Monthly Archives: January 2001

Checking Multiplications

Hi Friends . Here is a nice mathematical trick I learnt about in a book called ” The Trachtenberg speed system of Basic Mathematics ” . All of my high school I relied on this trick to verify  my calculations .

      How do you check if the answer of your multiplication is correct :

Lets try an example :

            64  multiplied by 34 is 2176 .

 

How do you verify something like this ? Here is the trick :

 take the number 64  …. 6 + 4 is 10 . 1 + 0 is 1    . Remember this 1 .

 take 34             …. 3 + 4 is 7                    Remember this 7 .

 

Now 7 multiplied by 1 is 7 .

 

Now the answer you want to check is 2176 . So 2 + 1 + 7 + 6 = 16 . 6 + 1 = 7 .

 

SO we get seven here also . The answer is correct .

The trick is this :

add the terms of the first multiplicand 1 and reduce it to a single digit .

Lets call this a .

add the terms of multiplicand 2 and reduce it to a single digit . Call this b .

Multiply a and b . Reduce the sum to a single digit ( by adding the digits ) .

Call this c .

Now reduce the product to be verified to a single digit . The digit should be

c if the answer is correct .

 

Lets try a bigger example :

   3124 * 4145 = 12948980

 

Lets reduce 3124 to a single digit : 3 + 1 + 2 + 4 = 10 . 1 + 0 = 1 …. (a)

Lets reduce 4145 to a single digit : 4 + 1 + 4 + 5 = 14 . 1 + 4 = 5  … (b)

 

Now 5 * 1 = 5 . This is what the product should give if it is reduced to a

single digit .

Lets try :

 

12948980  reduced to a single digit is 1 + 2 + 9 + 4 + 8 + 9 + 8 + 0 = 41 .

and 4 + 1 is 5   !!!!! Great it verifies !

See what an easy way to check lengthy calculations .

 

ANother trick : When you are adding numbers to reduce them to a single

digit you can ignore the 9s or any set of numbers that add up to 9 .

 

Take a number 911 . Reduce to single digit 9 + 1 + 1 = 11 . 1 + 1 = 2 .

If I had ignored the 9 the single digit would still have been 2 .

 

Or take 5411 . Ignore the 5 and 4 ( they add to 9 ) . The single digit

for it is 2 .

 

 enjoy !

 

Kanwar

 

Leidenfrost Effect: Walking on Hot coals

Have you ever wondered how people can walk on hot coals ?

      Today morning I was flipping through the pages of “The Fundamentals of Physics” by Resnisk , Halliday and Walker and I found something very very interesting . I thought I must tell everyone about it . Resnick and Halliday was my favourite book in 11 and 12 th . The latest edition is coauthored with Walker . The Walker guy used to write articles for the Amateur Scientist column in Scientific American . He is heck of cool .

      Why do you see bubbles when water starts to boil ? As you increase the temperature of a container containing water, the water in contact with the base of the container start to vapourize . The vapours start off as bubbles at the bottom of the container and rise to the top . As they rise they collapse because of the cooler middle layers . 

      Now there comes a temperature called the Leidenfrost point at which the entire base is full of vapours and the liquid is seperated from the base of the container by a sheet of vapour thus reducing the rate of flow of heat to the liquid .

      The German Physicist Leidenfrost was the first to observe this .

He did some experiments with water drops on hot surfaces which you can repeat in your kitchens : Take a pan and heat it … put a drop of water on it . It will evaporate away real fast … *sizzle* *sizzle* . Now keep heating the pan . Put a drop on it . It vapourizes away even faster

*sizzle* *sizzle* just a few secs. Now keep heating .At about 200 deg Celcius ( The Leidenfrost point in water ) the drop will stay on the pan for about a minute . It will dance all over the pan but it will evaporate real slowly .

The reason is that the lower part of the drop has vapourized and the liquid part is no longer in contact with the hot surface . It rests on the sheet of vapour , which is a bad conductor of heat .

      In the article Walker describes his experiments with the Leidenfrost effect . He wet his hands and put them in a beaker full of molten lead .

He felt no pain . The water vapour formed a propective sheet and protected his hands . However doing the same experiment with dry hands caused severe burns .

      Walker also describes how Leidenfrost effect is used by firewalkers .

The reason why people are able to walk on hot coals is this :

1) The wood coals are not very good conductors of heat. So they are hot  but they cant give away their heat so fast .

2) The firewalkers walk very fast and the surface area in contact with their  feet is very less . So less heat transfer .

3) The firewalkers usually wet their feet before walking . The leidenfrost effect causes a thin layer of vapour between the feet and the coal thus protecting the skin . The skin is not in contact with the coal .

       Walker himself describes how he walked on red hot coals 4 times with his feet wet and a book of Physics in his hands . The Physics book was for faith in the laws of Physics .

 

      I felt really thrilled after reading the article . The laws of Physics work everywhere , in all spheres of our existence . And they are the ultimate truth .