NUMBER SYSTEM

WHAT IS THE NEED FOR THE SYSTEM IN NUMBER SYSTEM?

Welcome to my blog and thanks for your time today.

Happy to inform everybody that I have been promoted to the middle grade. My math book has many chapters - Number System, Fractions, Decimals, Integers and so on. I am going to share some of the topics that I learnt in my MATH class. 

My teacher started explaining about one of the concepts:

What is the need for the system in Number System?  She started with this question and then continued:

Numbers 0 to 9 followed by 10 , 11 , ------- Why all this? 

We can write 1 as 01, 2 as 02, 9 as 09. The ones place has got all the numbers right from 0 till 9. Let us stop at 09. Now move towards getting the next number in the list. 

After 9, we come back to 0 in the ones place. But the 0 in 09 is moved to the next number 1. Now we get the next number as 10. Now 1 is fixed at the leftmost place and 0 moves to 1 thereby giving us the next number 11. This goes on till we reach 19. 

00 01 02 03 04 05 06 07 08 09

                                             10 11 12 13 14 15 16 17 18 19

                                                                                          20 21 ---- 29

                                                                                                          30

We see that a particular system is followed here and there is no insertion or deletion of any value. It is exactly in the same sequence 0 to 9 the only change being the place where it is located.  Yes that is the Place Value Chart. The number 10 is considered to be the base number. 

When the above list of numbers reaches 99, once again we move towards a higher value the 9's becoming 0's and 1 taking the leftmost place as usual. Yes we have got 100. 

      99

    100

We move towards the left not only to get higher values but also to avoid repetition and confusion. Take for example 09. If by chance we try to move towards the right following a particular system where will we place 1 and 0? 

The teacher explained further: So there is logic behind every Math concept. Now we will be able to understand the place value chart fully. This will also make us realize the need for the system that is present in the Number System. 

The digits, long form, short form, number names to distinguish between the numbers and place values and so many other mathematical concepts are all based on the number system.  There is a link between addition and multiplication the same way between subtraction and division. This in turn creates a relation between multiples and factors. The MATH class was over with this.

After listening to all this, I understood why we often hear that the list of natural numbers is infinite or countless. 

On an other day, my teacher taught about FRACTIONS.  The class started like this:

Normally we say that Fraction is a part of a whole. This is how we define fractions. Some of the types of fractions are proper, improper, mixed etc. Proper fraction goes well with the definition of fraction itself and its value is always less than 1.  Improper fraction has a value more than 1. Mixed fraction has a whole as well as a part.

My teacher did some sums and asked us whether we understood the concept. The whole class shouted YES mam YES mam.

After we finished doing the above sums, the teacher gave one more sum and asked us to do it.

I hurriedly finished doing the sum 3/5 +2/7 = 5/12 and asked my teacher whether it was right? I was confident that I did the numerator right, but since in the previous sums, the denominator was not added, I had a doubt whether 12 was right or either 5 or 7 was to be written. 

My teacher explained: The denominators have to be equal so that you can add the numerators directly. That is,  the fractions have to be like fractions. Here the denominators are different which means the given fractions are unlike fractions.  Unlike fractions are parts of different wholes. So, you cannot add them directly, instead you have to take least common multiple to make the denominators equal. While doing so, you have to see to it that the numerator is also multiplied with the same number with which the denominator is multiplied so that the original value is retained. 

She then continued, why do we need to do this? Let me make it more simpler. Go to a vegetable shop. How are the vegetables displayed? There are separate racks for each and every vegetable. How about a grocery shop? The varieties of rice and pulses are kept in separate sacks. 

If everything is mixed together, we will not be able to utilize it properly. What it means?  It means we can combine things only if they are of the same kind. The concepts we learn in MATH are all connected with the things we do in our daily life. The only thing we need to know and understand is, how and in what way it is connected.

Relating this to fractions, first of all, we make the denominators equal so that they become parts of the same wholes and then proceed further with the addition or subtraction of fractions whatever is required in the sum given. 

This explanation gave me a clear understanding about fractions and I started doing the same sum once again by taking LCM to make the denominators equal.

My teacher appreciated me for doing the sum right. So now, I have understood the concept of fractions, the method to be used as well as its importance in our daily life.

Very soon my teacher will start a new chapter. As usual give  me some time so that I will come up with the new chapter which my teacher takes and share some of the concepts and explanations I get to learn.

THANKS TO ONE AND ALL FOR YOUR VALUABLE TIME SPENT ON READING THIS BLOG OF MINE.