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. (4 points)
The relationship between rational numbers and whole numbers is that all whole numbers are rational numbers, but not all rational numbers are whole numbers.
A rational number is defined as a number that can be expressed as the ratio of two integers, where the denominator is not zero. Whole numbers are a subset of rational numbers, where they are the non-negative integers (including zero).
For example, the whole number 5 can be expressed as the ratio 5/1, where both the numerator and the denominator are integers. This makes it a rational number.
On the other hand, not all rational numbers are whole numbers. For instance, the rational number 3/2 is not a whole number because it is not an integer. However, it is still a rational number as it can be expressed as the ratio of two integers.
To summarize, while all whole numbers are rational numbers, not all rational numbers are whole numbers.
Rational numbers and whole numbers are different classifications of numbers.
Rational numbers include all numbers that can be expressed as a fraction, where the numerator and denominator are integers (whole numbers), and the denominator is not zero. Rational numbers can be written in the form p/q, where p and q are integers, and q is not zero.
Whole numbers, on the other hand, include all positive integers (0, 1, 2, 3, ...) and zero. They do not include negative numbers or fractions.
It is incorrect to say that all rational numbers are also whole numbers. While whole numbers can be rational, not all rational numbers are whole numbers. Examples of rational numbers that are not whole numbers include 1/3, -5/2, and 2/7.
On the other hand, every whole number can also be classified as a rational number. This is because every whole number can be expressed as a fraction with a denominator of 1. For example, 3 can be written as 3/1, 5 as 5/1, and 0 as 0/1.
In summary, while all whole numbers are rational numbers, not all rational numbers are whole numbers.