Please , I need help explaining why every natural number is also a rational number, but not every rational number is a natural number ?

Question

Examples to support the reasoning.

Answer 1

a rational number is any number that can be expressed in the form a/b where and b are integers and b≠0

the natural numbers are the counting numbers 1, 2, 3, 4, 5, 6, 7, 8, .....

some definitions include 0 as a natural number but most textbooks say that 0,1,2,3,4,5,6,7... make up the set of whole numbers (the natural numbers plus the number 0)

every natural number can be expressed in the form a/b

3=3/1, 5=5/1, 8=8/1, 7=35/5  for example

not every rational number is a natural number: 2/3 is less than 1, 8/3=2 2/3 which is between 2 and 3

6.125 is between 6 and 7, 9.666... is between 9 and 10

not every fraction, decimal, or mixed number is equal to a natural number; some are but you can see by the examples that some are not equal to a natural number

12/4 is a natural number, 12/4=3 which is a natural number

here's an interesting number that is a decimal but is equal to a natural number:

0.9999999999....., this repeating decimal is equal to the number 1 and it can be proved using mathematics

Answer 2

Natural number- is any whole positive number ex. 1,2,3,4,5,6,7,...100,101,.... ect

Rational number- is any positive number that can be written as a ratio or fraction ex. (1/2),(50/95), (100/5), ... ect

 

natural numbers can be written as fractions (1/1),(2/1),(3/1),... ect. Therefore every natural number is also a rational number

 

However (1/2) for example is a rational number because it is a fraction but it is not a whole number so it can not be natural becasue natural numbers are whole.