The relationship between rational numbers and integers is that integers are a subset of rational numbers. In other words, every integer is a rational number, but not every rational number is an integer.
To be more specific, rational numbers can be expressed as the quotient of two integers, where the denominator is not zero. This means that rational numbers can include both integers and fractions.
For example, let's consider the integer 5. It can be represented as the rational number 5/1, which is the ratio of 5 to 1. In this case, the denominator is 1, making it a rational number.
On the other hand, not all rational numbers are integers. For instance, let's take the rational number 3/4. It is the ratio of 3 to 4 and it is not an integer because the denominator is not 1.
Similarly, not all rational numbers are natural numbers. Natural numbers, also known as counting numbers, are positive integers that start from 1 and continue indefinitely. Therefore, fractions or negative numbers cannot be classified as natural numbers.
For example, the rational number -2/3 is a fraction and it is not a natural number. It falls under both rational numbers (as it can be expressed as the quotient of two integers) and integers (as it is a negative value), but it is not a natural number.
In conclusion, while all integers can be classified as rational numbers, not all rational numbers are integers or natural numbers.
Describe the relationship between rational numbers and integers. Are all rational numbers also integers? Are all rational numbers also natural numbers? Give examples to support your answers.
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