3rd Class Mathematics Playing with Numbers Introduction

        Introduction

Numbers are useful in counting quantities that we see around us in our daily life.

The numbers that we use our country is the Hindu - Arabic numerals. Aryabhatta developed the place value of Hindu Arabic numerals and Brahmagupta introduced the symbol for zero. Hindu Arabic numerals were basically developed in India and laterally accepted by Arabians so called Hindu Arabic numerals. In this chapter we will learn about Hindu - Arabic numbers and their comparison with Roman and International number system.

        Natural Numbers

Counting numbers are known as natural numbers. There are infinite natural numbers starting from 1. Natural number is denoted by N.  

 Which one of the following numbers is not a natural number?

(a) -3

(b) 3

(c) 2

(d) 50

(e) None of these

Answer (a)

               Whole Numbers

The counting numbers including 0 are known as whole numbers. If counting numbers start from 0 then they include the set of whole numbers. Whole number is denoted by W.

           Prime Numbers

The number which has only two factors, 1 and the number itself is called prime number. The number 2 does not have the factors other than 1 therefore, 2 is a prime number. 2 is only from the group of even numbers which has only two factors, so it is called even prime number.

Look at the following table of prime numbers between 1 and 100:

Highlighted numbers are prime numbers.

              Even Numbers

The numbers those are exactly divisible by 2 are called even numbers. The numbers 2, 4, 6, 8, 10.... etc. are even numbers.

Consider the following two statements:

Statement 1: The division of two even numbers is always an even number.

Statement 2: The division of an even number by 2 always leaves 0 remainder.

Which one of the following options is correct about the above statements?

(a) Statement 1 is true and 2 is false

(b) Statement 1 is false and 2 is true

(c) Both statements 1 and 2 are false

(d) All of these

(e) None of these

Answer (b)

Explanations:

Division of two even numbers is not always an even number.

Division of an even number by 2 always leaves 0 as a remainder.

             Odd Numbers

The numbers which are not divisible by 2 are called odd numbers. Odd numbers do not come in the table of 2. The numbers 1, 3, 5, 7, 9......... etc. are odd numbers.

 How many odd numbers are there from 1 to 10?

(a) 2

(b) 3

(c) 5

(d) 9

(e) None of these

Answer (c)

             Twin Primes

Two prime numbers having a difference of 2 are called twin primes. The difference of the prime numbers 3 and 5 is 2, therefore, they are called twin primes. Twin primes. 3 and 5, 5 and 7, 11 and 13, 17 and 19, etc are.

There are four prime numbers between 1 and 10 and again four prime numbers between 11 and 20. How many prime numbers are there between 91 and 100?

(a) 1

(b) 3

(c) 5

(d) All of these

(e) None of these

Answer (a)

Explanation The numbers from 91 to 100 are 92, 93, 94, 95, 96, 97, 98, 99.

The number 97 has two factors 1 and the 97 itself. Hence, 97 is the only prime number between 91 and 100.

             Composite Numbers

The numbers which have more than two factors other than 1 and the number itself are called composite numbers. Even numbers except 2 are composite numbers.

Composite Numbers between 1 and 100

Highlighted numbers are composite numbers.

 Which one of the following numbers is an odd number?

(a) 11

(b) 27

(c) 39

(d) All of these

(e) None of these

Answer (d)

Explanations

All the given numbers are odd because numbers are not exactly divisible by 2.