If p/q is in lowest form, what is true about p and q?
Answer and explanation
Correct answer: They have no common factor except 1
A fraction p/q is in lowest form when the numerator p and denominator q have no common factor greater than 1. Equivalently, their greatest common divisor is 1, so p and q are coprime; q must also be non-zero. For example, 6/8 is not in lowest form because both numbers are divisible by 2, while 3/4 is in lowest form. This condition is crucial in irrationality proofs: if later reasoning forces both p and q to be divisible by 2 or by 3, a contradiction is obtained. Thus option A is correct. The numbers need not both be even, divisible by 3, or equal. Those properties would actually show that the fraction can be reduced further in some cases.
Frequently asked questions
What is the correct answer to this question?
They have no common factor except 1
Why is this the correct answer?
A fraction p/q is in lowest form when the numerator p and denominator q have no common factor greater than 1. Equivalently, their greatest common divisor is 1, so p and q are coprime; q must also be non-zero. For example, 6/8 is not in lowest form because both numbers are divisible by 2, while 3/4 is in lowest form. This condition is crucial in irrationality proofs: if later reasoning forces both p and q to be divisible by 2 or by 3, a contradiction is obtained. Thus option A is correct. The numbers need not both be even, divisible by 3, or equal. Those properties would actually show that the fraction can be reduced further in some cases.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Proof of irrationality of square root 2 and square root 3.
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