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