by Ron Kurtus
Readers have sent in a total of 60 comments and questions on Algebra issues. They are listed according to date.
You can read them to further your understanding of the subject.
|Is zero a variable?||Variables and Constants||India|
|5^6 times 8^6||Multiplication with Exponents||USA|
|Where did naming conventions come from?||Variables and Constants||Australia|
|Is number 4 is variable term?||Variables and Constants||India|
|What is a value?||Variables and Constants||USA|
|Suggested algebra resource||Resources||USA|
|Multiplying exponential numbers with different bases||Multiplication with Exponents||USA|
|Find the square root of 5||Square Root Approximation||USA|
|Parts of a complex number||Terminology||USA|
|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|
Is zero a variable?
February 13, 2017
0 is variable or constant
Chandra - India (27877)
Since zero (0) does not change, it is a constant and part of the number system.
5^6 times 8^6
January 31, 2017
hi, i have a question that is 5 to the 6th power times, 8 to the 6th power... how do i do this i asked everyone and they don't know how
noelle - USA (27847)
5^6 (5 to the 6th power) times 8^6 = 40^6 (40 to the 6th power).
(5^6)*(8^6) = (5*5*5*5*5*5)*(8*8*8*8*8*8) = 40*40*40*40*40*40 = 40^6
In general, (x^a)*(y^a) = (xy)^a
Where did naming conventions come from?
August 9, 2016
Ron - from this abc usually constants and xyz variables, but any idea why linear algebra use ith and jth for row and column and then refers to a 2x3 matrix as an mxn matrix. Was wondering if ijkmn arent used so much - or could it be m for myrian and n for numberth nth - even non maths people know what to the nth degreee means? But I is often used for interest as is r for rate. K is most often a specific constant. n I can understand to the last n number but m has me stuck - unless it is like a-z m to n?
TIMOTHY - Australia (27199)
That is a puzzler. I haven't been able to find where the conventions for naming constants, variables, table rows and columns, and nth degree come from.
There must be some rationale hidden in the archives of mathematical history.
If you ever find out, let me know.
Is number 4 is variable term?
April 27, 2016
1. Is number 4 is variable term? If yes, how?
2. Are all constants are variables? if yes, how?
srilata - India (26968)
The number 4 is a constant value. "Constant" means the item does not vary. "Variable" means that it can change. Usually, variables are designated by letters.
What is a value?
April 17, 2016
I have a question which constantly troubles me.
what is a value ? I found many definitions for the term "value" in Math., i.e. the number represented by a symbol(which is called variable); number represented by a figure, symbol or alike; results of a function or calculation; a particular number; the magnitude(size or amount) of a number; an assigned or calculated numerical quantity (i.e. 3m/sec); etc.
So, what does "value" mean in engineering when we say a physical quantity(i.e. the pressure of the gas) assumes a set of values and when you say" a fixed or constant value of k = 1.38*10-23" ? Here, I think we mean " assigned or calculated numerical quantity" or "number represented by a figure ". We are not talking about numbers assigned to letters (variables in algebra) here, right ? Given many definitions of the term "value" in the math and engineering, I got confused what it means when it appears in a sentence.
Please help me to clear my mind and resolve the confusion I have had for a long time. If my question is not clear, please let me know.
Wei - USA (26938)
Some of these terms can be confusion, either because they are carelessly used or are different in other disciples.
If you have an Algebraic symbol that can vary, it is called a variable. Otherwise it is a constant. In either case, you can assign a number or value to it, such as a = 5.
But note that the Algebraic symbol can represent a physical entity, like is used in engineering. But typically, values in engineering or physics have units attached to them, such as a = 5 m/s.
Looking at examples and applications is probably the best way to get a feel for the definition.
I hope this helps.
Suggested algebra resource
March 2, 2016
I just want to say that I'm loving math and like to help people to learn it.
I know that many people struggle with Algebra, so I created some calculators to help students.
You can check them out here at: http://www.emathhelp.net/calculators/other/math-problem-solver/
Might be worth adding to the site or recommending to students.
Either way, have a great day!
Paul - USA (26830)
Thanks for the resource. I added your page with all calculators at Algebra Resources page.
Best wishes in your activities.
Multiplying exponential numbers with different bases
November 10, 2015
Hello! For Multiplying exponential numbers with different bases in algebra you said that rules do not apply. Can you please elaborate?
For example how can one answer this question:
Atta - USA (26511)
When you are multiplying exponential numbers with different bases, such as (4^y)*(5^2y), you cannot simply add the exponents.
However, if numbers can be factored out to achieve the same base, the rule applies. For example, (20^2) can be factored into (4*5)^2 = (4^2)*(5^2).
Thus (4^y)*(20^2y) = (4^y)*(4^2y)*(5^2y) = (4^3y)*(5^2y).
Try it by setting y = 1: (4^3)*(5^2) = 4(20^2) = 1600
Note that (4^y).(20^2y)=40^(y+3) is not valid.
Find the square root of 5
September 9, 2015
Please can you help for this ?
Show the result of each of the first 3 interactions (like the article) of computing the square root of 5 using Newton's Method.
How many digits of precision have you generated?
Amin - USA (26367)
Let's guess that the SQRT of 5 is 2. Then: (5/2 + 2)/2 = 2.25
Then (5/2.25 + 2.25)/2 = 2.2361
And (5/2.2361 + 2.2361)/2 = 2.23607.
Using a calculator to find the square root of 5 comes out to 2.23607.
So it took three steps to get to the right answer. Of course, it is easier to simply use a calculator, but it is an interesting exercise.
August 27, 2015
Mawuli scored 30% of the total marks in an examination and failed by 10 marks. However, Selasie who also wrote the same examination scored 40% of the total marks and got 15 marks more than the passing marks. Calculate
i) the total marks; and
ii) the passing marks in the examination.
Adu - Ghana (26341)
That is not an easy Algebra problem to solve. Let T = total marks and X = passing grade.
Mawuli scored 0.3T = X - 10
Selasi scored 0.4T = X + 15
Subtract to get 0.1T = 25 such that T = 250 total marks.
0.3(250) = X - 10, so X = 85.
Likewise 0.4(250) = x + 15 and X = 85, which is the passing grade.
Parts of a complex number
June 5, 2015
What parts are necessary for a complex number?
How can a conjugate be created from a complex number?
Julie - USA (26068)
A complex number is one that includes an "imaginary" number, designated as i. For example 5 + 3i is a complex number.
The square root of -1 is called an imaginary number there is no number multiplied by itself that equals -1. However, it does have uses in some fields, such as electronics.
Since x^2 - y^2 = (x - y)(x + y), x - y and x + y are conjugates. Thus for a complex number x + yi, its conjugate is x - yi. Likewise, the conjugate of 5 - 3i is 5 + 3i.
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.
Explain negative term in proof
November 26, 2014
On page http://www.school-for-champions.com/algebra/product_of_two_negative_numbers.htm
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.
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.
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.
Exponent of large number
July 20, 2014
Is there a simple solution to know the ans of any digit raise to power as-
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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