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Mental arithmetic

  1. Mar 17, 2005 #1
    (a) Calculate this in your head: 314*159
    (b) What's so special about these digits?

    I would like to see how people solve this in different ways.
     
  2. jcsd
  3. Mar 17, 2005 #2
    Answer is = 2226.

    2^3 = 6

    2^3 is equal to 2+2+2 as it happens the initial answer is 2226 which is the sum itself. 2^3=6 all the two's being the question and the last digit, 6, being the answer.

    ?
     
  4. Mar 17, 2005 #3
    its als the first dgits of pi
     
  5. Mar 17, 2005 #4
    Haley got the right answer to (b).
    @Paul Wilson: I am not sure what you mean.

    With respect to (a): I am asking you to write down how you
    calculated 314*159 in your head.

    Here's how I did it:

    Step 1:
    314*159 = 314*(160-1)


    Step 2:
    What's 314 * 160 ?
    314*16
    = 314 * (10 + 6)
    = 3140 + 1884
    = 3140 + 2000 - 116
    = 5024

    Therefore, 314*160 = 50240


    Step 3 (Final Step):
    We go back to Step 1, which was:
    314*159 = 314*(160-1)
    = 314*160 - 314
    = 50240 - 314
    =50000 - (314 - 240)
    =50000 - 74
    =49926
     
  6. Mar 17, 2005 #5
    I thought 2 to the 3rd was 8 ??
    and what is 2226 the answer to ???

    Edgardo: your keeping those steps all seperat in your head - good for you!

    How about 314*159 =
    314 *100
    plus 1/2
    plus 3140
    minus 314
    ===============
    31400
    add 1/2 one diget at a time working right to left
    31600
    32100
    47100
    now add the 3140
    50240
    and subtract the 314 working right to left
    50236
    50226
    49926
     
  7. Mar 17, 2005 #6

    Gokul43201

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    What ??

    My sentiments exactly !



    I'd do it Randall's way : 159 = 100 * ( 1 + 0.5 + 0.1 - 0.01 )
     
  8. Mar 17, 2005 #7
    Same way, but I subtract things differently:

    314 00 (314/2 = 150 + 7)
    +157 00 (471 00)
    +031 40 (471 + 31)~40
    =502 40
    240 + 74 = 314
    50240 - 314
    = 50000 - 74
    = 499 26 (it's faster mentally for me to subtract from zeroes)

    :confused: don't get it...
     
  9. Mar 17, 2005 #8
    I followed these steps:

    314*6 = 1884
    1884*10 = 18840
    18840 - 314 = 18526
    18526 + 31400 = 49926
     
  10. Mar 18, 2005 #9
    well, believe it or not, i solved it in my head in 20-25 seconds. :bugeye:

    actually, a few days back i was reading a book which deals with a special branch of mathematics called VEDIC MATHEMATICS. actually it is an ancient Indian way of solving complex mathematical problems orally, and believe me they are very easy to learn. till now i could only read the part about multiplication, as my exams are just around the corner, but it deals with division, fractions(the vulgur ones), linear equations, etc. and all those can be solved without much difficulty and orally. you dont need to form equations or anything like that.


    i solved this one using the criss cross method, which is very easy to learn, but i think i'll post it sometime later.




    i hope some you must have heard about this, specially those who belong to india, as it is fairly popular here.
     
  11. Mar 18, 2005 #10

    T@P

    User Avatar

    maybe im not that sophisticated but i would just do
    (3*100 + 10 + 4)* 159... really the biggest problem to me was remembering what the previous sum was...
     
  12. Mar 19, 2005 #11
    Hello vikasj007,

    I believe you. I once read about this criss-cross method. But I was too lazy to learn it.

    @ T@P
    I don't know how you do it, but if I try to remember all the numbers from each step to sum them up, I repeat them loudly. But sometimes, if the number is very long, I use some sort of coding (Major/Master system) to encode them.

    --------------------------------------------------------------

    NEW TASK:
    Calculate 111*111 ( :biggrin:)
     
  13. Mar 19, 2005 #12
    12321

    Its just to take the number of digits and write them front and back. Works only upto 9 though.
     
  14. Mar 22, 2005 #13
    well, believe me it is very easy to learn, and if you find it interesting as i did, then i am sure you will not be able to leave it till you are done with it.
     
  15. Mar 22, 2005 #14
    I did it in my head, standard multiplication way.
    314
    159
    so 9*314 + 50*314 + 100*314
    it took about 2 minutes, and a lot of talking to myself to keep the numbers from fading
    I basically did
    9*314,
    then added 50*4, then 50*10, then 50*300
    then added 100*4, 100*10, and 100*300
    I had to talk outloud to myself though. Makes it easier.
     
  16. Mar 22, 2005 #15
    Here's how I calculated 111*111:

    I used the formula [itex] (a+b)^2 = a^2 + 2ab + b^2 [/itex].

    111*111 = [itex] (111)^2 [/itex] = [itex] (110 + 1)^2 [/itex]
    = [itex]110^2 + 2 \cdot 110 + 1^2= [/itex]
    = [itex]12100 + 220 + 1 = 12321[/itex]
     
  17. Mar 22, 2005 #16

    Gza

    User Avatar

    Sorry, I just had to add my WTF? to this post as well. :confused:
     
  18. Mar 22, 2005 #17
    I did basic long multiplication and got 50556. I don't really know any other way to work it out.

    The Bob (2004 ©)
     
  19. Mar 22, 2005 #18
    111² is too easy. Calculate 11^4 and 111^3. Show how you did it. Tools allowed: pen and paper.
     
  20. Mar 23, 2005 #19
    Toxic, the question is whether one can calculate things in his/her head.
    Otherwise with paper and pencil it's nothing special calculating 11^4 and 111^3

    I calculated 11^4 in my head the following way:
    11^4 = (121)*(121) = (120 +1 ) ^2
    = 14400 + 2*120 + 1 = 14641

    As for the second problem 111^3 I am still searching for an easy way to calculate this one in my head.
     
  21. Mar 24, 2005 #20
    Ok, here's how I calculated 111^3:

    111^3 = (111^2)*111 = 12321*111

    Calculate 12321*111:
    12321*111 = 12321*(100+10+1) = 1232100 + 123210 + 12321
    = 13 676 31

    I found calculating 12321*111 in my head difficult.
     
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