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Algebra Feedback

by Ron Kurtus

Each day readers send in questions and feedback concerning the various lessons in the School for Champions website. A total of 64 letters have been answered.

List of most recent 15 letters




Why are letters used in equations? Purpose Nigeria
Formula without constant and variable Variables and Constants UAE
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
Examination problem General Ghana
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

Next 15 letters


Why are letters used in equations?

March 11, 2017


why did they choose to use letter of alphabets or other symbols as a subject of the formular when numbers can still serve and is even easier to be used in rounding up calculation?

Chidi - Nigeria (27935)


Numbers are used in specific cases. The letters of the alphabet are considered variables, such that the equation or formula can be used with any numbers.

See Variables and Constants in Algebra for an explanation.

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Variables and Constants

Formula without constant and variable

March 1, 2017


Using formula without constant and Variable is right or wrong.(4-9/2)square 2 please clear it.thanks

Jamil - UAE (27918)


Just having numbers in the expression is simply an arithmetic exercise. What you have written is (4 - 9/2)^2, which would be (-1/2)^2 = 1/4.

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Variables and Constants

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.

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Multiplication with Exponents

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
thank you

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

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Variables and Constants

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.

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Variables and Constants

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.

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Variables and Constants

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.

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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:

Might be worth adding to the site or recommending to students.

Either way, have a great day!

Best wishes,

Paul - USA (26830)


Thanks for the resource. I added your page with all calculators at Algebra Resources page.

Best wishes in your activities.

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Multiplication with Exponents

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.

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Square Root Approximation

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.

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Examination problem

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.

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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.

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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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