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.
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Rational numbers are numbers that can be expressed as a fraction, where the numerator and the denominator are both integers and the denominator is not zero. Whole numbers are a subset of rational numbers that include all positive integers (including zero) and their negatives.
Not all rational numbers are whole numbers. A rational number can be a fraction where the numerator and denominator are integers, but the numerator is not divisible evenly by the denominator. For example, the rational number 3/2 is not a whole number because it is not an integer.
All whole numbers, on the other hand, are rational numbers. Whole numbers can be expressed as fractions where the denominator is 1. For example, the whole number 5 can be written as 5/1, which is a rational number.
In conclusion, all whole numbers are rational numbers, but not all rational numbers are whole numbers. The relationship between rational numbers and whole numbers is that whole numbers are a subset of rational numbers.
The relationship between rational numbers and whole numbers is that all whole numbers are also rational numbers, but not all rational numbers are whole numbers.
To understand this, we need to first define what rational numbers and whole numbers are.
A rational number is any number that can be expressed as a fraction, where the numerator and denominator are both integers and the denominator is not zero. For example, 2/3, -4/7, and 5 are all rational numbers.
On the other hand, whole numbers are a set of numbers that include positive integers (0, 1, 2, 3, ...) and their negatives (-1, -2, -3, ...). Whole numbers do not include fractions or decimals. For example, 0, 1, -2, and 5 are all whole numbers.
Now, let's consider whether all rational numbers are whole numbers. This is not the case because rational numbers can include fractions that are not whole numbers. For example, 2/3 is a rational number but not a whole number because it is a fraction between 0 and 1.
However, all whole numbers are rational numbers. This is because whole numbers can be expressed as fractions with a denominator of 1. For example, 5 can be written as 5/1, which is a fraction and therefore a rational number.
In summary, all whole numbers are rational numbers because they can be expressed as fractions with a denominator of 1. However, not all rational numbers are whole numbers because they can include fractions that are not whole numbers.