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Feedback Q&A on Algebra

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 10 letters




General What is linear algebra? Nigeria
General Trying to solve math problem USA
General Multiplying two negative numbers India
Multiplying Binomial Expressions Helping students with Algebra Sri Lanka
General Understanding vectors Zambia
General Difference between linear polynomial and linear equation India
General Geometric representation of linear polynomia India
Multiplication with Exponents Exponential laws RSA
General Where do exponents go in Algebra course? USA
Square Root Approximation I have a better theory India

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First 10 letters

What is linear algebra?

Topic: General


March 23, 2014

what is linear algebra

ISMAIL - Nigeria



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

Topic: General


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



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

Topic: General


September 18, 2013

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

- India



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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Helping students with Algebra

Topic: Multiplying Binomial Expressions


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



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

Topic: General


August 10, 2013

i want to understand the concept of vectors

kennedy - Zambia



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

Topic: General


June 8, 2013

what is the difference between linear polynomial and linear equation?

sameer - India



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

Topic: General


June 7, 2013

what is geometric representation of linear polynomial?

sameer - India



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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Exponential laws

Topic: Multiplication with Exponents


May 27, 2013

Can you please tell me everything about exponential laws?

Kgalalelo - RSA



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?

Topic: General


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



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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I have a better theory

Topic: Square Root Approximation


November 2, 2012

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

Sachin - India



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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