RS Aggarwal Solutions Class 6 Chapter-1 Number System (Ex 1A) Exercise 1.1

In this chapter, we will discuss how the students learn the number system. We will briefly discuss how a student learns to count from the time they start to learn. We will then discuss the number system in the first class and show how this subject can be taught and how it can be learned. For this chapter of our study, we will base ourselves on the syllabus given by Dr. R.C.J. Aggarwal.

Learning of Number System

At the time a child is born he/she has no understanding of numbers. The only thing that they can do is touch, feel and listen. As the child grows up he/she starts to observe the things around him. He/she watches the toys and things on the table. These toys and things are nothing but numbers and he/she gradually learns to relate them with the number 0. He/she starts by relating each toy with the number 0. For example, the toy car is zero. The ball is one, the pencil is two and the book is three. The numbers are used to relate the things. Each number is given a name of its own. The names of these numbers and their relations are what the teacher teaches. 

Learning how to Count

The student learns to count with the teacher in a positive way. The student also learns to count in a negative way. For example, if the student tries to count four by touching the number four he/she would count the number 1 by touching the number 0 and add 4 and this will give him/her 4+1=5. If the student tries to count four with the number 3 it will also count the number 1 and give 4+1=5. The negative counting is done in the same way. If the student says zero when he/she touches the number 3, it will count the number -4 and add 3 and this will give him/her -4+3=1. In the negative counting also the number -1 is used. If the teacher asks for numbers between 0 and 4 the student will have to answer by counting in a positive way. If the teacher asks for numbers between 4 and 8, the student will have to answer in a negative way. If the student starts counting in a positive way, he/she will start answering in a negative way. So the counting does not continue for all numbers but stops with some numbers. When the counting stops, the teacher will say that is enough. 

The Number 4

The number 4 for example can be counted in one of two ways: with the number zero and the number four can be counted with the numbers one and three. The number 4 is used to explain how counting is done. The student is supposed to know the four by themselves and count how to count. For example, the student will know that four is used to count and will try to use this knowledge by counting how many he/she touches and count again how many he/she touches and so on.

Contents of the Chapter

This chapter deals with concepts and basic topics related to the number system in detail. It provides a clear explanation of some important concepts related to the number system. Concepts explained in this chapter:

• Number line

• Numbers in whole numbers system

• Representation of numbers in integer system

• Representation of numbers in the fractional system

• Arithmetic operations on numbers

• Rules of operations on numbers

• Algorithm of operations on numbers

• Rules of operations on integers

• Rules of operations on fractional numbers

• Rules of operations on products and quotients

• Rational numbers in number line

Significance of Numbers

A number is a system of counting objects, and numbers are used to represent quantities. The term number is often used to refer to a collection of items with a fixed arrangement and, by extension, the arrangement itself. The arrangement, in the context of the number system, can be a linear arrangement, which represents a set of objects sequentially (e.g. 1, 2, 3), or a circular arrangement, which represents a set of objects according to a count from one of the points of the circumference. Numbers and their relationships are generally arranged from smallest to largest.

Number System and Arithmetic System Comparison

The number system is often contrasted with the arithmetic system, which operates over other kinds of numbers, in particular rational numbers. Arithmetic is the part of mathematics concerned with operations on numbers, which include addition, subtraction, multiplication, and division. Arithmetic is also referred to as algebra. While the arithmetic system (especially in the forms of arithmetic and algebra) is used to represent the numbers and operations upon the numbers in many different applications (particularly in applied mathematics and in the design of electronic and mechanical devices), the number system is the primary way that humans communicate the quantities they are speaking or writing about.