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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




Resources Suggested algebra resource USA
Multiplication with Exponents Multiplying exponential numbers with different bases USA
Square Root Approximation Find the square root of 5 USA
General Examination problem Ghana
Terminology Parts of a complex number USA
General Need skill in solving equations South Africa
Product of Two Negative Numbers is Positive Explain negative term in proof UK
Terminology Number with nine letters India
Quadratic Formula Should include completing the square method Sri Lanka
Division with Exponents Exponent of large number India

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First 10 letters

Suggested algebra resource

Topic: Resources


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



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

Best wishes in your activities.

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Multiplying exponential numbers with different bases

Topic: Multiplication with Exponents


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



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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Find the square root of 5

Topic: Square Root Approximation


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



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

Topic: General


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



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

Topic: Terminology


June 5, 2015

What parts are necessary for a complex number?
How can a conjugate be created from a complex number?

Julie - USA



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

Topic: General


December 31, 2014

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

Welcome - South Africa



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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Explain negative term in proof

Topic: Product of Two Negative Numbers is Positive


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



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

Topic: Terminology


November 25, 2014

Nine lettered word to be written in the base of 10

suhani - India



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

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Should include completing the square method

Topic: Quadratic Formula


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



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.

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Exponent of large number

Topic: Division with Exponents


July 20, 2014

Is there a simple solution to know the ans of any digit raise to power as-
2^5123 or
Without multiplying it 984 times

Sushant - India



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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