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December 22, 2011

Shortcuts in Multiplications

77 comments

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NOTE : These techniques are for Mental Maths. You should do calculations in your mind only. Please avoid using Pen/Pencil and Paper. 




Multiplication using multiples
Assume that we should find out the result of 12X15. 
12 x 15   (Here we can write this 15 as 5x3)
=  12 x 5 x 3 (now 12x5 becomes 60)
=  60 x 3 (For this you just calculate 3x6, that is 18 and add one Zero to it. that is 180)
=  180 (see, how simple it is?)



Multiplication by distribution 
Assume that we should find out the result of 12x17
12 x 17   (Here we can divide this 17 as 10+7. here, multiplying 12 with 17 is same as multiplying 12 with 10 and 7 separately and then adding the results)
so, we can write it as
= (12 x 10) + (12 x 7) 
= 120 + 84
= 204 



Multiplication by "giving and taking"
12 x 47  (Here its little difficult for us to calculate the multiplication of 12 and 47 mentally. so just check for the ROUNDED number nearer to 47. Yes it is 50. so.....

= 12 x (50 - 3) 
= (12 x 50) - (12 x 3)  (we have discussed this rule earlier)
= 600 - 36
= 564



Multiplication by 5
* If we have to multiply a number with 5, just divide the number with 2 and then multiply the result with 10. Confused? Its very simple step actually....
428 x 5   (Now just divide the number with 2)
= 428 x 1/2 = 214 (Now multiply it with 10. I mean just add a zero at the end :P)
= 214 x 10
= 2140 (This is our result)

Whats the logic behind this step? 
Very simple. 
* Lets say the number is X. 
* Now we are dividing the number with 2.  so here X becomes X/2. 
* And then we are multiplying it with 10.  So it will become 10x / 2  
* Now cancel it with 2. so it becomes 10x / 2 = 5X = 5 multiplied by X. Thats it ;)



Multiplication by 10  ------------  just move the decimal point one place to the right
16 x 10
= 160
5.9 = 159
169.93 = 169.3   (Need an explnation for this too??? :P)

Multiplication by 50 ------ divide with 2 and then multiply by 100
Well, this is also same process as we did for 5. Here we should add an extra zero. Thats it
18 x 50
= (18/2)  = 9
= 9 x 100
= 900



Multiplication by 100 -------- move the decimal point two places to the right
45 x 100
= 4500  



Multiplication by 500-------- divide with two and multiply with 1000 
21 x 500
= 21/2 x 1000
= 10.5 x 1000
= 10500



Multiplication by 25 ---------- use the analogy Rs 1 = 4 x 25 Paise
25 x 14 (just divide the 14 as 10+4)
= (25 x 10) + (25 x 4) 
= 250 + 100 --->  Rs2.50 + Rs1
= 350


Hey one more thing. Here you can use another technique too. Which we have used for multiplication with 5.

Multiplication by 25 -----------  Divide by 4 and multiply by 100 
36 x 25
= (36/4) x 100
= 9 x 100
= 900  
Multiplication by 11 (if sum of digits is less than 10)
72 x 11
= 7+2 =9, it is Less than 10. so,
= place this term 9 between 7 &2

= 792 (That's the answer)


Multiplication by 11 (if sum of digits is greater than 10)
87 x 11
=>  8 + 7 = 15 
because here 15 is greater than 10, first use 5 and then add 1 to the first term 8, 
which gives you the answer
= 957 

Multiplication of numbers ending in 5 with the same first terms (square of a number)
25 x 25 
first term = (2 + 1) x 2 = 6
last term = 25
answer = 625 ---> square of 25

75 x 75 
first term = (7 + 1) x 7 = 56
last term = 25
answer = 5625 ---> 75 squared


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77 comments:

  1. not clear the meaning of last term.if we take an example of 75*75 than 7+1*7=56 than if we take a last term ie. 75 than the answer is 5675 but that is wrong .right answer is 5625 plz clear it

    ReplyDelete
    Replies
    1. Look if we need to find square of any no ending with 5 like 175*175
      write 25 at the unit and tenth place blindfoldly then for the later part just find 17*(17+1)= 17*18=306. so the ans will be 30625 rather 30675.
      The correct ans is 30625, you can check it out.
      other example 195*195= 19*20=380 & 25 at ones & tenth place so ans is 38025.
      It's handy concept for finding square of the no ending with 5.
      Hope you concept is clear now:)

      Delete
    2. @ Anonymous : The last term is not 75. Its 25 (5 X 5). Please do check it...

      Delete
    3. its always 25 at the last for any suares like 25, 35,45....check once
      ex: 75*75

      7(7+1)=7*8=56 and last is 25


      it is 5625




      Delete
    4. gr8ambitionz is really providing gr8 tips,.,.
      thanks a lot

      Delete
    5. nice tricks..thankx....you can also do this:
      75*75=7*8=56(7 multiply by its next digit)
      5*5=25
      you can use this method till 10 coz its difficult sometime to multiply 13*14 etc...after 10 you can follow above mention method.
      thanks all the best folks

      thanks once again admin :)

      Delete
    6. thnks for ur grt work !! really halpful tips !

      Delete
    7. for square we can use a(square)+2ab+b(square) formula as below:
      suppose 75*75
      take a=7, b=5
      so a*a=49 and b*b=25 and 2ab=2*7*5=70
      now put from last as 5 of b*b, in hand=2, put (2*a*b+in hand)=2, in hand=7, now (a*a+in hand)=49+7=56......so the result is 75*75=5625

      Delete
    8. yes mam, it's really helpful

      Delete
    9. short cut for square of the number which ends with 5
      example: square of 65
      first step 5*5= 25
      second step 6*next number(7)= 42
      so answer is 4225

      Delete
    10. dude listen clearly ;) 7+1*7 =56
      u have to square the last digit of 75 and 5 square is 25 ;)
      so that answer is 5625 ;) got it?

      Delete
    11. Hi dude normally, square the numbers ending with 5 the last two digits must be 25.take some example 5*5=25
      15*15=225
      25*25=625
      35*35=1225
      45*45=2025
      55*55=3025
      65*65=4225
      75*75=5625
      85*85=7225
      vice versa

      Delete
  2. thnks....!! its helpful..! :)

    ReplyDelete
  3. can u plz tell how to find cube roots apart frm factor method

    ReplyDelete
    Replies
    1. We are going to post the procedure in a few days Friend. Keep Checking :)

      Delete
  4. Its so helpful.
    Awsum work.Thank u so much

    ReplyDelete
  5. last term will be always 25 only
    75*75=
    f.t=(7+1)*7=56
    L.T=25(fix for all)
    answer=5625

    ReplyDelete
  6. thanks for all the stuff provuded by this webpage .....................

    ReplyDelete
  7. Really gud nd usefull

    ReplyDelete
  8. Thanks a lot for providing such a useful website for us......

    ReplyDelete
  9. gud tricks.......
    super like.......

    ReplyDelete
  10. THANKS ..REALLY GUD TRICKS ......APPRECIABLE WORK.......

    ReplyDelete
  11. Thanking for all of u, who are involved in this creation. Thanks again. I didn't open my institute books to prepare for IBPS as you have provided all subjects.

    ReplyDelete
  12. another method:multiplication of no. ending in 5with same first term
    25*25
    first term is 2
    next number is 3
    2*3=6
    squre of 5=25
    so ans is 625
    more e.g.35*35=1225
    45*45=2025
    115*115=12125

    ReplyDelete
    Replies
    1. Thanks for the update Tina

      Good Day

      Delete
    2. @tina your last answar is wrong.Correct answer is 115*115=13225(trick: 5*5=25; and 11*12=132)

      Delete
  13. another method:multiplication of number ending in 5 with same first term
    25*25
    2 is first term and 5 is second term
    cosecutive no. of first term is 3
    multiply both no.2*3=6
    squre of second term =25
    so ans is 625
    more e.g.35*35=1225
    45*45=2025

    ReplyDelete
  14. Replies
    1. you can double any of the number and then multiply Aman. At last you simply should divide the number with 2.

      See you can do the above calculation as

      90*55 = 4950/2 = 2475

      or

      45*110 = 4950/2 = 2475

      Hope it helps

      Delete
    2. applying ......(a+b)(a-b) i.e (50+5)*(50-5)=2500-25=2475








      Delete
  15. Thank you so much...you helped me a lot

    ReplyDelete
  16. Its superb....................thank you

    ReplyDelete
  17. Its gr8...it will helps a lot... but need more and difficult sums with shortcuts....

    ReplyDelete
  18. thx a lot frds.... these tricks are very useful:)

    ReplyDelete
  19. thnq gaining shrtcut n easyway

    ReplyDelete
  20. mam will u publish quick reference guide for ibps po exam it will be very usefull if u do so

    ReplyDelete
  21. mam will u help us by publishing quick reference guide for ibps po exam

    ReplyDelete
  22. Multiplication by 11 (sum of no. less than 10)

    shortcut not working for 53*11
    According to shortcut it should be 593 but right ans is 583.

    Please help

    ReplyDelete
    Replies
    1. 53*11
      STEP 1= 5_3 (LEAVE ONE DIGIT SPACE IN BETWEEN THE SQUARING DIGITS...)
      STEP 2= 5+3=8 (FILL 8 IN BETWEEN THEM...)
      NOW THE ANS IS 583...:)

      Delete
    2. 53*11
      5_3 (leave one digit space in between them.)
      then 5+3=8
      fill 8 in between the squaring digit...
      ans is 538

      Delete
    3. @anonymous yes its working ..without any problem
      53*11 -----> using shortcut 5+3=8(8<10) so place 8 b/w 5 & 3 which is 583

      Delete
  23. For multiplication by 11 , if the number is a 4 digit number or more like 1234 or so?

    ReplyDelete
  24. hie everybody, a very chilly mrng to all my fellows.
    can any 1 tell me a simple trick to solve 55*11.

    advance tnx to the buddy

    ReplyDelete
    Replies
    1. simple yaar 5_5 leave one place gap as usual and now 5+5=10 which is not less than 10 right ....so now add that borrowed one to first digit i.e 5+1=6 so answer is 605 hope you understood but there is other simple method i.e55*(10+1)=550+55=605 this one is better one for such multiplication

      Delete
    2. simple yaar 5_5 leave one place gap as usual and now 5+5=10 which is not less than 10 right ....so now add that borrowed one to first digit i.e 5+1=6 so answer is 605 hope you understood but there is other simple method i.e55*(10+1)=550+55=605 this one is better one for such multiplication

      Delete
  25. hie everybody, a chilly mrng to all of my fellows
    thanks to the blog admin, fro sharing their idea with us.
    please if any 1 could give me a trick to solve 55*11.

    ReplyDelete
  26. APPLY >10 FORMULA... 5+5=10 SO ADD 0 FIRST and THEN ADD 1 TO FIRST TERM.. ie 605

    ReplyDelete
  27. its an wonderfull tricks , it helps me a lot , thanks for providing such good things

    ReplyDelete
  28. these type of tricks i have not seen any where..thank u so much...great job u had done..

    ReplyDelete
  29. what is the multiplication rule for 11 if the number to be multiplied is greater than 99 ?

    ReplyDelete
  30. I don't think this is helpful . Its time taking more than normal calculation.

    ReplyDelete
  31. OSM tips...
    could u plz clarify the multiplication of 3 or more digits number with 11?
    Eg:-

    11*151 = ?
    11*9563= ?
    etc...

    ReplyDelete
  32. REALLY APPRECUABLE TECHNIQUES OF LEARNING :)

    ReplyDelete
  33. appreciable techniques of learning (Y)

    ReplyDelete
  34. Is there any shortcuts for multiplying prime with prime number? eg. 17*23*19*29=?

    ReplyDelete
  35. could u plz clarify the multiplication of 10

    here 16*10=160 this is correct
    how 5.9=159
    the correct one is 59 right?
    &
    169.93=169.3
    the answer is 1699.3
    how 169.3?

    clarify it. mam/sir

    ReplyDelete
  36. how to solve this Q
    how many six letter word can be formed with the letters of word POLICY such that the vowels occur only at even places.

    ReplyDelete
  37. i never find multiplication much easier before.. thanks for posting this :-)

    ReplyDelete
  38. can u tel any short cut for 44*44

    ReplyDelete
  39. I came across this post just now...and i really regret that i had not found this earlier....have been wasting so much time doing calculations in bank exams :((
    but thank u sooooo much for making things easier for us....God bless ur whole team...pls keep up this amazing work...thanks again :D

    ReplyDelete
  40. mam/sir
    pls explain hw 5.9*10 has been solved???
    169.93*10 has been solved???

    ReplyDelete

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