# Algebra Feedback

by Ron Kurtus

Readers have sent in a total of **58** 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 most recent 15 letters

## Title |
## Topic |
## Country |

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 |

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 |

### Variables and Constants

## Where did naming conventions come from?

August 9, 2016

### Question

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)

### Answer

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.

### Variables and Constants

## Is number 4 is variable term?

April 27, 2016

### Question

1. Is number 4 is variable term? If yes, how?

2. Are all constants are variables? if yes, how?

srilata - **India** (26968)

### Answer

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.

### Variables and Constants

## What is a value?

April 17, 2016

### Question

Hi:

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.

Thanks,

Wei - **USA** (26938)

### Answer

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.

### Resources

## Suggested algebra resource

March 2, 2016

### Question

Hello,

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!

Best wishes,

Paul - **USA** (26830)

### Answer

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

Best wishes in your activities.

### Multiplication with Exponents

## Multiplying exponential numbers with different bases

November 10, 2015

### Question

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:

(4^y).(20^2y)=40^(y+3)

Atta - **USA** (26511)

### Answer

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.

### Square Root Approximation

## Find the square root of 5

September 9, 2015

### Question

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)

### Answer

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.

### General

## Examination problem

August 27, 2015

### Question

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)

### Answer

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.

### Terminology

## Parts of a complex number

June 5, 2015

### Question

What parts are necessary for a complex number?

How can a conjugate be created from a complex number?

Julie - **USA** (26068)

### Answer

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.

### General

## Need skill in solving equations

December 31, 2014

### Question

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

Welcome - **South Africa** (25676)

### Answer

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.

### Product of Two Negative Numbers is Positive

## Explain negative term in proof

November 26, 2014

### Question

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)

### Answer

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

I hope that helps.

### Terminology

## Number with nine letters

November 25, 2014

### Question

Nine lettered word to be written in the base of 10

suhani - **India** (25591)

### Answer

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

### Quadratic Formula

## Should include completing the square method

October 8, 2014

### Question

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.

Regards

Dr. S. Shrikharan

Shanmugalingam - **Sri Lanka** (25433)

### Answer

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.

### Division with Exponents

## Exponent of large number

July 20, 2014

### Question

Is there a simple solution to know the ans of any digit raise to power as-

2^5123 or

9^984

Without multiplying it 984 times

Sushant - **India** (25131)

### Answer

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.

### General

## What is linear algebra?

March 23, 2014

### Question

what is linear algebra

ISMAIL - **Nigeria** (24807)

### Answer

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.

### General

## Trying to solve math problem

January 6, 2014

### Question

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)

### Answer

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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