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Algebra Feedback

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 most recent 15 letters

Title

Topic

Country

Multiply terms with different base Multiplication with Exponents USA
 
Raise number to the zero power Division with Exponents Canada
 
Solving a problem Variables and Constants USA
 
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
 

Next 15 letters

 





Multiplication with Exponents

Multiply terms with different base

November 3, 2017

Question

I need to find out how to multiply terms with different base and exponents but i looked online and nothing shows up something like this. XY* in a radical multiplied by x*y to the third power inside a radical. Please help it feels hopeless right now

Lester - USA (28307)

Answer

I'm not sure I understand what you are trying to do. Are you trying to multiply something like (2^3)(5^2)?

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Division with Exponents

Raise number to the zero power

October 16, 2017

Question

(3x^-3)^0

Does the exponent -3 x 0 = 0?

Jonathan - Canada (28290)

Answer

Any number raised to the zero power equals 1. For example x^0 = 1.

Thus (3x^-3)^0 = 1

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Variables and Constants

Solving a problem

March 28, 2017

Question

kindly solve for me an algebra problem that is similar to the problem below and give me a step by step procedures:
b=ka+3, k is a constant, if the possible solutions are in the forms (a, b) is (2,3) a solution to the equation?

moifee - USA (27967)

Answer

What are you trying to find a solution for? a, b, or k?

If a = 2 and b = 3, then 3 = 2k + 3, and k = 0. But I don't think that is what you are looking for.

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Purpose

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)

Answer

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

Question

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

Jamil - UAE (27918)

Answer

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

Question

0 is variable or constant

Chandra - India (27877)

Answer

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

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)

Answer

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

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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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