# 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

### Country

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

### Question

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.

## Formula without constant and variable

March 1, 2017

### Question

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.

## Is zero a variable?

February 13, 2017

### Question

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

### Question

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

## 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)

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

### Question

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

### 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)

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

### 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)

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

## 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)

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

### 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)

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.

## 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.

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

### Question

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

### Question

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

### 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)

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

### Question

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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