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.
Whole numbers include all positive integers (1, 2, 3, ...) and zero (0). These numbers can be expressed as fractions with a denominator of 1. For example, 5 can be written as 5/1, which is a rational number.
However, not all rational numbers are whole numbers. Rational numbers include any number that can be written as a fraction, where the numerator and denominator are both integers. This includes fractions, decimals, and whole numbers. For example, 1/2 and 3/4 are rational numbers that are not whole numbers.
To summarize, all whole numbers are rational numbers, but not all rational numbers are whole numbers.
Give examples to support your answer.
The relationship between rational numbers and whole numbers can be described as follows:
1. All whole numbers are rational numbers: Every whole number can be expressed as a fraction with a denominator of 1. For example, the whole number 5 can be written as 5/1, which is a fraction where both the numerator and denominator are integers. Therefore, all whole numbers are rational numbers.
2. Not all rational numbers are whole numbers: Rational numbers include all numbers that can be expressed as a fraction, where both the numerator and the denominator are integers. Whole numbers, on the other hand, only include non-negative integers (0, 1, 2, 3, ...). Therefore, rational numbers can include fractions and decimals that are not whole numbers. For example, the rational number 1/2 is not a whole number.
To summarize, while all whole numbers are rational numbers, not all rational numbers are whole numbers.
The relationship between rational numbers and whole numbers is that every whole number is a rational number, but not every rational number is a whole number.
Whole numbers are the set of numbers that include all positive integers from zero onwards. They do not include fractions or decimals. Examples of whole numbers are 0, 1, 2, 3, and so on.
Rational numbers, on the other hand, are numbers that can be expressed as a ratio of two integers, where the numerator and denominator are both integers and the denominator is not zero. This means that rational numbers include both whole numbers and fractions. Examples of rational numbers are 1/2, 3/4, -2/7, and so on.
To understand why every whole number is a rational number, let's take an example. Consider the whole number 5. It can be represented as the fraction 5/1. Since both the numerator (5) and the denominator (1) are integers, 5 is a rational number.
However, not every rational number is a whole number. Let's consider the example of the rational number 3/2. It is not a whole number because it represents a fraction between two whole numbers. The numerator (3) and the denominator (2) are both integers, but it is not a whole number.
In conclusion, while all whole numbers are also rational numbers, not all rational numbers are whole numbers. Whole numbers include only positive integers and zero, whereas rational numbers encompass fractions and decimals as well.