30 May 2016

Multiplication Concept: Distributive Property of Multiplication

Multiplication is a very important and useful concept if you understand it correctly. It helps in large calculations. Through this article, I will try my best to give an insight of the multiplication concept and its importance in calculations.

Let's get the basic idea about the multiplication.

Example.  Can you do this 8 + 8 + 8 + 8 + 8 + 8 + 8

You can go by the usual method i.e. 8 plus 8 plus 8 plus 8 plus 8 plus 8 plus 8 the answer you will get 56. Of course after adding these numbers one can say 56 is the answer. Here the answer is not important. The important thing is how much time we have taken to calculate it. 

Multiplication Concept & Distributive Property of Multiplication
Photo Credits: ngmnexpo.com
Now is there any technique by which we can reduce the time of calculation. The answer is Multiplication. But, before using that we should understand the meaning of multiplication. 

Multiplication Concept 

When we have to add up the SAME QUANTITY many a times, we multiply the GIVEN NUMBER  by the NUMBER OF TIMES it appears repeatedly. 

So in the given question 8 is the SAME QUANTITY and it want us to add it 7 TIMES repeatedly. So we will multiply 8 with 7 and that is equals 56, and I think this is way more easier and faster than the usual method.

So, as you can see you just have to learn the table of 8 for this calculation and things become easier and fast.

THE ABOVE METHOD OF MULTIPLICATION WILL WORK IF AND IF YOU HAVE LEARNED THE TABLES UP TO 20 AT LEAST.

Again, this is just to refresh your mind what actually a multiplication is and why it is used in place repeated addition of numbers and why you should have strong grip over the Number Tables.

Now the question is, Is it enough to learn the tables. What about big numbers and their multiplication. For example: 8375 X 274 or 235 X 63 

Multiplication of Large Numbers

Firstly, you should have clarity in your mind that you will use multiplication and other basic operations of Maths like addition, subtraction and division of numbers in between the steps of questions.

Of course you are not giving any 6th standard exam in which you will be asked question like this but you can have this kind of situation in between the process of questions.

For example you stuck in a question in which you are required to multiply the numbers given above only then your answer will come out. What you are going to do? You are not going to multiply the numbers in a usual fashion (speed is factor).

There are many short-cut methods given in the books and also on the websites but in my opinion they are useless because your brain can remember the things which happen to it repeatedly. Short-cuts given in multiplication chapters only become useful when the question comes as it is given the book otherwise it is useless.

And also you don't need to remember short-cuts for everything. Just remember the short-cut if any particular calculation/question or situation repeats more often and becomes important.

So, the ultimate question is what to do when you stuck in a question or step of question involving large multiplication calculation.

THE ANSWER IS DISTRIBUTIVE PROPERTY

I don't know you have heard about it or not, but it starts with class 6th maths, anyhow, that's not important. So how to use it. I will take the above two examples.

8375 X 274

8375 X (200 + 70 + 4) ------ Just split one of the numbers like this.

(8375 X 200) + (8375 X 70) + (8375 X 4)---It looks lengthy but it is not.

1675000 + 586250 + 33500

2294750

Although, it looks lengthy but it is 100% efficient and you don't have to learn condition for it. For example short-cuts given in the books are like like this:
  1. Multiplication by the number ending 9.
  2. Multiplication by the number ending 5.
  3. Multiplication of the numbers whose sum is 10.
  4. Multiplication of the numbers whose difference is 10.
  5. And much more crap. 
How somebody can remember these types of short-cuts which are useful when they situation posses the condition given by them. Why not use a short-cut or property which is universal in nature.

And I can assure you, for small calculations you don't even need paper and pencil. This method is so powerful that after some practice you will be able to do these calculation in your mind. Yeah, for some exceptional cases like the above you will require paper and pen.

For closing of this article let me solve the other one also.

235 X 63
235 X (60 + 3)
14100 + 705
14805

GOOD LUCK & SEE YOU IN THE COMMENTS

Multiplication Series:

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