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#1 2017-05-21 01:55:22

awholenumber
Member
Registered: 2017-04-18
Posts: 42

Learning math from 6th grade text onwards , Where to from here ?

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

Algebraic_expression.png


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.

 
class_8_a.png
class_9_a.png
class_9_b.png
class_9_c.png
class_10_a.png
class_10_b.png


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







Factor_by_Distributive_law_method.png
Factor_by_grouping.png

very_famous_polynomials_1.png

very_famous_polynomials_2.png

very_famous_polynomials_3.png



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)

factor.png




SOLVING EQUATIONS
Algebraic_equations.png

http://www.sosmath.com/algebra/solve/solve0/solve0.html

https://2012books.lardbucket.org/books/ … g-algebra/
https://2012books.lardbucket.org/pdfs/b … lgebra.pdf

Last edited by awholenumber (2017-06-07 07:37:54)

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#2 2017-05-21 21:41:01

iamaditya
Member
From: Planet Mars
Registered: 2016-11-15
Posts: 692

Re: Learning math from 6th grade text onwards , Where to from here ?

Hi tonyjaa,

You are in Help Me. What help do you want?


Practice makes a man perfect.
There is no substitute to hard work
All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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#3 2017-05-22 03:37:58

awholenumber
Member
Registered: 2017-04-18
Posts: 42

Re: Learning math from 6th grade text onwards , Where to from here ?

There are these Algebraic equations involving fractions , I am looking for some worked out examples , Not sure where to find such problems
I am looking for Books or Websites with worked out examples , Not sure which book to look at ?

Please help

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#4 2017-05-22 21:41:29

iamaditya
Member
From: Planet Mars
Registered: 2016-11-15
Posts: 692

Re: Learning math from 6th grade text onwards , Where to from here ?

Oh, for that you can easily buy some books, there are plenty of books available in the shop. You can buy the offiical ncert books (may I know in which state you live in?) . Others include R.D. Sharma and R.S. Aggarwal 's Maths books and many others. You will find plenty of examples there. Hope it helps.


Practice makes a man perfect.
There is no substitute to hard work
All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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#5 2017-05-25 06:25:17

awholenumber
Member
Registered: 2017-04-18
Posts: 42

Re: Learning math from 6th grade text onwards , Where to from here ?

Thanks for the reply iamaditya .I just went through all those ncert books from grade 6 to grade 12 , which is why updated the first post .Its missing notes on Rational equation and Radical equations which is a bit weird .
I still managed to learn a bit about Rational equations from other books .

But i could not get a good book or website to  learn about Radical equations . Do you know any ?

Last edited by awholenumber (2017-06-05 07:25:46)

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#6 2017-05-25 23:20:11

iamaditya
Member
From: Planet Mars
Registered: 2016-11-15
Posts: 692

Re: Learning math from 6th grade text onwards , Where to from here ?

You can get radical equations in the chapter surds. You can find it in some IIT foundation books for class 9.


Practice makes a man perfect.
There is no substitute to hard work
All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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#7 2017-06-05 07:25:16

awholenumber
Member
Registered: 2017-04-18
Posts: 42

Re: Learning math from 6th grade text onwards , Where to from here ?

Sorry for the late reply iamaditya , i found a really good book for my problems after searching for a very long time :-)

https://2012books.lardbucket.org/books/ … g-algebra/

Last edited by awholenumber (2017-06-05 07:26:14)

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#8 2017-06-08 22:17:31

iamaditya
Member
From: Planet Mars
Registered: 2016-11-15
Posts: 692

Re: Learning math from 6th grade text onwards , Where to from here ?

Hi tonyjaa;

This site seems good. You may practice them.


Practice makes a man perfect.
There is no substitute to hard work
All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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