If someone would ask you to solve math queries like:
- 150 x 36 ?
- 125 x 84 ?
- 35 x 12 ?
For answering these math questions, most of us would immediately search for a piece of pen & paper or a calculator to obtain the results. However, if you are sitting for some major competitive exams, then you are not given the option to carry a calculator with you. Moreover, you do not have ample time to solve each question of this complex multiplication type as it could be time consuming and you might miss out on other questions.
Worried about how to solve such complex multiplications instantly? Here is a simple mathematics trick that would save you a great amount of time and efforts to solve such problems.
Multiplication by Doubling and Halving Technique
Every positive integer has its unique prime factorization. This implies that there is always a unique way of expressing each whole number as the product of prime factors. Therefore, whenever there is a need to multiply two positive integers, this can be thought of as the product of the prime factors of one time the product of the prime factors of the other. This is the two big collections of the factors being multiplied together. Moreover, the associative law & the commutative law signify that multiplication can be done in any order. Even when the factor from number is swapped to the other, the result of multiplication would not alter.
Doubling and Halving
Suppose there is one factor that ends in 5, and the other factor is even. In this case, we understand that the even factor must be divisible by 2. Therefore, we can easily remove a factor of 2 from the same. This implies halving. Then, we can multiply the multiple of 5 by 2. This is doubling. This will make it a multiple of 10. In the process of doubling & halving for complex multiplication, both the positive integers are simplified and thus, multiplication can be done with much ease without any aid.
Consider the multiplication of 15 x 16. We proceed by removing a factor of 2 from 16 (even number). Therefore, 16 becomes 8 (halving). We would give that spare factor of 2 to 15 (odd number) and then multiply them, resulting in 30 (doubling). Therefore, our result of the multiplication of 15 x 16 = 30 x 8 = 240.
Similarly for 25 x 44: 44 becomes 22 upon halving and 25 becomes 50 upon doubling. To obtain the result of 25 x 44, we get 22 x 50. This calculation can be further halved and doubled to simplify the result. Thus, it becomes 11 x 100 =1100.
Once the trick of doubling & halving is used, the complex multiplication problem becomes a one-digit multiplication process, with just an extra zero at the end. Thus, you can boost your mathematical knowledge by knowing these simple mathematical tricks. Become a pro in mathematics by learning these simple tricks!