The magic of Vedic math - Gaurav Tekriwal

Magija vedske matematike - Gaurav Tekrival (Gaurav Tekriwal)

Transcriber: Andrea McDonough Reviewer: Bedirhan Cinar

Prevodilac: Tereza Ivanovic Lektor: Mile Živković

Nameste.

Nameste.

I'm from India,

Ja sam iz Indije,

and India is one of the oldest civilizations in the world.

a Indija je jedna od najstarijih civilizacija u svetu.

It has contributed to the world

Dala je svoj doprinos svetu

concepts such as yoga,

putem joge,

ayurveda,

ajurvede,

spicy chicken tikka,

pikantne "tika" piletine

and Vedic math.

i vedske matematike.

Vedic math is one of the world's easiest

Vedska matematika je najlakša

and simplest way to do math.

i najjednostavnija matematika na svetu.

We are going to combine together

Zajedno ćemo kombinovati

and do some number crunching today.

i baratati brojkama.

So what we are going to first do is multiply by 11.

Prvo ćemo množiti sa 11.

We're going to do it together,

To ćemo zajedno,

so if you blink, you're going to miss it.

zato nemojte da trepnete, jer ćete propustiti.

So just watch it, OK.

Samo gledajte.

So we're going to do 32 times 11, OK.

Uradićemo 32 puta 11.

So we split 3, and we split 2,

Razdvojićemo 3 i 2,

and we add 3 and 2 and paste it on top,

sabraćemo 3 i 2 i dodati

and we get the answer as 352.

i odgovor je 352.

That's it.

To je to.

Let's try another sum.

Probajmo drugi zbir.

45 times 11.

45 puta 11.

Let's hear it.

Da čujem.

Exactly, that's 495.

Tačno, to je 495.

And 75 times 11.

Sad 75 puta 11.

So it gives you 7,125,

To vam je 7 125,

1 gets carried over and it becomes 825.

prebacite 1 iznad i dobićete 825.

That's how simple it is.

Toliko je ovo jednostavno.

OK, this is the principle behind it

Princip je da je "a" koeficijent.

where a is the coefficient.

Let's move on.

Hajdemo dalje.

OK, now what we're going to do is the base method.

Sada ćemo raditi osnovni metod.

OK, this is used to multiply numbers

On se koristi da bismo množili brojeve

very close to the powers of 10,

moćne kao desetice,

like 10, 100, 1,000, and so on.

kao 10, 100, 1 000 i tako dalje.

So we have a sum here, say 99 times 97.

Recimo da imamo 99 puta 97.

OK, now tell me, is 99 more than 100 or less than 100?

Recite mi da li je 99 manje ili više od 100?

Less by how much?

Za koliko manje?

So we write minus 01.

Prema tome zapišite minus 01.

And 97 is less than 100 by how much?

A za koliko je 97 manje od 100?

So we write minus 03.

Zapisaćemo minus 03.

So what we're going to do is

Ono što ćemo uraditi je, da

we're going to cross subtract

oduzmemo unakrst,

and get the first part of the answer, like this.

i dobićemo prvi deo odgovora, ovako.

We're going to do cross subtraction.

Oduzećemo unakrst.

97 minus 01 would give us

97 minus 01 daće nam

96.

96,

and we multiply 03 times 01 vertically,

a vertikalno ćemo pomnožiti 03 puta 01

and we get an answer of 03.

i dobiti rezultat 03.

Let's check another sum.

Da proverimo još neki zbir.

Try and do it yourselves.

pokušajte da uradite sami.

We got 98, which is,

Sad imamo 98, što je,

is it more than a 100, less than 100?

da li je to više od 100 ili manje?

By how much?

Za koliko?

And 97 is 3.

I 97 je 3.

So we got 98,

Imamo 98,

we go crosswise,

idemo unakrst,

we got 98 minus 3,

imamo 98 minus 3,

or we can do 97 minus 2,

ili možemo 97 plus 2,

they'll all give you the same answer.

oba rešenja su ista.

So that would give us 95.

To je 95.

And the second part would be

Drugi deo bi bio

06.

06.

So that's our answer.

To je naš odgovor.

OK, let's take a bigger number.

Hajde da uzmemo sad neki veći broj.

Let's try this one.

Da probamo ovaj.

Here the base is 1,000.

Osnova je 1 000.

So we got -004,

Imamo 004,

and 997 would be

a 997 bi bio

-003.

-003.

We go crosswise like this,

Idemo ovako unakrst,

and we get 996 minus 003 would give us

pa dobijamo 996 minus 003,

993,

što daje 993,

and 004 times 003 would give us

a 004 puta 003 daju

012.

012.

And that's our answer.

To je rešenje.

Thank you.

Hvala.

14 times 12.

14 puta 12.

OK, here the base is 10.

Ovde je osnova 10.

OK, so is 14 more than 10 or less than 10?

Dakle, da li je 14 više od 10 ili manje?

More, so we got plus 4,

Više, imamo plus 4,

and 12, we got plus 2.

i 12, imamo plus 2.

Again, we apply the same rule,

Primenite opet isto pravilo,

so we do 12 plus 4,

uradimo 12 plus 4,

which gives us 16, like this.

što daje 16, ovako.

And we multiply 2 and 4, that gives us 8.

Pomnožimo 2 i 4, što daje 8.

So now, all of us here,

A sada ćemo svi

we're going to do mental squaring, OK.

uraditi stepenovanje na 2.

Everybody is going to participate here,

Svi ćete učestvovati,

and we're going to do squares of numbers

i stepenovaćemo brojeve

more than 100 mentally right now.

veće od sto, mentalno, odmah.

So we got 101,

Uzmimo 101.

OK, now visualize on the board,

Gledajte na tabli

what's going to be on the right hand side.

šta će biti sa desne strane.

Plus 01, so we got that.

Plus 01, evo.

OK, now we add plus sides, right?

Sada sabiramo plus strane.

Yes? No?

Da? Ne?

So we got 101 plus 01,

Imamo 101 plus o1,

that would give us

što daje

102,

102,

and, see here, like this.

evo, vidite, ovako.

And 01 is getting squared, right?

I kvadrat od 01,

So that would give us

to nam daje

01, and that's your answer.

01, i to je rešenje.

Try the next one.

Probajte sledeći.

Let's try 102 squared.

Pokušajmo 102 na kvadrat.

Let's try, everybody.

Hajde,pokušajte svi.

So 100,

Znači 100,

so 102 would be

102 će biti

10404.

10404.

OK, now the next one, try it everybody together.

Hajde, sada sledeći, pokušajte svi zajedno.

I'll give you 5 seconds.

Daću vam pet sekundi.

OK, let's say it together, let's say it together, OK.

Recite zajedno, zajedno.

[10609]

(10609)

10609 and that's the answer.

rešenje je 10609.

Woo!

Bravo!

104 squared, how much would that be?

Koliko je 104 na kvadrat?

Calculate it, 5 seconds.

Računajte, pet sekundi.

Come on, girls in the back.

Hajde, devojke, tamo nazad.

OK, so the answer would be

Dobro, rešenje je

10816.

10816.

OK, let's do the next one: 105 squared.

Hajde sledeće: 105 na kvadrat.

Oh, no, no, no, no,

A, ne, ne, ne, ne,

we're going to try over, we're going to try over, OK?

pokušaćemo ponovo.

OK. I'll give you 5 seconds, just think about it.

Dajem vam pet sekundi, razmislite.

OK, now we're going to go, OK?

Hajde sad.

11025.

11025.

OK, let's going to do the next one, 106 squared.

Hajde sad 106 na kvadrat.

Try it, come one, everybody, it's simple and easy.

Hajde, svi, jednostavno je i lako.

[11236]

(11236)

OK, let's do it one more time.

Hajde još jednom.

11236.

11236.

Now 107, think, hold on, don't say anything out loud,

Sada 107, nemojte naglas,

just think mentally,

samo u mislima.

107 squared.

107 na kvadrat.

OK, now let's say it out loud.

Recite sad glasno.

11449.

11449.

And 108 squared.

A 108 na kvadrat.

[11664]

11664.

Fantastic, give yourself a round of applause, come on!

Fantastično, zaslužujete aplauz, hajde!

And this is the principle behind this,

Princip je sledeći:

where a and b are the excesses

gde su a i b viškovi

or the deficiency from the base.

ili nedostaci osnove.

I'm going to teach you

Naučiću vas

in Vedic math, there are 16 sutras,

vedskoj matematici, gde ima 16 sutri

or word formulas, OK.

ili formula.

They are very visual

One su veoma vizualne

and one of them is called, "vertically and crosswise,"

i jedna od njih se zove "vertikalno i unakrst"

through which you can multiply any number

i pomoću nje možete pomnožiti bilo koje brojeve

by any number in a single line.

u jednom redu.

So I'm going to do a two-digit by a two-digit multiplication.

Pomnožicu dvocifreni broj sa dvocifrenim.

Let's do this.

Ovako.

So we got 31 times 12.

Imamo 31 puta 12.

OK, so we're going to apply

Primenićemo pravilo

the vertically and crosswise sutra.

"vertikalno i unakrsno".

So we're going to do like this:

Ovako ćemo:

vertically, and then we're going to go crosswise,

prvo vertikalno, onda unakrst

and then we're going to do vertical again.

i ponovo vertikalno.

So, 2 times 1 gives us

Znači, 2 puta 1 daju

[2],

(2)

2 times 3 gives us

2 puta 3 daju

[6],

(6)

and 1 times 1 gives us

a 1 puta 1 daje

[1].

(1),

6 plus 1,

6 plus 1,

[7].

(7),

1 times 3 gives us

1 puta 3 daju

[3].

(3).

And that's it, and that's our answer.

I evo rešenja.

No more tedious calculations,

Nema više zamornih kalkulacija,

no more going through the rough work,

nema više grubih radova,

it's simple in one line.

jednostavno je, u jednom potezu.

I want to show you a sum again,

Ponovo ću vam pokazati sabiranje,

this time with carry-overs.

ovog puta sa ostacima.

The same formula, all of us here can do this, OK.

Ista formula, svi možete ovo da uradite.

Same formula.

Ista formula.

So let's get started.

Da krenemo,

4 times 2 gives us

4 puta 2 daju

[8].

8.

OK, now we go crosswise like this,

Idemo ovako unakrst,

so we're going to multiply 4 times 1,

pomnožićemo 4 puta 1,

[4],

(4),

and 3 times 2,

i 3 puta 2,

[6]

(6),

4 plus 6 gives us

4 plus 6 su

[10].

10.

So we put down 0, carry the 1.

Zapišemo 0, prenesemo 1.

And 3 times 1 gives us

3 puta 1 daju

[3],

3,

plus 1,

[4].

plus 1,

4.

Exactly, that's our answer, 408.

Tačno, naš odgovor je 408.

OK, thank you for being such a participative audience,

Hvala što ste učestvovali,

and we had a great time number crunching.

sjajno smo se proveli baratajući brojevima.

Now I want to end with a question:

Završiću jednim pitanjem:

whether you'd like math to be dull or boring,

da li više volite da matematika bude dosadna

or fun and interesting?

ili zabavna i zanimljiva?

The choice is yours.

Izbor je vaš.