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p/q is a rational number, so p and q must be
- a)Any two integers
- b)One of them positive and the other negative
- c)Both natural numbers
- d)Both integers but q must be non zero
Correct answer is option 'D'. Can you explain this answer?
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p/q is a rational number, so p and q must bea)Any two integersb)One of...
A rational number is a number that is in the form of p/q, where p and q are integers, and q is not equal to 0
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p/q is a rational number, so p and q must bea)Any two integersb)One of...
**Explanation:**
A rational number is a number that can be expressed as a fraction, where both the numerator (p) and the denominator (q) are integers and q is not zero.
Let's analyze each option given:
**a) Any two integers:**
If p and q are any two integers, it does not guarantee that the fraction p/q will be a rational number. For example, if p = 3 and q = √2, then p/q is not a rational number. So, this option is not correct.
**b) One of them positive and the other negative:**
If one of p or q is positive and the other is negative, then the fraction p/q can be a rational number. For example, if p = -4 and q = 2, then p/q is -2, which is a rational number. So, this option is partially correct.
**c) Both natural numbers:**
If both p and q are natural numbers, then the fraction p/q can be a rational number. For example, if p = 3 and q = 2, then p/q is 3/2, which is a rational number. So, this option is partially correct.
**d) Both integers but q must be non-zero:**
If both p and q are integers and q is not zero, then the fraction p/q will always be a rational number. This is because any integer can be expressed as a fraction with a denominator of 1. For example, if p = 3 and q = -2, then p/q is -3/2, which is a rational number. So, this option is correct.
Therefore, option 'D' is the correct answer because it ensures that p and q are both integers and q is not zero, which guarantees that the fraction p/q will always be a rational number.
A rational number is a number that can be expressed as a fraction, where both the numerator (p) and the denominator (q) are integers and q is not zero.
Let's analyze each option given:
**a) Any two integers:**
If p and q are any two integers, it does not guarantee that the fraction p/q will be a rational number. For example, if p = 3 and q = √2, then p/q is not a rational number. So, this option is not correct.
**b) One of them positive and the other negative:**
If one of p or q is positive and the other is negative, then the fraction p/q can be a rational number. For example, if p = -4 and q = 2, then p/q is -2, which is a rational number. So, this option is partially correct.
**c) Both natural numbers:**
If both p and q are natural numbers, then the fraction p/q can be a rational number. For example, if p = 3 and q = 2, then p/q is 3/2, which is a rational number. So, this option is partially correct.
**d) Both integers but q must be non-zero:**
If both p and q are integers and q is not zero, then the fraction p/q will always be a rational number. This is because any integer can be expressed as a fraction with a denominator of 1. For example, if p = 3 and q = -2, then p/q is -3/2, which is a rational number. So, this option is correct.
Therefore, option 'D' is the correct answer because it ensures that p and q are both integers and q is not zero, which guarantees that the fraction p/q will always be a rational number.
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p/q is a rational number, so p and q must bea)Any two integersb)One of...
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p/q is a rational number, so p and q must bea)Any two integersb)One of them positive and the other negativec)Both natural numbersd)Both integers but q must be non zeroCorrect answer is option 'D'. Can you explain this answer?
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