The Number System Unit Test
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Question
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)
Math Short Answer Rubric (4 points)
Points Awarded Criteria
4
The answer is clear and correct.
The answer shows that the student used problem-solving skills and reasoning.
All work is shown or explained.
3
The answer is mostly correct. The student made small errors while solving.
The answer shows that the student used some problem-solving skills and reasoning.
Most work is shown or explained.
2
The answer is partially correct. The student made errors while solving.
The answer shows that the student used some problem-solving skills or reasoning.
Some work is shown or explained.
1
The answer is incorrect. The student made errors while solving.
The answer shows little problem-solving skills or reasoning.
Little or no work is shown.
0 The question is not answered.
Rational numbers and whole numbers are related, but they are not the same. All whole numbers are rational numbers because they can be written as a fraction with a denominator of 1. For example, 4 can be written as 4/1, which is a fraction and therefore a rational number.
However, not all rational numbers are whole numbers. Rational numbers include fractions and decimals that can be written as a fraction. For example, 1/2, 3/4, and 0.25 are all rational numbers but they are not whole numbers.
In summary, all whole numbers are rational numbers, but not all rational numbers are whole numbers.
Rational numbers and whole numbers are both types of real numbers.
A rational number is any number that can be expressed as a fraction of two integers. This means that it can be written in the form a/b, where a and b are integers and b is not equal to 0. Whole numbers are a subset of rational numbers, and they are the numbers 0, 1, 2, 3, and so on, including all positive integers.
Not all rational numbers are whole numbers. For example, the number 1/2 is a rational number because it can be written as the fraction 1/2. However, it is not a whole number because it is not an integer. Similarly, the number -3/4 is a rational number, but not a whole number.
On the other hand, all whole numbers can be considered rational numbers. For example, the number 5 can be written as the fraction 5/1, and it satisfies the definition of a rational number.
In summary, not all rational numbers are whole numbers, but all whole numbers can be considered rational numbers.
To describe the relationship between rational numbers and whole numbers, we first need to understand what each of these terms means.
Whole numbers are a set of numbers that include all the natural numbers (also known as counting numbers) from 0 onwards. Whole numbers do not include any fractions or decimals. Examples of whole numbers include 0, 1, 2, 3, and so on.
Rational numbers, on the other hand, are numbers that can be expressed as a ratio or fraction of two integers. In other words, rational numbers can be written as a fraction in the form a/b, where a and b are integers, and b is not zero. Rational numbers include whole numbers as a subset since any whole number can be written as a fraction with a denominator of 1. For example, 3 can be expressed as 3/1, which is a rational number.
Now, to answer the question:
No, not all rational numbers are whole numbers. Rational numbers include fractions and decimals that are not whole numbers. For example, 1/2, 3/4, and 0.25 are rational numbers, but none of them are whole numbers.
Yes, all whole numbers are also rational numbers. As mentioned earlier, any whole number can be expressed as a fraction with a denominator of 1. For example, 5 can be expressed as 5/1, which is a rational number.
To support this answer, you can provide additional examples of rational numbers that are not whole numbers, such as -1/3 or 0.75. And you can show that any whole number can be written as a fraction with a denominator of 1.
Remember to provide clear and correct explanations, show your reasoning, and include relevant examples to support your answer. This will help you score higher on the Math Short Answer Rubric.