"Every integer is a rational number" Is the statement true? Justify your answer.
Every integer is a rational number but a rational number need not be an integer.
We know that 1 = 1/1, 2 = 2/1, 3 = 3/1, 4 = 4/1 and so on ……. .
also, -1 = -1/1, -2 = -2/1, -3 = -3/1, -4 = -4/1 and so on …….. .
In other words, any integer a can be written as a = a/1, which is a rational number.
Thus, every integer is a rational number.
Clearly, 3/2,-5/3, etc. are rational numbers but they are not integers.
Hence, every integer is a rational number but a rational number need not be an integer.
Let us determine whether the following rational numbers are integers or not:
(i) 2/5
2/5 is not an integer. Since we cannot express 2/5 without a fractional or decimal component
(ii) 8/4
8/4 is an integer. Since if we simplify 8/4 to its lowest term we get 2/1 = 2, which is an integer.
Every integer is a rational number but a rational number need not be an integer.
We know that 1 = 1/1, 2 = 2/1, 3 = 3/1, 4 = 4/1 and so on ……. .
also, -1 = -1/1, -2 = -2/1, -3 = -3/1, -4 = -4/1 and so on …….. .
In other words, any integer a can be written as a = a/1, which is a rational number.
Thus, every integer is a rational number.
Clearly, 3/2,-5/3, etc. are rational numbers but they are not integers.
Hence, every integer is a rational number but a rational number need not be an integer.
Let us determine whether the following rational numbers are integers or not:
(i) 2/5
2/5 is not an integer. Since we cannot express 2/5 without a fractional or decimal component
(ii) 8/4
8/4 is an integer. Since if we simplify 8/4 to its lowest term we get 2/1 = 2, which is an integer.
