Competition Exams Tricks | Quantitative Tricks | Maths Tricks | Complex Multiplication Tricks

   

           

                   In this era of competition , where not only the knowledge though the knowledge with speed is being appreciated.So i brought a multiply trick for you gyan seekers to solve the complex positive integer multiplication with in the fraction of moments. Here below the trick is given and explained.

 For Now Without a calculator, what is

1. 35 x 12 ?
2. 150 x 36 ?
3. 125 x 84 ?

       No No No!...no calculator search.....With the doubling and halving trick, all of these become much easier.

  Thinking about multiplication 

                         Every positive integer has a unique prime factorization — that is to say, there is a unique way to express each whole number as a product of prime factors. Therefore, whenever we multiply to positive integers, we can think of this the product of the prime factors of one times the product of the prime factors of the other — two big collections of factors being multiplied together. Furthermore, the associative law the commutative law tell us we can multiply in any order — we could even swap around factors from one number to the other, and the overall result of the multiplication would not change.                

    Doubling and halving 

                        Suppose one factor ends in 5, and suppose the other factor is even. In this case, we know the even factor must be divisible by 2, so we can easily remove a factor of 2 from that one (thereby “halving” it) and multiply the multiple of 5 by 2 (thereby “doubling” it), which will make that one a multiple of ten. In this process, both numbers become simpler, and the multiplication often becomes something you could easily do in your head.

       EXAMPLE

                           Consider the multiplication 15 x 16. At first glance, that looks not-fun without a calculator. Now, we will perform “doubling and halving.” Remove a factor of 2 from 16, so 16 becomes 8 — it “halves.” Give that spare factor of 2 to 15 — multiply 15 by 2 to get 30. Therefore, 15 x 16 = 30 x 8 = 240. After using the doubling-and-halving trick, the problem just becomes one-digit multiplication, with an extra zero along for the ride. In the case of 25 x 44, we can do doubling-and-halving once —- 44 becomes 22 and 25 becomes 50 —- to get 25 x 44 = 50 x 22. That’s better, but we can do doubling-and-halving again —- 22 becomes 11 and 50 becomes 100 —- so that 25 x 44 = 50 x 22 = 100 x 11 = 1100.