## How to learn about radical expressions and equations ?

For the discussion of math. Duh.

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monkey3
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### How to learn about radical expressions and equations ?

Where should i start ?
Last edited by monkey3 on Sun May 28, 2017 3:42 am UTC, edited 1 time in total.

Demki
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### Re: How to learn about rational expressions and equations ?

A bit more information about your current mathematical education would be helpful for us to guide you in the correct direction.

monkey3
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### Re: How to learn about rational expressions and equations ?

I am someone who lost a bsc computer science degree because i suck at mathematics ucim
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### Re: How to learn about rational expressions and equations ?

monkey3 wrote:I am someone who lost a bsc computer science degree because i suck at mathematics "suck at mathematics" isn't really helpful. Math builds on itself; we need to know what you know well before we can help you go from there to what you don't know well. Somebody posted a test for you to take; did you take it? It had questions covering arithmetic through calculus. If you can't add fractions, it's useless to discuss polynomials. If you already understand algebra, it's a waste of time to "teach" you about negative numbers because you already know them. You can't be good at algebra unless you already understand negative numbers.

I am beginning to suspect that one of the reasons you "suck at math" is that you don't want to do the work.

I say this because you ask questions here of the "how can I learn about [x]", where [x] covers the range from arithmetic to calculus, and you ask these questions as if your lack of understanding is just an isolated blip in the overall field of math. It's not. It's fundamental. You need to understand from the beginning, or you will never understand to the end.

And then you don't tell us what your 'beginning' is.

So, here's how to prepare to learn about rational expressions and equations. Find a place, such as a high school, a website (e.g. freemathtest.com, which was the first hit in duckduckgo with the search phrase "math tests"), or a group like this message board, and take a test to see how well you can do fourth grade math. Then fifth grade math. Then sixth grade math. Continue on until you aren't doing well (say, 80%). Then stop. That's what you need to master first. Notice that I'm starting way early. The first tests should be really easy, but if they are not, stop right there and master that material. We'll help you, but you have to show evidence that you're doing the work too. Here's an example:
Spoiler:
In the example below, I'm using * for "times" and / for "divided by".

Evaluate:
4 + 12 * 6 + 2 / 5 * 7 + 4 - 9
You should get (see spoiler) and be able to explain why.
Spoiler:
= 73 4/5
(seventy three and four fifths)

This is fundamentally a question about priority and order of operations. Priority comes from the idea that some operations are shorthands for other operations, for example, multiplication is shorthand for repeated addition. Because of this, multiplication is evaluated first ("the shorthand is expanded").

Subtraction is the inverse of addition; it can be considered adding the additive inverse:
4 - 7
is the same as
4 + (-7)

Division is the same as the inverse of multiplication; it can be considered multiplying by the multiplicative inverse.
3 / 5
is the same as
3 * (1/5)
(that is, three times one-fifth)

Addition and multiplication are each commutative. All the operations we've discussed here are binary or unary.

Anything in parenthesis is evaluated before being "merged" with the rest of the expression. That's what parenthesis are for. But this example doesn't have any.

So...

4 + 12 * 6 + 2 / 5 * 7 + 4 - 9

= 4 + 72 + 2 * (1/5) * 7 + 4 + (-9)

= 4 + 72 + (14/5) + 4 + (-9)

= 4 + 72 + (2 + 4/5) + 4 + (-9)

= 4 + 72 + 2 + 4/5 + 4 + (-9)

= 73 4/5
(seventy three and four fifths)
If you screwed this up, study how I got the answer. If you don't understand how I got the answer, stop right there. Do not pursue higher math until you get this, because the explanations to higher math all rely on your knowing this cold.

If this grade level was easy, great; move on to the next grade level and test yourself.

Let us know how you do. We can't help you without knowing this.

From a standing start, it's ten years from arithmetic to differential equations. There are no shortcuts.

I suspect however that you are not at a standing start, but have actually taken some math and did poorly, and am guessing that you did poorly because you didn't understand the prior material. If that is the case, you should progress faster, but only if you start far enough back for it to be easy. That may mean arithmetic. If so, so be it. It will feel good to do math (of any sort) easily.

Jose
Last edited by ucim on Thu May 25, 2017 6:19 pm UTC, edited 4 times in total.
Order of the Sillies, Honoris Causam - bestowed by charlie_grumbles on NP 859 * OTTscar winner: Wordsmith - bestowed by yappobiscuts and the OTT on NP 1832 * Ecclesiastical Calendar of the Order of the Holy Contradiction * Heartfelt thanks from addams and from me - you really made a difference.

monkey3
Posts: 59
Joined: Thu Apr 20, 2017 3:50 pm UTC

### Re: How to learn about rational expressions and equations ?

Thanks for the reply , I am from india and i always thought there was something wrong with our syllabus
You know i have been trying to narrow it down for some time now from those materials ,
Let me show you that first .
Spoiler:
http://ncert.nic.in/textbook/textbook.htm
http://ncert.nic.in/textbook/textbook.htm?femh1=0-14

To factor’ means to break up into multiples.

Factors of natural numbers

The numbers other than 1 whose only factors are 1 and the number itself are called Prime numbers
Numbers having more than two factors are called Composite numbers.

Greatest common factor

The Greatest Common Factor (GCF) of two or more given numbers is the greatest of their common factors

Lowest Common Multiple

The Lowest Common Multiple (LCM) of two or more given numbers is the lowest (or smallest or least) of their common multiples.

You will remember what you learnt about factors in Class VI. Let us take a natural number,
say 30, and write it as a product of other natural numbers, say
30 = 2 × 15
= 3 × 10 = 5 × 6
Thus, 1, 2, 3, 5, 6, 10, 15 and 30 are the factors of 30.
Of these, 2, 3 and 5 are the prime factors of 30 (Why?)
A number written as a product of prime factors is said to
be in the prime factor form; for example, 30 written as
2 × 3 × 5 is in the prime factor form.
The prime factor form of 70 is 2 × 5 × 7.
The prime factor form of 90 is 2 × 3 × 3 × 5, and so on.
Similarly, we can express algebraic expressions as products of their factors. This is
what we shall learn to do in this chapter.

Simplifying algebraic expressions Factors of algebraic expressions

We have seen in Class VII that in algebraic expressions, terms are formed as products of
factors. For example, in the algebraic expression 5xy + 3x the term 5xy has been formed
by the factors 5, x and y, i.e.,
5xy = 5 * x * y
Observe that the factors 5, x and y of 5xy cannot further
be expressed as a product of factors. We may say that 5,
x and y are ‘prime’ factors of 5xy. In algebraic expressions,
we use the word ‘irreducible’ in place of ‘prime’. We say that
5 × x × y is the irreducible form of 5xy. Note 5 × (xy) is not
an irreducible form of 5xy, since the factor xy can be further
expressed as a product of x and y, i.e., xy = x × y.      What is Factorisation?
When we factorise an algebraic expression, we write it as a product of factors. These
factors may be numbers, algebraic variables or algebraic expressions.
Expressions like 3xy, 5x2y , 2x (y + 2), 5 (y + 1) (x + 2) are already in factor form.
Their factors can be just read off from them, as we already know.
On the other hand consider expressions like 2x + 4, 3x + 3y, x2 + 5x, x2 + 5x + 6.
It is not obvious what their factors are. We need to develop systematic methods to factorise
these expressions, i.e., to find their factors.

Methods of Factoring

Method of common factors
Factorisation by regrouping terms
Factorisation using identities
Factors of the form ( x + a) ( x + b)
Factor by Splitting     Factorise 6x2 + 17x + 5 by splitting the middle term

(By splitting method) : If we can find two numbers p and q such that
p + q = 17 and pq = 6 × 5 = 30, then we can get the factors

So, let us look for the pairs of factors of 30. Some are 1 and 30, 2 and 15, 3 and 10, 5
and 6. Of these pairs, 2 and 15 will give us p + q = 17.

So, 6x2 + 17x + 5 = 6x2 + (2 + 15)x + 5
= 6x2 + 2x + 15x + 5
= 2x(3x + 1) + 5(3x + 1)
= (3x + 1) (2x + 5) SOLVING EQUATIONS http://www.sosmath.com/algebra/solve/solve0/solve0.html

That last part about "radical equation " is something i don't have any clue at all .
I am looking for a book which has that particular part

Soupspoon
You have done something you shouldn't. Or are about to.
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### Re: How to learn about rational expressions and equations ?

monkey3 wrote:That last part about "radical equation " is something i don't have any clue at all .
I am looking for a book which has that particular part

You include so much other stuff in there, seemingly apropos of nothing, that I'm wondering if you're saying "I understand everything mathematical there, except why 'root of (ax plus b) equals c' is called a 'radical equation'. So why is it?"...

Is it that? Because (speaking for myself) I don't understand what other single point in the whole gamut you might be getting stuck at. It could be anywhere.

e.g., can you rewrite √a=b or c=³√d without the root symbols?

ucim
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### Re: How to learn about rational expressions and equations ?

monkey3 wrote:You know i have been trying to narrow it down for some time now from those materials ,
Let me show you that first .
This doesn't help. What we need to know is what it is that you know, in an "I can solve the equation" sense as well as in the "I know what the words mean" sense.

To that end, for the little arithmetic example I gave you, which of the following is true:
1: I solved it easily and got the right answer.
2: I solved it with effort and got the right answer.
3: I tried to solve it and got the wrong answer, but I understand my mistake.
4: I could not solve it and don't understand it.

That kind of thing is what will be helpful to us.

You post things like:
The prime factor form of 70 is 2 × 5 × 7.
The prime factor form of 90 is 2 × 3 × 3 × 5, and so on.
Similarly, we can express algebraic expressions as products of their factors. This is
what we shall learn to do in this chapter.

But you don't say whether you actually learned the material in that chapter. You need to start with the first chapter where you didn't learn the material. Disregard the rest.

Jose
Order of the Sillies, Honoris Causam - bestowed by charlie_grumbles on NP 859 * OTTscar winner: Wordsmith - bestowed by yappobiscuts and the OTT on NP 1832 * Ecclesiastical Calendar of the Order of the Holy Contradiction * Heartfelt thanks from addams and from me - you really made a difference.

Eebster the Great
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Location: Cleveland, Ohio

### Re: How to learn about rational expressions and equations ?

If you find some problems online in a given topic (solving exponential equations, for instance) and you don't see the answers right away, try to solve as many as you can. If you can solve almost all of the questions in a given topic without too much difficulty before seeing any answers or asking anyone for help, and then you check and see that your answers are almost all correct, only then have you mastered the topic sufficiently to move on.

I don't know too many resources or this specifically, but google should help. And I agree that you have to start with the easy stuff (which, if it really is easy, won't take long anyway) before moving up.

monkey3
Posts: 59
Joined: Thu Apr 20, 2017 3:50 pm UTC

### Re: How to learn about rational expressions and equations ?

Thanks for the replies ,

I will answer your questions after i go through a revision of some material , which is from 6th grade to grade 12 mathematics texts found here

http://ncert.nic.in/textbook/textbook.htm

I was a bit busy arranging some texts in some order so that i could learn it in this order . http://www.sosmath.com/algebra/solve/solve0/solve0.html

I think this should be a good start ,

http://ncert.nic.in/ncerts/l/hemh106.pdf

With the help from couple of texts like these I should be able to improve my math .

Soupspoon
You have done something you shouldn't. Or are about to.
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### Re: How to learn about rational expressions and equations ?

monkey3 wrote:I will answer your questions after i go through a revision of some material , which is from 6th grade to grade 12 mathematics texts found here

Please take your time to do that, if you find it necessary.

monkey3
Posts: 59
Joined: Thu Apr 20, 2017 3:50 pm UTC

### Re: How to learn about rational expressions and equations ?

Yes , Thanks for the replies

LaserGuy
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### Re: How to learn about rational expressions and equations ?

monkey3, I would like you go to back to this post that I made to you a few weeks ago on this topic. I gave you five mathematics problems covering some of the topics that you're interested in. Did you attempt any of these? If so, can you post what you did?

There's something really important that you seem to be missing about mathematics. You will never be able to learn mathematics by just reading about it. You absolutely must do problems--lots of them--to learn mathematics. Stop reviewing material. Start solving problems. Figure out the boundaries of your knowledge, then start looking for educational materials to help you expand it. There's no point in reading about algebra if you can't do arithmetic; there's no point in reading about calculus if you can't do algebra.

monkey3
Posts: 59
Joined: Thu Apr 20, 2017 3:50 pm UTC

### Re: How to learn about rational expressions and equations ?

LaserGuy ,

i needed to arrange some texts in order , before i could start working on problems . I am going to take print outs of a few texts and i am going to start practicing with problems from monday

i found this really awesome text online , it has everything that a beginner needs .

https://hillcrestmath.files.wordpress.com/2010/08/8th-grade-algebra-i-textbook.pdf
This below website has rest of the texts from grade 1 to grade 12 .
http://ncert.nic.in/textbook/textbook.htm

I am a commerce degree student right now , and i am also working
I will start practicing whenever i have free time

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