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Home » Articles » LESSON NOTES (Mathematics) » Lower Secondary


Natural And Whole Numbers NWN001ARTC

Natural And Whole Numbers

When we count numbers from one (1) to infinity i.e. 1, 2, 3, 4, 5…..  In mathematics when you put dots at the end it indicates that the numbers continue with no end. Ok such numbers are called natural numbers. In definition natural numbers are numbers counted from 1, e.g. 1, 2, 3, 4, 5, 6, 7, 8, 9 …… These numbers are sometimes known as counting numbers and they are represented by N.

 

(i) Natural numbers on the number line   

 

There is another group of numbers which start from 0, e.g. 0, 1, 2, 3, 4, 5, 6, 7, 8 ……. These numbers are called whole numbers.

Whole numbers are the numbers which start from 0, e.g. 0, 1, 2, 3, 4, 5, 6, 7, 8 …….  And they are represented by W.

 

(i) Whole numbers on the number line   

Note:

All natural numbers are whole numbers but not all whole numbers are natural numbers.

Arrows in both number lines indicate that numbers continue with no end.

These are not only group of numbers in mathematics, others will be discussed later.

 

Even, odd and Prime numbers

Even number:

Even number is any integer which is exactly divisible by 2, e.g. 2, 4, 6, 8, 10, 18, 100, 150 etc.

 

Odd number:

Odd number is any integer which is not exactly divisible by 2, e.g. 1, 3, 5, 7, 11. 153, 37 etc.

Odd number is an opposite of even number, so if any number isn’t divisible by 2 that number is exactly odd number.

 

Prime number:

Prime number is any number greater than one (1)  that is divisible only by one and itself e.g. 11, 13, 17, 43, 113 etc. to find a prime number you should remove all even numbers and numbers containing 5 in the place value of ones such as 25, 115, 45, 305, 245 etc. then after removing those, you should test the remaining to make sure that they are not divisible by both 3 and 7. Note that if it is not divisible by 3 but divisible by 7 that number is not prime number because the principle here is that should not be divisible by both and not only one. Example number 57, this number is not divisible by 7 but divisible by 3 so this is not a prime number.

 

Note:

The first four numbers before ten are prime numbers even if they are divisible by 3 and 7 those numbers are 2, 3, 5 and 7 so in listing prime numbers from the beginning those numbers should be included.

 

Examples:

 

(i) List all even numbers between 10 and 20.

Solution:

Step one, list all numbers between 10 and 20 but exclude 10 and 20, this becomes

11, 12, 13, 14, 15, 16, 17, 18 and 19

Step two, to get even numbers you should write those exactly divisible by 2, these are:-

12, 14, 16 and 18.

Therefore the answer is 12, 14, 16 and 18.

 

(ii) List all odd numbers between 10 and 20.

Solution:

Step one, list all numbers between 10 and 20 but exclude 10 and 20, this becomes

11, 12, 13, 14, 15, 16, 17, 18 and 19

Step two, to get odd numbers you should write those exactly not divisible by 2, these are:-

11, 13, 15, 17 and 19.

Therefore the answer is 11, 13, 15, 17 and 19.

 

(iii) What are the prime numbers between 25 and 34?

Solution:

Step one, list all numbers between 25 and 34 but exclude 25 and 34, this becomes

26, 27, 28, 29, 31, 32, 33.

 

Step two, remove all even numbers and that with 5 in ones position, and this becomes:-

27, 29, 31, 33.

 

Step three, the remaining should be tested if each number is divisible by 3 or 7, and we need the number which is not divisible by any of 3 and 7. Now let’s check it out:-

 

27 is divisible by 3                            (this is not prime number)

29 is not divisible by any of 3 and 7       (this is prime number)

31 is not divisible by any of 3 and 7       (this is prime number)

33 is divisible by 3                           (this is not prime number)

Therefore we only got two numbers which are not divisible by both 3 and 7, those numbers are 29 and 31

Therefore the answer is 29 and 31.

(iv) Which number is even and prime?

Solution:

The number which is even and prime is 2

 

QUESTIONS

(1) What do you understand by:

            i.  Natural and whole numbers

ii.  Even numbers

iii. Odd numbers

iv. Prime numbers

(2) Write number having 5 in hundreds position, 4 in thousands position, 0 in ones position and 4 in tens position.

(3) List all odd numbers between 60 and 70

(4) What are prime numbers between 1 and 20?

(5) Write the sum of all even numbers between 100 and 110.

(6)  List all odd natural numbers up to 10 on the number line.

(7)  Show prime numbers between 30 and 40 on the number line.           

(8) State whether the sum of the following is an even or odd

       i. When adding any two odd numbers

      ii. When adding any two even numbers

     iii. When adding any odd number and any even number.

(9) Is the product of any two even numbers even or odd?

(10)  Write down the first six prime numbers.

 

© Yahyou M. (Math's tutor)

 

 



Source: http://whole number, natural numbers, prime, even, odd
Category: Lower Secondary | Added by: Admin (27/Aug/2013) | Author: Yahya Mohamed E W
Views: 1113 | Rating: 0.0/0
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