escribe 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 every whole number is also a rational number, but not every rational number is a whole number.
A rational number is defined as a number that can be expressed as the quotient (or fraction) of two integers, where the denominator is not zero. Whole numbers, on the other hand, are a subset of rational numbers that include all positive integers (including zero).
Examples:
1. Every whole number is a rational number. For instance, the whole number 5 can be expressed as the fraction 5/1, where 5 is the numerator and 1 is the denominator.
2. However, not all rational numbers are whole numbers. For instance, the fraction 3/2 is a rational number, but it is not a whole number since it is not an integer.
In conclusion, while all whole numbers are rational numbers, not all rational numbers are whole numbers.
The relationship between rational numbers and whole numbers is that all whole numbers can be considered as rational numbers, but not all rational numbers can be considered as whole numbers.
To understand this relationship, it is important to first define rational numbers and whole numbers:
1. Rational Numbers: Rational numbers are numbers that can be expressed as a ratio (or fraction) of two integers, where the denominator is not zero. They can be represented on a number line and include fractions, decimals (both terminating and repeating), and integers.
2. Whole Numbers: Whole numbers are a set of positive integers (0, 1, 2, 3, 4, ...) and include zero as well. They do not include negative numbers or fractions.
Based on these definitions, we can conclude the following:
1. Not all rational numbers are whole numbers: Rational numbers can include fractions and decimals that are not whole numbers. For example, the number 3/2 is a rational number but not a whole number because it is a fraction.
2. All whole numbers are rational numbers: Whole numbers can be expressed as fractions with a denominator of 1. For example, the whole number 4 can be written as 4/1, making it a rational number.
In summary, while all whole numbers can be considered rational numbers, not all rational numbers are whole numbers. Rational numbers include fractions and decimals that are not whole numbers.