Basic Concept of Addition and Multiplication

As I usually try to explain some of the topics of mathematics in which I used to try to take some basic concepts too,

similarly today I aren't taking any of the topic but at the same time in this tutorial I'm going to explain a very deep concept i.e.

Belongs to Addition and Multiplication which I encountered today while I was teaching in my class & I found to be shareable with you all.

Basic Concept : Addition and multiplication

let me tell you the whole story
A group of curious student has asked me..!!

Question:-  If it is
 2×2 =4 and 2+2=4
and
3+3=6
then likewise why not it is
3×3= 6 instead of 3×3=9.

Ans:-
I explained this problem in such manner which might also helpful for others...

yes..! this is true that if we multiply and add 2 with 2 then answer will remain same i.e. 4.
I also states that this is the only number in Mathematics which have this specific behaviour but for other numbers the situation becomes different.

for addition it is okay i.e.
2+2= 4       &      3+3 = 6

but when we tend to multiply any number
to itself it gives different values,
I explained this happens because when 3 is multiplied with 3 this means 3 is being added 3 times i.e.
3×3 = 3+3+3
which equals to 9.
similarly for any other example
like
 4×4 = 4+4+4+4 = 16.

so the conclusion accordingly is the concept of multiplying arises to comprise or saturate the long addition process for such big additions like
25+25+25+25+25.........(25 time)= 25×25
625                                                 = 625.

Alternative Method of addition :-

3×3    
or we can write
3+3+3
common out 3
3 (1+ 1+ 1)
3× 3
9.


hence 3+3 = 6
but 3× 3 = 9


hence I explained my students, while reading this article I hope you also come across this concept and finds interesting.

so, here I'm ending this post now If you find some suggestions or any topic you want me to explain via my tutorials, then let me know by commenting under the comment section.
till then check out our recent and most readed tutorials over web:-

• Exponents and their rules

• Divisibility test of 3,5,7,9,11,13....

• Fractions Solutions with ease

• BODMAS rule - how and when to apply

Divisibility rules for 2,3,4,5,6,7,8,9,10,11,13,15,17,19.

Hello everyone,

Today I'm going to explain the concept of

  Divisibility

    •    Divisibility:- This is the best way to predict whether any number is divisible by any other whole number or not without doing calculation.

interesting...!!!? isn't it ?

yes, of course...!!!

by following the rules we can identify this.

now I'm going to explain each rule,

• Test of Divisibility of 2 :-

If any number ends with an even number

example  290, 156, 654 etc.

• Test of Divisibility of 3 :-

If the sum of digits of any number is divisible by 3 then the number is divisible by 3.

example 54/3

 = 5+4 = 9   

 9/3= 3

hence 54 is also divisible by 3 

i.e. 54/3 = 18

but if it is 53 

then 5+3 =8 which is not divisible by 3 so 53 will also not divisible by 3.

• Test of Divisibility of 4 :-

A number is divisible by 4 if the number formed by last two digits is divisible by 4 

example  316 /4 = 79

here 16 is forming by last two digits which is divisible by 4.

Must read tutorials: 

• BODMAS RULE: how and when to apply

• Algebraic Fractions

• Test of Divisibility of 5 :- 

A number is divisible by 5 if the last digit of that number is either 5 or 0.

example  545

545/5 = 109

620/5 = 124

• Test of Divisibility of 6 :-

A number which is divisible by 2 and 3 both, means the number should satisfy the Divisibility of 2 and 3, then the number must be divisible by 6.

example  168 

168/2 = 84

168/3 = 56

now 

168/6 = 28.

• Test of Divisibility of 8 :-

A number is divisible by 8 if the number is formed by it's last three digit is divisible by 8.

example . 7,120

so 120 last three digit number is divisible by 8 120/8 = 15

hence 7,120 will also be divisible by 8

7,120/8= 890

• Test of Divisibility of 9 :-

it is likely to the rule for number 3

A number is divisible by 9 if the sum of the number is divisible by 9.

example . 549 

5+4+9 =18

18/9= 2

hence 

549 /9 = 61

• Test of Divisibility of 10 :-

Any number which ends with 0 will be divisible by 10.

example 10, 100, 1000, 10000...

• Test of Divisibility of 7 :-

Double the last digit and subtract it from the remaining leading truncated number. If the result is divisible by 7, then so was the original number. Apply this rule over and over again as necessary.
Example: 826. Twice 6 is 12. So take 12 from the truncated 82. Now 82-12=70. This is divisible by 7, so 826 is divisible by 7 also.

There are similar rules for the remaining primes under 50, i.e. 11,13, 17,19,23,29,31,37,41,43 and 47.

• Test for divisibility by 11:- 

Subtract the last digit from the remaining leading truncated number. If the result is divisible by 11, then so was the first number. Apply this rule over and over again as necessary.
Example: 19151--> 1915-1 =1914 -->191-4=187 -->18-7=11, so yes, 19151 is divisible by 11.

• Test for divisibility by 13.

Add four times the last digit to the remaining leading truncated number. If the result is divisible by 13, then so was the first number. Apply this rule over and over again as necessary.
Example: 50661-->5066+4=5070-->507+0=507-->50+28=78 and 78 is 6*13, so 50661 is divisible by 13.

• Test for divisibility by 17.

Subtract five times the last digit from the remaining leading truncated number. If the result is divisible by 17, then so was the first number. Apply this rule over and over again as necessary.
Example: 3978-->397-5*8=357-->35-5*7=0. So 3978 is divisible by 17.

• Pi: rational or irrational

• Test for divisibility by 19.

Add two times the last digit to the remaining leading truncated number. If the result is divisible by 19, then so was the first number. Apply this rule over and over again as necessary.

example : 101156-->10115+2*6=10127-->1012+2*7=1026-->102+2*6=114 and 114=6*19, so 101156 is divisible by 19.

So I tried to collect the best explanation of Divisibility.
If you are any doubts and if you have suggestions then comment under this article.
Thank you,

Math: Good or Bad

Neil DeGrasse Tyson

• Somebody has asked this Question which is generally Why are we bad at math?

Before starting this post I'm going to give you a question , give this a try-

Replace the "?" by the correct (Mathematics- Wikipedia ) symbol to make the expression true

18 ? 12 ? 4 ? 5 = 59.

Now here is the answer of the query asked in the beginning of the article,

Explained by the famous astronomer Neil DeGrasse Tyson

OK, let us try to understand why this is Neil Degrasse Tyson came up with a conclusion that when we say ,”we are bad at math” or “I am not a math person” the only conclusion that comes to mind is that we are not equipped for logical thinking which is highly contradictory because the human brain is designed to think logically, why is this?

Because we are taught mathematics in such a way that we are forced to perceive it as alienish. The teachers themselves teach it in such a way that students really can’t understand it no matter how many times we try. The only way out of this is following these methods.

If you want to excel in maths you should follow these principles

1. Determination : Be determined that you will understand everything that you want to know about maths no matter what.
2. Rid yourself from negative thoughts: When we keep on telling ourselves that we can’t do it we just can’t we are feeding ourselves with negative energy and then we seriously can’t even solve simple algebra, instead develop a positive attitude and tell yourself “IT IS JUST MATH AND NOTHING ELSE”
3. Passion: Develop a passion for it and you are bound to gain success.
4. Understand which mode of instruction is better for you: Are you an autodidact? Do you learn best by reading? Do you learn best by watching, listening or are you a hands on learner.
5. Use resources available to you— the Internet, books, videos such as khan academy you tube videos, JM patrick’s tutorials edx,coursera etc.
6. Develop a positive mind set.
7. Have fun.
8. Take it slow.
9. Work hard.
10. Never quit.

I had the same problem math frightened me because my teachers were not able to understand it clearly when one day I was in a do or die situation and decided to taught myself mathematics and now I enjoy it. The thing I used to hate in my childhood became dear to me.

This method is proven effective for studying mathematics.(Courtesy of Professor Michael Star bird)

Try to understand the basic concept of a given topic and build upon it do a practice problem and if you made mistakes it is okay. It is a stage of learning. Try to understand why you made those mistakes then deeply understand the ideas correct them and form a solid ground for those concepts. After that apply them to real life situations. You can also create your own way of solving questions just for fun :).

Then steadily increase your difficulty. Build upon the concepts you previously learned and also do this if you think you faced yourself with a difficult question. Retreat to your basic ideas or do a question you can easily solve and deeply understand what you did there.

Finally take it easy. Go out enjoy and never lose sight of your goal.

If I tell you about myself ( SM Faizan Ali) ,I had developed some of the concepts to solve Math problems likewise  taking LCM of two or more fractions,

table formation using vedic maths tricks etc

I will show some of them later on my next articles, Surely..!

If anyone of you seeking some of the extra stuff here in my articles just let me know,

surely I'll get back with those stuffs.