Monday, June 16, 2008

Magic of Numbers- 2

Earlier post about maths made me feel that I have so many people around who have some resonance with my thoughts! Made me feel really enthusiastic to work on and present few more in this

1.Subtracting any number from 100, 1000

1. Subtract 689 from 1000

Step 1: Subtract numbers 6, 8 from 9
Step 2: Subtract unit's place value 9 from 10

1000 - 689 =
9 9 10
-6 8 9
---------
3 1 1

Ans : 1000-689 = 311
2. To divide any number from 9

Example: 32142 / 9

Step 1 : Put down 3 as it is
Step 2 : Add 3 + 2 = 5
Step 3: Add 5(From previous Step) to 1 = 6
Step 4: Add 6(From Previous Step) to 4 = 10 (Carry over 1 to previous Step.So Value in Step 3 becomes 7)
Step 5: Add 10 (From Previous Step) to 2 = 12
Step 6: Divide 12 from 9 and quotient is 1

So The answer is 3 5(6+1)(0+ 1- Quotient value) = 3571

For Demo of this trick check here

3.To quickly divide by 5, 50 and 500

/ 5 - * by 2 and move decimal left 1 time
/50 - * by 2 and move decimal left 2 times
/500 - * by 2 and move decimal left 3 times

Example:

3456 * 5 = (3456 *2) and move decimal left 1 time = > 691.2
3456 * 50 = (3456 *2) and move decimal left 2 times = > 69.12
3456 * 500 = (3456 *2) and move decimal left 3 times = > 6.912

For Demo of this trick check here

4.To add large numbers

238 + 644

238 = 240 - 2 (Number added to 238 to round it off)
644 = 650 - 6 (Number added to 644 to round it off)

240
650
-----
890 - 8 [6+2]
-----
882
-----
This works fine for larger numbers also. But I feel the a better way is

456 + 567

Start adding from left to right

Adding 4 + 5 = 9.Now before concluding the digit see the numbers in next place. It is 5,6 we know that 5+6 = 11 so we have a carry over so the step becomes
(4+5) (5+6) (6+7)
9(1) 1
11 1
Now first place value from left is complete and the sum is 10

See the next place value which is 6, 7 again we have a carry over. So the step becomes
(4+5) (5+6) (6+7)
9(1) 1(1) 3
10 2 3

Ans = 1023
This method is the best and quickest method which can be achieved only with PRACTICE and able to visualize numbers.

5. To get square of a number

(12)^2

Step 1: Square 2 = 4
Step 2: Multiply (1*2) and double it => (2+2 = 4)
Step 3: Square 1 = 1

(12)^2 = 144

(123)^2

Step 1: Square 3=9
Step 2: Consider 12 as a single number. So (12*3) +(12*3) => 36+36 = 72 (Here 7 becomes carryover)
Step 3: Square 12 = 144

(123)^2 = (144+7)29 = 15129

For additional quicker and informative tricks check out Mathemagics videos

18 comments:

  1. விஜய் said...

    HI Ramya,
    Have you read Vedic mathematics? You would be very much interested with that.

    Regards,
    Vijay

  2. ambi said...

    ம்ம், நல்லா எழுது தாயி, என் புள்ளைக்கு சொல்லி கொடுக்கும் போது உதவியா இருக்கும்.

    நான் மேத்ஸ்ல கொஞ்சம் வீக். :)

  3. Priya Murthi said...

    Ramya... ore kalaks dhan po... 12 th maths la evalo centum/99 renduthula onnadhan irrukanum...

  4. ஜி said...

    Ramya teacher.. Ramya teacher... Ithellaam enga irunthu kaththukitteenga teacher??

    ethavathu link with all these tricks or any books suggest pannunga teacher...

    I'll try to provide those info to school going students...

  5. Divya said...

    Good one Ramya:))

  6. Divya said...

    \\Ramya teacher.. Ramya teacher... \\

    அட, உங்களை கணக்கு டீச்சர் ஆக்கிட்டாரா கதாசிரியர்:))

  7. EnvyRam said...

    Hey ...
    Good ones here. I have seen books for this (Vedic mathematics?), but never ventured into reading it.
    I prefer my own way - i.e. making silly mistakes right from my school days to today's GRE/GMAT maths! :D
    Smiles,
    Vinayak

  8. Deepa said...

    கணக்கிலே புலி !!

    ம்ம்மே...ம்ம்மே

  9. மோகன் கந்தசாமி said...

    There is something in this post I object

    @//4.To add large numbers///
    First,
    238 + 644
    238 = 240 - 2 (Number added to 238 to round it off)
    644 = 650 - 6 (Number added to 644 to round it off)

    240
    650
    -----
    890 + 8 [6+2]
    -----
    898
    -----

    This should be like this
    238 + 644
    238 = 240 - 2 (Number added to 238 to round it off)
    644 = 650 - 6 (Number added to 644 to round it off)

    240
    650
    -----
    890 - 8 [6+2]
    -----
    882
    -----

    Second,
    ///456 + 567
    Start multiplying from left to right///

    This should be like this
    Start adding from left to right

    Third,
    a possible confusion with your explanation,
    ///
    (4+5) (5+6) (6+7)
    9(1) 1
    11 1///
    Will you always encounter numbers which would be soved in two simple steps? What's the explanation if the carry-over numbers add up to more than 10?

    How about the explanation below,
    345 + 8697 = ?
    ABC + EFGH = ?

    1.Add corresponding digits of both numbers from left to right

    (0+E) (A+F) (B+G) (C+H)
    (0+8) (3+6) (4+9) (5+7)
    (08) (09) (13) (12)

    2. Divide each result with 10, add eve to the remainder of previous result.
    (08) (09) (13) (12)
    [0] [8+0] [9+1] [3+1] [2]
    (0) (08) (10) (04) (02)

    3. Do the step 2 again until you see each result gets only one digit.

    (0) (08) (10) (04) (02)
    [0+0] [8+1] [0+0] [4+0] [2]
    (00) (09) (00) (04) (02)

    4. Now get rid off the unnecessary zeros in the front of each result

    0 9 0 4 2 = 9042

    The demo for dividing by 9 is awesome!

    Squaring trick is the same as (a+b)^2 = a^2 + 2*a*b + b^2

    Trick 1 and 3 are nothing new


    Another worthful post, again.

    [Pattezhuthi peyar vaangum pulavargal irukkiraargal, aanaal kutram kandu pidiththu peyar vaangum puzhavargal irukkiraargalaa? of course, yes. Adhu naandhaan. :-)]

  10. Ramya Ramani said...

    @Vijay,
    I know very little about "Vedic Mathematics".But I am very much interested in it and would try to learn it in future atleast .Thanks for comments!

    @Ambi Anna,
    Kandippa ennoda maruamannukku nallave sollitharalame :)
    BTW Kozhandai eppadi irukku?Per vechancha??

    @Priya
    Ippadi publicla ellam kekka koodadhu :)

    @Geeya
    Kadasiriyare! Enna idhu nalla kummi adikareenga??Namakku ellam google irukka bayamen..Naan youtube links koduthirukken illiya follow that you have good set information :))

    @Divya
    Vanga Madam..yeah geeya nallave nakkal adichirukkar :(

    @Vinayak
    Thanks sir...they are couple of interesting ones..Silly mistakes in maths is like water in milk Inseperable :))

    @Deepa
    Welcome! "கணக்கிலே புலி !!" ellam illa naan oru chinna எலி :P

    @Kandaswamy
    Thanks for comments. Have corrected the places you have mentioned...You have Sharp eyes..you should be a good teacher..My Amma does find mistakes always easily.

    Wow your explanation is clear and easy to follow. Nandri Hai :))

  11. Shwetha Robert said...

    Useful post Ramya:))

    sema brainy-aa neenga, ipdi asathureenga!!

  12. Ramya Ramani said...

    @Shwetha

    Brainyah appadi ellam illengo.illengooo (echo ...)Chumma namakku terinja interestingana visyatha sollalamenu dhan :)

  13. பரிசல்காரன் said...

    Interesting Blog. Its new to me!
    அப்பாலிக்கா வந்து என் பொண்ணுகள வெச்சுட்டு பாக்கோணும்!
    இன்னும் எளுதுங்க!

  14. gils said...

    //Step 1: Subtract numbers 6, 8 from 9
    Step 2: Subtract unit's place value 9 from 10//

    reminds me of vassol raja :d kamal room number 7 kondu vara logic mari iruku :D nice post..unga postlam padicha enaku thirumbavum maths problems poda asai varutu :)

  15. Pspot said...

    Your blog has been listed in Pathivuspot
    And please tell me some more Taminglish Blogs to add this Taminglish aggregator. Thanks.

  16. இரா. வசந்த குமார். said...

    Ramya,

    it seems you can see this post of mine.

    http://kaalapayani.blogspot.com/2008/07/blog-post.html

  17. மணிமொழியன் said...

    I think u can consider border cases as well in these methods

    ex
    for #1 -if you are doing A - B, failure case would be when B end with zero(s). Then u can shift-left i.e ignore terminating zeros(in both A & B) and apply the same principle.

    for #2 - what if the number starts with 9? - u shud put down 1 for all preceding 9s and then start the usual stuff

    hope you wud understand that I point out these in the spirit of refining them.

    Interesting, keep posting such stuff !!

  18. Ramya Ramani said...

    @Manimozhiyan,

    Your comments are welcome :))

    Sure I will refine them !!