Exam-style question
Try this first
A student says, "An integer cannot be a rational number because it is not normally written as a fraction." Explain why this statement is incorrect, and include the meaning of ℚ in your answer.
Model answer
What a good answer should say
- The statement is incorrect because a number does not have to be displayed as a fraction to be rational.
- An integer can be represented as a fraction with 1 as the denominator.
- For example, 7 is equal to 7/1.
- Therefore, integers are included in ℚ, the set of rational numbers.
Explanation
Why this works
The key idea is that rationality depends on whether a number can be written as a ratio of integers, not on whether it is usually displayed in fraction form. The response should also identify ℚ as the set of rational numbers.
Common mistake
No common mistake is linked to this question yet.