - 2 + 8x.

In this case, you subtract y from both sides of the equal sign and subtract 4x from both sides, resulting in: 2y = 4x - 2. Then divide both sides by 2 to get

y = 2x - 1.

The method involves writing down each step and going step-by-step. Of course, you need to know the basics of working with equations.

Go through the lessons to give you some of the basics needed.

Best wishes in understanding the subject. Once you catch on, it can be easy.

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Product of Two Negative Numbers is Positive

Explain negative term in proof

November 26, 2014


On page
in section Proof, subsection Factor out b, you have a line :
x = b[a + (-a)] + (-a)(-b)
I don't understand the reason for the negative sign for b in (-a)(-b)
Can you help please?

John - UK (25593)


I updated the page with color-coding that should help clarify the material.

I hope that helps.

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Number with nine letters

November 25, 2014


Nine lettered word to be written in the base of 10

suhani - India (25591)


This looks like a puzzle. Seventeen (17) has nine letters.

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Quadratic Formula

Should include completing the square method

October 8, 2014


You understanding algebra was very well done.

I like to point out one particular omission you have made in the section of solving quadratic equation problems. You have left out an important method of solving quadratic equation problems by 'completing the square' By this method you could always solve quadratic problems by factoring.

I hope you would take note of this and add this to your otherwise excellent teaching material.


Dr. S. Shrikharan

Shanmugalingam - Sri Lanka (25433)


Thank you for your kind words and for reminding me of the completing the square method.

I updated Quadratic Equations and added Solving Quadratic Equations by Completing the Square Method.

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Division with Exponents

Exponent of large number

July 20, 2014


Is there a simple solution to know the ans of any digit raise to power as-
2^5123 or
Without multiplying it 984 times

Sushant - India (25131)


Both of those numbers would be extremely large. I'm not sure of the point in getting such an answer.

Usually, you can get the answer by using the calculator that comes with your computer. Change the View to Scientific and then enter the first number--like 9--and use the x^y button to enter 984 and get your answer.

Unfortunately, with such a large number, you would an answer in the exponential form, something like 9.43255...e+938.

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What is linear algebra?

March 23, 2014


what is linear algebra

ISMAIL - Nigeria (24807)


Linear algebra starts with finding the solutions of a number or set of linear equations, which are equations with no exponents. An example of a set of linear equations is:

2x + 3y = 6
4x + 9y = 15

You can solve for x and y by substitution, such that y = 1 and x = 3/2.

But linear algebra can become complex when there are many variables and equations. In such a case you use matrices to solve the equations.

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Trying to solve math problem

January 6, 2014


I have a question I have been working on this math problem below and can't seem to understand it. I hope you can help and tell me where I might be able to find worksheets to help me more? Positive and negative (product of two factors.) Thank you, Robert

4 1/2 -7 1/2 (they are written vertical)

Robert - USA (24410)


Since the fractions are the same, 1/2 - 1/2 = 0 and 4 - 7 = -3.

However, if the mixed numbers had different denominators in the fractions, you would usually change the fractions to have the same denominator. For example, with 4 1/2 - 7 1/3, you would multiply 1/2 by 3/3 and 1/3 by 2/2 to get:
4 3/6 - 7 2/6 = -3 1/6.

But also, if in the subtraction, the second fraction was bigger than the first, you would change the mixed number to be improper fractions:

For example:
4 1/3 - 7 1/2 = 4 2/6 - 7 3/6 = (24/6 + 2/6) - (42/6 + 3/6) =
26/6 - 45/6 = -19/6 = -3 1/6

It can be tricky.

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Multiplying two negative numbers

September 18, 2013


what is the proof for the mathematical formula (-*-)=+. how the mathematicians found it?

- India (24026)


The proof is explained at Product of Two Negative Numbers is Positive.

I don't know of any historical facts about who first derived the proof.

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Multiplying Binomial Expressions

Helping students with Algebra

August 17, 2013


I am an engineer and coaching children in their studies when I am free. Your article helped me a lot to organize what I was to teach. I would like to show a slip of the pen in your example of the multiplication of numbers as binomials.

Thanks again

Shantha - Sri Lanka (23941)


Thank you for bringing the problem to my attention. in reviewing the lesson, I can see that the part on multiplying numbers as binomials could be confusing. I updated the lesson Multiplying Binomial Expressions with some improvements.

It is good that you are helping the students. You are a true champion to help them become champions in their studies. Best wishes in your efforts.

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Understanding vectors

August 10, 2013


i want to understand the concept of vectors

kennedy - Zambia (23921)


A vector is a way to represent a quantity and its direction by drawing an arrow on your paper. For example, an automobile traveling north at 20 km/hr can be represented by an arrow of a given length on the paper.

Combining vectors can be done geometrically.

See: Vectors in Gravity Equations and Vectors for more information.

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Difference between linear polynomial and linear equation

June 8, 2013


what is the difference between linear polynomial and linear equation?

sameer - India (23758)


A polynomial is an expression made up of variables and constants or numbers. A linear polynomial means the variables are not raised to a power.

3x + 7y is a linear polynomial but 3x^2 + xy is not.

A linear equation consists of a linear polynomials separated by an equal sign.

y = 2x + 3 is a linear equation, but y = xy + 3 is not.

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Geometric representation of linear polynomia

June 7, 2013


what is geometric representation of linear polynomial?

sameer - India (23757)


Linear relates to a straight line. If there are two variables in the polynomial, it would be a straight line on a piece of paper (two dimensions). If there are three variables, it would be a straight line in 3-D space.

With more than three variables, it would be an imaginary line.

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Multiplication with Exponents

Exponential laws

May 27, 2013


Can you please tell me everything about exponential laws?

Kgalalelo - RSA (23723)


Telling everything would take a lot of space. The rules can be summarized as:

When you multiply two numbers, you add the exponents.
When you divide, you subtract the exponents.
The reciprocal of a number has a negative exponent.
An exponent that is a fraction is a root.

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Where do exponents go in Algebra course?

December 17, 2012


Hello Ron,

I am a teacher and I am preparing a lesson on "multiplication with exponents". Where would this traditionally fall in the algebra sequence and what would follow? I am preparing this lesson for an interview as I have recently relocated. I will start with an explanation as to what exponents are and what they mean, then get into multiplication of numbers with exponents and finally variables with exponents. I am unsure to where this lesson would traditionally fall because I did not bring my textbooks with me on the move and I have been teaching engineering design for the last years. Thanks for your help.

Kind Regards,

Nicholas - USA (23071)


Sometimes explanation of exponents come after solving linear equations, because the next step would be solving quadratic equations. However, in our section on Algebra, dealing with exponents comes after the laws of addition and multiplication.

Either case is OK. Often it depends on the textbook used.

Best wishes for success in your interview.

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Square Root Approximation

I have a better theory

November 2, 2012


I have more theory's better than of newton's theory !i!

Sachin - India (23016)


Newton's square root approximation was created in 1669. Since then, Mathematicians have devised better and easier methods. However, these days most people use a calculator to determine the square root of a number.

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