Friday, November 03, 2006

 

Maths Tricks




Multiply Up to 20X20 In Your Head

In just FIVE minutes you should learn to quickly multiply up to 20x20 in your head. With this trick, you will be able to multiply any two numbers from 11 to 19 in your head quickly, without the use of a calculator.

I will assume that you know your multiplication table reasonably well up to 10x10.

Try this:

  • Take 15 x 13 for an example.
  • Always place the larger number of the two on top in your mind.
  • Then draw the shape of Africa mentally so it covers the 15 and the 3 from the 13 below. Those covered numbers are all you need.
  • First add 15 + 3 = 18
  • Add a zero behind it (multiply by 10) to get 180.
  • Multiply the covered lower 3 x the single digit above it the "5" (3x5= 15)
  • Add 180 + 15 = 195.

That is It! Wasn't that easy? Practice it on paper first!

Finger Math: 9X Rule


To multiply by 9,try this:
(1) Spread your two hands out and place them on a desk or table in front of you.
(2) To multiply by 3, fold down the 3rd finger from the left. To multiply by 4, it would be the 4th finger and so on.
(3) the answer is 27 ... READ it from the two fingers on the left of the folded down finger and the 7 fingers on the right of it.

This works for anything up to 9x10.

Square 2 Digit Number: UP-DOWN Method

Square a 2 Digit Number, for this example 37:

  • Look for the nearest 10 boundary
  • In this case up 3 from 37 to 40.
  • Since you went UP 3 to 40 go DOWN 3 from 37 to 34.
  • Now mentally multiply 34x40
  • The way I do it is 34x10=340;
  • Double it mentally to 680
  • Double it again mentally to 1360
  • This 1360 is the FIRST interim answer.
  • 37 is "3" away from the 10 boundary 40.
  • Square this "3" distance from 10 boundary.
  • 3x3=9 which is the SECOND interim answer.
  • Add the two interim answers to get the final answer.
  • Answer: 1360 + 9 = 1369


With practice this can easily be done in your head




# posted by Unknown @ 6:17 AM 0 comments

Thursday, November 02, 2006

 

stirling's formula for factorials

Unbelievably large numbers are sometimes the answers to innocent looking questions.For instance,imagine that you are playing with an ordinary deck of 52 cards.As you shuffle and re-shuffle the deck you wonder:How many ways could the deck be sheffled?That is how many different ways can the deck be put in order?You reason that there are 52 choices for the first card,then 51 choices for the second card,then 50 for the third,etc.This gives a total of
52x51x50x......2x1.
ways to order a deck of cards.We call this number "52 factorial"and write it as the numeral 52 with an exclamation point:52! this number turns out to be the 68 digit monster

which means that if every one on earth shuffled cards from now until the end of the universe,at a rate of 1000 shuffles per second,we wouldn't even scratch the surface in getting all possible orders.Whew!No wonder we use exclamation marks!

For any positive integer n we calculate "n factorial" by multiplying together all integers up to and including n, that is,

n!=1x2x3x....xn

1!=1 ; 2!=2 ; 3!=6 ; 4!=24 ; 5!=120

6!=720 ; 7!=5040 ; 8!=40320 ; 9!=362880 ; 10!=3628800

STIRLING'S FORMULA

Factorials start off reasonably small, but by 10! we are already in millions, and it doesn't take along until factorials are unwieldly behemoths like 52! above.Unfortunately there is no shortcut formula for n! ,you have to do all of the multiplication.On the other hand,there is a famous approximate formula,named after the Scottish mathematician James Stirling(1692-1770),that gives a pretty accurate idea about the size n!

n!=√2∏n*(n/e)ˆn


# posted by Unknown @ 5:04 AM 0 comments

Saturday, October 14, 2006

 

proof of 0!=1

CAN U PROVE 0!=1

we know that the formula n!=n*(n-1)!

just substitute n=1

1!=1*(1-1)!

1!=1*(0)!

1=0!

0!=1


# posted by Unknown @ 6:58 AM 0 comments

Saturday, August 12, 2006

 

short cuts in maths

MULTIPLICATION WITH '11'
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IF You want to multiply any number with ''11'' follow these steps

  1. from right to left ,frist take last number at right side,i.e., 4
  2. then 4+3=7
  3. 3+2=5
  4. 2+1=3
  5. 1+0=1
  6. the answer is "13574"
  1. take 02489 ,from right to left
  2. i.e., first of all '9'
  3. then 9+8=17,take 7 and remainder (let r1)r1=1
  4. 8+4+1=13('.' r1=1)take 3,remainder (let r2)r2=1
  5. 4+2+1=7('.'r2=1)
  6. 2+0=2

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# posted by Unknown @ 11:12 PM 0 comments

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