Every Integer is a Rational Number but a Rational Number need not be an Integer. Check out the statements, examples supporting whether or not All Rational Numbers are Integers.
We know 1 = 1/1, 2 = 2/1, 3 = 3/1 ……..
Also, -1 = -1/1, -2 = -2/1, -3 = -3/1 ……..
You can also express integer a in the form of a/1 which is also a Rational Number.
Hence, every integer is clearly a Rational Number.
Clearly, 5/2,-4/3, 3/7, etc. are all Rational Numbers but not Integers.
Therefore, every integer is a Rational Number but a Rational Number need not be an Integer. Check out the following sections and get a complete idea of the statement.
Determine whether the following Rational Numbers are Integers or not
(i) 3/5
3/5 is not an Integer and we can’t express it other than a fraction form or decimal value.
(ii) 6/3
6/3 is an integer. On simplifying 6/3 to its lowest form we get 6/3 = 2/1 which is an integer.
(iii) -3/-3
-3/-3 is an integer. On reducing -3/-3 to its reduced form we get -1/-1 =1 which is an integer.
(iv) -13/2
-13/2 is not an integer and we can’t express it other than a fraction form or decimal value.
(v) -36/9
-36/9 is an integer as we get the reduced form -36/9=-4 which is an integer.
(vi) 47/-9
47/-9 is not an integer and we can’t express it other than fraction form or decimal value.
(vii) -70/-20
-70/-20 is not an integer and we can’t express it other than fraction form or decimal value.
(viii) 1000/-10
1000/-10 is an integer as we get 1000/-10 = -100 on reducing to its lowest form and -100 is an integer.
From the above instances, we can conclude that Not Every Rational Number is an Integer.
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