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 every rational number can be considered a whole number.
A rational number is any number that can be expressed as a fraction or ratio of two integers, where the denominator is not zero. Whole numbers, on the other hand, are the set of numbers that includes all positive integers (1, 2, 3, ...), zero, and their negatives (-1, -2, -3, ...).
All whole numbers can be expressed as fractions where the denominator is 1. For example, 3 can be written as 3/1, -5 as -5/1, and 0 as 0/1. Since whole numbers can be expressed as fractions with a non-zero denominator, they are considered rational numbers.
However, not all rational numbers can be whole numbers. For example, 1/2 is a rational number since it can be expressed as a fraction of two integers. But it is not a whole number since it is not an integer.
In conclusion, all whole numbers are considered rational numbers, but not all rational numbers are whole numbers.
The relationship between rational numbers and whole numbers can be described as follows:
1. Are all rational numbers also whole numbers? No, not all rational numbers are whole numbers. Rational numbers are numbers that can be expressed as the ratio of two integers, where the denominator is not zero. Whole numbers, on the other hand, are non-negative integers (including zero). Therefore, any rational number that is not an integer (e.g., fractions) is not a whole number. For example, the rational number 3/4 is not a whole number.
2. Are all whole numbers also rational numbers? Yes, all whole numbers are also rational numbers. It is because whole numbers can be expressed as the ratio of an integer and the integer 1. For example, the whole number 5 can be expressed as the rational number 5/1.
In summary, all whole numbers are rational numbers, but not all rational numbers are whole numbers.