Yes, all integers are indeed rational numbers. To understand why, let’s break down the definitions.
A rational number is defined as any number that can be expressed in the form of a fraction where both the numerator and the denominator are integers, and the denominator is not zero. In simpler terms, a rational number can be written as p/q, where p and q are integers, and q ≠ 0.
Now, consider an integer, say 5. We can express this integer as a fraction by assuming it to be 5/1. In this case, the number 5 serves as the numerator, and 1 is the denominator, which is clearly a non-zero integer. Hence, we can represent 5 as a rational number.
Similarly, if we take negative integers like -3, we can also write it as -3/1, which fits the definition of a rational number. This pattern continues for all integers, whether they are positive, negative, or zero.
In conclusion, since every integer can be expressed as a fraction with a denominator of 1, it follows that all integers are also rational numbers. Thus, the statement is justified.