Multiplication: The Vedic Way

What would 873 x 982 look like? Lots of lines. But still intrigu­ing. Thanks Alli­son for send­ing this our way. Feel free to sug­gest a good link here

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Comments (19)
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  • My Japan­ese wife says she has nev­er seen such a way of mul­ti­ply­ing. But very inter­est­ing any­way!

  • Ines says:

    Vedic Maths! :-)

  • Tony says:

    Yeah appar­ent­ly it’s not Japan­ese, but Vedic.. check out this wikipedia arti­cle:

  • Dr Silverrose says:

    This is real­ly no dif­fer­ent from mul­ti­ply­ing the way we (west­ern­ers) do it with dig­its: mul­ti­ply each dig­it in one num­ber by each dig­it in the oth­er, and car­ry over as need­ed. It seems to be a bit faster our way, espe­cial­ly for mul­ti-dig­it mul­ti­pli­ca­tion, because you don’t have to draw all those lines.

  • Dr Silverrose says:

    Actu­al­ly, it’s not real­ly mul­ti-dig­it mul­ti­pli­ca­tion that is a pain to do this way (with lines), it’s high-dig­it mul­ti­pli­ca­tion. Try mul­ti­ply­ing 89 x 78 using lines, and you’ll quick­ly go back to mul­ti­ply­ing the way you were taught.

  • Jen says:

    This is not a Japan­ese means of teach­ing mul­ti­pli­ca­tion, but Vedic.

  • Ramasubramaniyan says:

    This method is ok for small num­bers such from 1 to 5 but for 6,7… it is tedious to work out but this method of mul­ti­pli­caion is suit­able to teach for kids so that don’t get out of maths

  • Sarah says:

    Don’t be sil­ly, Doc­tor.
    It’s not the lines that make this eas­i­er and faster, it’s the ori­en­ta­tion of the mul­ti­pli­can­ds, the order that you do the mul­ti­pli­ca­tion and adding.
    In the west­ern way, you make a large inter­me­di­ate answer for every place in your mul­ti­pli­cand. So for 193x16, you get the answers for 193x6 and 193x10 before you get any­thing.
    The flaw in this is that you’re always going to be adding the result of every one place dig­it by anoth­er one place dig­it, ten place mul­ti­plied by a one place togeth­er, then adding every ten by ten and hun­dred by one togeth­er and so on, but instead of per­form­ing *those* oper­a­tions rel­e­vant to the final answer, we make a series of inter­me­di­ate answers that are spaced with place hold­ing zeros. When you’re doing a three dig­it num­ber by a three dig­it num­ber, the amount of added steps is real­ly slow and cum­ber­some, and except for the first oper­a­tion, these inter­me­di­ate answers don’t give you any of the dig­its in the answer.
    In this ver­sion, the vedic ver­sion, regard­less of whether or not you draw any lines, you get the answers for each place dig­it indi­vid­u­al­ly.
    So, typ­i­cal west­ern way goes like this: mul­ti­ply, car­ry, add, car­ry, get the answer.
    The vedic way, you mul­ti­ply, add, car­ry, and then you have a dig­it from the answer. Each inter­me­di­ate answer is sim­ply anoth­er dig­it of your final answer, not a strange large num­ber that serves mere­ly as an oppor­tu­ni­ty to make a mis­take. The third time I tried the vedic way, I got an answer pret­ty quick­ly, then I checked my work using the way I’d grown up with, and the answers did­n’t match. I used a calculator–the vedic way was cor­rect, the west­ern way had sev­er­al mis­takes, even though I took longer to do it.

  • Allie says:

    Bril­liant. I think that this is a lot faster than long mul­ti­pli­ca­tion for 3 or 4 dig­it num­bers. As long as you draw it at the cor­rect angle and car­ry the tens over cor­rect­ly there are no mis­takes. Real­ly great!!

  • Kc says:

    The kids at the school where. I worked did their home­work so they could find where it would fail.

  • Daniel says:

    It’s nice, but it’s obvi­ous it’s not faster than “West­ern” mul­ti­pli­ca­tion”.

  • Zannr1 says:

    well here is the thing. math is math is math. you can make proofs of dif­fer­ent con­cepts in many ways due to the nature of math. myself, i help my daugh­ter with her school work and she is just now learn­ing mul­ti­pli­ca­tion, shes in 2nd grade. one of the tech­niques i taught her was the fin­ger trick when mul­ti­ply­ing num­bers 1–9 by 9. i also showed her some oth­er tricks. any­way when i saw this Japanese/Vedic way i could­n’t believe it. LOL I looked in to how it works with larg­er num­bers like 1234X1232 etc… and it works. so i emailed her teacher with the link say­ing that I think that it is a tech­nique that should sup­ple­ment the times table. the rea­son is easy. when i was learn­ing my times table it was a slow process. you don’t just learn them all right away. it takes prac­tice. So, with this tech­nique kids can use it as a proof of cor­rect­ness while they are learn­ing their times table. All kids have to do is know how to add. ITS GREAT!! when i saw this i felt stu­pid for not know­ing this technique…lol and i pret­ty much minored in math. lol any­way that’s that on

  • Spencer says:

    This is the same way I was taught to mul­ti­ply poly­no­mi­als. For two dig­its we called it FOIL (first out­er inner last). 21x13= (2x+1)*(x+3)=2x^2+(1+6)x+3 where x=10. The only dif­fer­ence is the visu­al­iza­tion.


    The dec­i­mal num­ber sys­tem and the place val­ue sys­tem in use today was first record­ed in Indi­an math­e­mat­ics.

    2. THE ZERO
    Indi­an math­e­mati­cians made ear­ly con­tri­bu­tions to the study of the con­cept of zero as a number.the ancient romans did not know the num­ber o but the Indi­ans had the knowl­edge of large num­bers like mahogham(1 fol­lowed by 62 zeros) and It was the indain math­e­mati­cian Aryab­hat­ta who invent­ed 0 . with­out 0 there would be no bina­ry sys­tem and no com­put­er: count­ing would be clum­sy and cum­ber­some.

    This method of grad­u­at­ed cal­cu­la­tion was doc­u­ment­ed in the Pan­cha-Sid­dhan­ti­ka (Five Prin­ci­ples) in the 5th Cen­tu­ry But the tech­nique is said to be dat­ing from Vedic times cir­ca 2000 B.C

    4. VALUE OF PI
    The val­ue of pi was first cal­cu­lat­ed by Bud­hayana, & he explained the con­cept of what is now known as the Pythagore­an The­o­rem. British schol­ars have last year (1999) offi­cial­ly pub­lished that Bud­hayan’s works date back to the 6th Cen­tu­ry, which is long before the Euro­pean math­e­mati­cians

    5. ALGEBRA
    In ancient India con­ven­tion­al math­e­mat­ics termed Gani­tam was known before the devel­op­ment of alge­bra. This is borne out by the name — Bija­gani­tam, which was giv­en to the alge­bra­ic form of com­pu­ta­tion the infer­ence that Bija­gani­tam was the orig­i­nal form of com­pu­ta­tion is derived.

    Even in the area of Geom­e­try, Indi­an math­e­mati­cians had their con­tri­bu­tion. There was an area of math­e­mat­i­cal appli­ca­tions called Rekha Gani­ta (Line Com­pu­ta­tion). The Sul­va Sutras, which lit­er­al­ly mean ‘Rule of the Chord’ give geo­met­ri­cal meth­ods of con­struct­ing altars and tem­ples.

    Cal­cu­lus, an Indi­an inven­tion, was picked up by the Jesuit priests from Ker­ala in the sec­ond half of the 16th cen­tu­ry and tak­en to Europe. This is how the West­ern­ers got their cal­cu­lus.

    The famous Pythago­ras the­o­rem is explained sev­er­al cen­turies before in the shul­va sutras of the Vedas. It is believed that the much trav­elled Pythago­ras was a stu­dent at the tak­shashila uni­ver­si­ty in undi­vid­ed india and he car­ried with him the knowl­edge of math­e­mat­ics to the west­ern world.

    The largest num­bers the Greeks and the Romans used were 10**6(10 to the pow­er of 6)
    Hin­dus used num­bers as big as 10**53(10 to the pow­er of 53) with spe­cif­ic names as ear­ly as 5000 BCE dur­ing the Vedic peri­od
    Even today, the largest used num­ber is Tera 10**12(10 to the pow­er of 12)

    10 Bina­ry Sys­tem and Hash­ing Algo­rithms are also invent­ed in india thou­sands of years before.


    For­got to men­tion Vedic Maths has lots of short­cuts for cal­cu­lat­ing large num­bers.


    Also for­got Con­cept of Infin­i­ty in maths is also Orig­i­nat­ed in india.


    Vedas and Upnishad are ocean of knowl­edge (Sci­ence, Maths, Phi­los­o­phy, etc.)

  • Gaurish Borkar says:


    Curi­ous if you may quote the Stan­za or Chap­ter & Stan­za num­ber. I want to know more about this. I have pan­chasid­dhan­ti­ka.

  • vamsi says:

    it is were nice’

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