Describe the relationship between rational numbers and whole numbers. Are all rational numbers also whole numbers? Are all whole numbers also rational numbers? Give examples to support your answer
The relationship between rational numbers and whole numbers is that every whole number can be considered a rational number, but not all rational numbers can be whole numbers.
A rational number is any number that can be expressed as a fraction, where the numerator and denominator are both integers. For example, 1/2, 4/3, and -3/5 are all rational numbers.
On the other hand, a whole number is a non-negative integer, including zero. Examples of whole numbers are 0, 1, 2, 3, and so on.
Since every integer can be expressed as a fraction with a denominator of 1, we can say that every whole number is a rational number. For instance, 5 can be represented as 5/1, and 0 can be represented as 0/1.
However, not all rational numbers are whole numbers. For example, 1/2 is a rational number but not a whole number because it is not an integer. Similarly, -3/5 is a rational number but not a whole number since it is negative.
In summary, every whole number can be considered a rational number, but not every rational number can be a whole number.
The relationship between rational numbers and whole numbers is that every whole number can be expressed as a rational number, but not every rational number is a whole number.
Whole numbers, such as 0, 1, 2, 3, and so on, are integers without fractional or decimal parts. They include all positive integers (natural numbers) and zero.
On the other hand, rational numbers are numbers that can be expressed as a ratio of two integers, where the denominator is not zero. This includes fractions (such as 1/2, 3/4, and 2/5) and integers (since they can be expressed as a ratio with a denominator of 1, like 3/1 or 7/1).
All whole numbers can be expressed as rational numbers because they can be written as a fraction with a denominator of 1. For example, the whole number 5 can be expressed as the rational number 5/1.
However, not all rational numbers are whole numbers. For example, the rational number 2/3 is not a whole number because it has a fractional part. Similarly, the rational number 7.5 (which can be expressed as 15/2) is not a whole number because it has a decimal part.
To summarize, while every whole number is a rational number, not every rational number is a whole number.