I am trying to learn some basic mathematics (Pre-algebra ) and Algebra

[bayukutten]

Good Basic mathematics or Pre-algebra books were hard to find

Then i found some good materials here ,

Pre-Algebra

https://www.math-only-math.com/

Algebra

https://nios.ac.in/online-course-material/secondary-courses/Mathematics-(211)-Syllabus.aspx

I am planning to spent at least 1 hour daily to learn Basic mathematics and Algebra

I am trying to prepare for a test , that is why i wanted to learn all these from the beginning

Now i need to find me some energy and motivation to sit and practice these books daily for at least 1 hour

I am planning to study after 11 at night everyday , since i have to work till evening 6:30 everyday

 

Thanks

 

 

 

Edited March 5, 2021 by bayukutten

[studiot]

33 minutes ago, bayukutten said:

I am planning to study after 11 at night everyday , since i have to work till evening 6:30 everyday

Good luck and don't try to do too much at once.

[bayukutten]

Thanks studiot ,

Finding the proper books to learn the basics was the hardest part .

I like the math-only-math website . Everything is explained in simple English

Now at least i know where to look and study these .

Yes ,  i am only going to make small small steps forward

Let me see where i can reach in 2 or 3 months if i study a little everyday

I am going to start from here ,  today itself
 

https://www.math-only-math.com/5th-grade-math-problems.html

 

i have a 4 year old daughter ,so  i can only find time to study after she goes to sleep .

That would be at 11 or before 11'30

I have bought some new diaries so that i can write down and practice in it .

I will begin this today itself ,its almost 10.30 PM here

 

 

[tylers100]

Just letting you know that you're not alone with that. I'm one of those who performed poorly with math way back in high school and still need to re-learn some basics of mathematics onward to advanced ones if I'm well motive to do so.

 

No Math, Yes Smash

"Me no math, me smash!" Green Hulk talk, lol. Just kidding.

Normally I don't comment because I don't really know or have a firm grasp of math, as my math knowledge has declined to low since my high school. But I have other comments based on my other strength areas if you don't mind.

 

Conceptualization

An ability to conceptualize math in your head and writing down math might will help you. Don't be afraid to make mistakes if practising. If you happen to make mistakes, self-assess your own cognition to find out why. Make sure to have a calculator with you (app on computer or IRL device) - it might could help you with that - to make an inference of your cognitive methods to understand and actualize math answers. Of course, I have to take this to my own mouth. Still, I feel compelled to comment anyway.

I think the important thing to understand math is:

• understand why math (any field) is for
• find out how (i.e. step-by-step or similar to algorithms) to do a math

Website

I checked the www.math-only-math.com , it seems decent. I once tried to find some good websites that can get me from basic mathematics (arithematics) to advanced ones (idk termed fields), but I didn't get furthered with that - at this moment for now.

Good with Math

I hope you will become good at math, because it enables you to develop and be better at self-governance with billings, taxes, etc and / or specialize in fields or something like that.

 

[bayukutten]

@tylers100

Yes , i know there are more people struggling with basic mathematics and algebra

i think it is because the materials are spread out in different class text books and you can easily get fed up when you cannot find everything in one place .

i tried to read a lot of basic mathematics books online , there was 2 problems .

1, there is not enough content in it
2,some books are cluttered with pictures instead of good proper content

It can be very frustrating to learn from books like those .

I think this website www.math-only-math.com is one of the best to learn elementary mathematics .

 

Yes , i must improve this within a 3 month or 6 month time otherwise i wont be able to attend some tests .

Let me see how much i can improve .

Today i learned about different types of numbers to different types of fractions with the help of that website .

Everything is here , i started here

https://www.math-only-math.com/5th-grade-math-problems.html

 

Thanks for the reply

Edited March 5, 2021 by bayukutten

[ahmet]

I do not know very well what you exactly look for but if you are willing to do maths (category: algebra) , I think your prerequisites are to obtain knowledge about :

--- >> normal operations (summation, mltiplication in R)

--- >> sets (and all operations)

--- >> what function is and properties of functions. (1-1,onto ,bijective and types and all other relevant properties of functions)

Then slightly pass please into pure maths ("entry to algebra" in other words)

but as studiot advises, do not try to do too much at once. I think even if anyone is so much intelligent ,there are some limitations that that one would not be able to pass them. 

 

 

[studiot]

17 hours ago, bayukutten said:

Thanks for the reply

I have tried to be encouraging, rather than directly helpful with the mathematics at the moment.

I don't want to confuse you with a different approach from the one offered in your chosen course. That is I want to offer consistent help if needed.

So remember you can always ask here about anything you are unsure of.

[bayukutten]

@ahmet ,

Yes , i am only doing mathematics daily for half an hour or 1 hour .

The mathematics i am trying to practice is spread out in many webpages of the mah-only-math website . so it takes some time to organize things in my mind to practice .

Only trying to make small small steps forward .

openstax intermediate algebra is a good algebra book , i will let you know when i begin going through that book . first i have to be get very familiar with the basic mathematics before i begin that .

 

@studiot

Thanks , Yes i will ask if i have more questions .

 

 

 

[bayukutten]

Narrowed it down this much , there was no one book with all of these little basics in it

I collected notes from many books and wrote it down like this  , i am a little happy now

 

[studiot]

OK that's good but what you are doing is thinking about maths.

Unless you do some  (lots of) maths you will soon loose this and also get bogged down in pages and lists of useless information.

In my opinion you should practise many examples, until you get them right more often than not, and then assemble the theoretical framework.

 

You might find the BBC website for schools useful.

It is free and has explanations, examples, videos and lots of online practice questions to attempt, with help and repeat to get them right.

It is all free.

Here is a worksheet on factors, but you might like to look further

https://www.bbc.co.uk/bitesize/guides/ztcxwnb/test

Edited March 12, 2021 by studiot

[bayukutten]

Thanks a lot for the reply studiot ,

I have one question regarding finding the prime factorization of numbers

 

Which method do we use mostly to find the prime factorization of numbers ?

by Listing factors

by factor tree

by short division

 

?

I am planning to practice from example questions from tomorrow on wards .

Thanks

 

[studiot]

Can I just say that I think you might be making too much of this ?

The number of occasions that anyone (including mathematicians) might require to find the factors of a given difficult number in ther whole lives can probably be counted on the fingers of one hand.

Further, looking at your definition of a factor I am a little worried.

A factor is a number that evenly divides a given number with remainder 0.

What do you mean by evenly ?

I would go with the words completely or fully, but evenly is reserved for even numbers.

Mathematicians don't usually bother with any such qualifier and just use the word divides on it own.

The all important statement is that the remainder is zero.

 

So as to your question,

I would start by noting if the given number is odd or even (ie is divisible by 2 or not)

If it is divisible by 2 then that immediately cuts your work in half since you have found one factor and halved the size of the number you are working on.

After 2 comes 3, which can also provide a large reduction in the work.

Do you know how to test for divisibility by 3 ?
 

The sum of the digits are themselves divisible by 3.

 

The next prime number is 5 and again divisibility by 5 makes a big reduction

Can you tell the condions on the original given number to be divisible by 5 ?
Could this number also have been divisible by 2  or 3 ?

 

[Phi for All]

!

Moderator Note

Moved from The Lounge.

 

[bayukutten]

@studiot ,

I was trying to prepare for a state government test and its full of quantitative aptitude questions , otherwise i would not have given this much importance to all these basic mathematics problems .

Also thanks for explaining the steps involved in factorization of numbers .

Quote

Divisibility Rule of 1

Every number is divisible by 1. Divisibility rule for 1 doesn’t have any condition. Any number divided by 1 will give the number itself, irrespective of how large the number is. For example, 3 is divisible by 1 and 3000 is also divisible by 1 completely.

Divisibility Rule of 2

If a number is even or a number whose last digit is an even number i.e.  2,4,6,8 including 0, it is always completely divisible by 2.

Example: 508 is an even number and is divisible by 2 but 509 is not an even number, hence it is not divisible by 2. Procedure to check whether 508 is divisible by 2 or not is as follows:

• Consider the number 508
• Just take the last digit 8 and divide it by 2
• If the last digit 8 is divisible by 2 then the number 508 is also divisible by 2.

Divisibility Rules for 3

Divisibility rule for 3 states that a number is completely divisible by 3 if the sum of its digits is divisible by 3.

Consider a number, 308. To check whether 308 is divisible by 3 or not, take sum of the digits (i.e. 3+0+8= 11). Now check whether the sum is divisible by 3 or not. If the sum is a multiple of 3, then the original number is also divisible by 3. Here, since 11 is not divisible by 3, 308 is also not divisible by 3.

Similarly, 516 is divisible by 3 completely as the sum of its digits i.e. 5+1+6=12, is a multiple of 3.

Divisibility Rule of 4

If the last two digits of a number are divisible by 4, then that number is a multiple of 4 and is divisible by 4 completely.

Example: Take the number 2308. Consider the last two digits i.e.  08. As 08 is divisible by 4, the original number 2308 is also divisible by 4.

Divisibility Rule of 5

Numbers, which last with digits, 0 or 5 are always divisible by 5.
Example: 10, 10000, 10000005, 595, 396524850, etc.

Divisibility Rule of 6

Numbers which are divisible by both 2 and 3 are divisible by 6. That is, if the last digit of the given number is even and the sum of its digits is a multiple of 3, then the given number is also a multiple of 6.

Example: 630, the number is divisible by 2 as the last digit is 0.
The sum of digits is 6+3+0 = 9, which is also divisible by 3.
Hence, 630 is divisible by 6.

Divisibility Rules for 7

The rule for divisibility by 7 is a bit complicated which can be understood by the steps given below:

Example: Is 1073 divisible by 7?

• From the rule stated remove 3 from the number and double it, which becomes 6.
• Remaining number becomes 107, so 107-6 = 101.
• Repeating the process one more time, we have 1 x 2 = 2.
• Remaining number 10 – 2 = 8.
• As 8 is not divisible by 7, hence the number 1073 is not divisible by 7.

Divisibility Rule of 8

If the last three digits of a number are divisible by 8, then the number is completely divisible by 8.

Example: Take number 24344. Consider the last two digits i.e.  344. As 344 is divisible by 8, the original number 24344 is also divisible by 8.

Divisibility Rule of 9

The rule for divisibility by 9 is similar to divisibility rule for 3. That is, if the sum of digits of the number is divisible by 9, then the number itself is divisible by 9.

Example: Consider 78532, as the sum of its digits (7+8+5+3+2) is 25, which is not divisible by 9, hence 78532 is not divisible by 9.

Divisibility Rule of 10

Divisibility rule for 10 states that any number whose last digit is 0, is divisible by 10.

Example: 10, 20, 30, 1000, 5000, 60000, etc.

Divisibility Rules for 11

If the difference of the sum of alternative digits of a number is divisible by 11, then that number is divisible by 11 completely.

In order to check whether a number like 2143 is divisible by 11, below is the following procedure.

• Group the alternative digits i.e. digits which are in odd places together and digits in even places together. Here 24 and 13 are two groups.
• Take the sum of the digits of each group i.e. 2+4=6 and 1+3= 4
• Now find the difference of the sums; 6-4=2
• If the difference is divisible by 11, then the original number is also divisible by 11. Here 2 is the difference which is not divisible by 11.
• Therefore, 2143 is not divisible by 11.

A few more conditions are there to test the divisibility of a number by 11. They are explained here with the help of examples:

If the number of digits of a number is even, then add the first digit and subtract the last digit from the rest of the number. 

Example: 3784

Number of digits = 4

Now, 78 + 3 – 4 = 77 = 7 × 11

Thus, 3784 is divisible by 11.

If the number of digits of a number is odd, then subtract the first and the last digits from the rest of the number. 

Example: 82907

Number of digits = 5

Now, 290 – 8 – 7 = 275 × 11

Thus, 82907 is divisible by 11.

Form the groups of two digits from the right end digit to the left end of the number and add the resultant groups. If the sum is a multiple of 11, then the number is divisible by 11.

Example: 3774 := 37 + 74 = 111 := 1 + 11 = 12 

3774 is not divisible by 11.

253 := 2 + 53 = 55 = 5 × 11

253 is divisible by 11.

Subtract the last digit of the number from the rest of the number. If the resultant value is a multiple of 11, then the original number will be divisible by 11.

Example: 9647

9647 := 964 – 7 = 957

957 := 95 – 7 = 88 = 8 × 11

Thus, 9647 is divisible by 11.

Divisibility Rule of 12

If the number is divisible by both 3 and 4, then the number is divisible by 12 exactly. 

Example: 5864

Sum of the digits = 5 + 8 + 6 + 4 = 23 (not a multiple of 3)

Last two digits = 64 (divisible by 4)

The given number 5846 is divisible by 4 but not by 3; hence, it is not divisible by 12.

Divisibility Rules for 13

For any given number, to check if it is divisible by 13, we have to add four times of the last digit of the number to the remaining number and repeat the process until you get a two-digit number.  Now check if that two-digit number is divisible by 13 or not. If it is divisible, then the given number is divisible by 13.

For example: 2795 → 279 + (5 x 4) 

→ 279 + (20) 

→ 299 

→ 29 + (9 x 4) 

→ 29 + 36 

→65

Number 65 is divisible by 13, 13 x 5 = 65

Thanks a lot

[studiot]

18 hours ago, bayukutten said:

@studiot ,

I was trying to prepare for a state government test and its full of quantitative aptitude questions , otherwise i would not have given this much importance to all these basic mathematics problems .

Also thanks for explaining the steps involved in factorization of numbers .

If you are going for actual examinations then

practise, practise, practise.

🙂

That was a good list of test factors you posted -  stick with it.

 

As a further aid I recommend looking at the Wolfram Alpha website.

https://www.wolframalpha.com/

This free and allows you to type in specific mathematics questions (calculations) and then provides the answer and working.

It will enable you to check your own working when you do not have the answers.

Here is a screenshot of factorising a long number.

 

When you come to factorising alegrbraic expressions rather than numbers you can put those in too.

eg

factorise 10x² + 7x -15

Which comes to

(2x-3)(x+5)

This ability is really useful.

Edited March 13, 2021 by studiot

[bayukutten]

@studiot ,

Thanks for the Wolfram Alpha screenshot .

The openstax book ,  intermediate algebra is a good book to learn algebra and all the factoring techniques .

Quote

FIND THE GREATEST COMMON FACTOR (GCF) OF TWO EXPRESSIONS.

Factor each coefficient into primes. Write all variables with exponents in expanded form.

List all factors—matching common factors in a column.In each column,circle the common factors.

Bring down the common factors that all expressions share.

Multiply the factors.

Quote

FIND THE LEAST COMMON DENOMINATOR OF RATIONAL EXPRESSIONS.

Factor each denominator completely.

List the factors of each denominator. Match factors vertically when possible.

Bring down the columns by including all factors, but do not include common factors twice.

Write the LCD as the product of the factors.

 

I can manage to learn some algebra too from that book ,

But the examination syllabus is a bit weird because it has questions from these which i am not that familiar with ,

Percentages    
Average    
Ratio and Proportion
Profit and Loss    
Simple Interest    
Compound Interest    
Partnership    
Mixtures (or) Alligations    
Problems on Ages    
Time and Work    
Pipes and Cisterns    
Time and Distance    
Problems on Trains    
Boats and Streams    
Clocks    
Calendars
    
Mensuration - 2D    
Mensuration - 3D    

I am still looking for a book to learn the last part

 

OK , got that too

Quantitative Aptitude and Reasoning - R. V. Praveen

 

now that i have everything organized in my head properly ,

i can start practicing from all the above .

Thanks for all the help studiot

[studiot]

That's an unusual combination and spread of subjects.

Alligation is used in Pharmacy for instance.

Thre will be lots of 'word problems' where you have to extract the relevent information from the text to peform some calculation or deduction.

[bayukutten]

Thanks for all the help studiot

Yes , the syllabus is from a lot of subjects . It was very difficult finding the proper books to learn all these