When a rational number is written in lowest form as p/q, what is true about p and q?
Answer and explanation
Correct answer: They are coprime
The governing concept is the lowest or simplest form of a rational number. A rational number is written as p/q with q not equal to zero, and the fraction is in lowest form when p and q have no common factor greater than 1. Equivalently, their highest common factor is 1, so p and q are coprime. Therefore option A is correct. They do not have to be both even; in fact, if both were even, the fraction could be reduced further. They also need not both equal 3, and the denominator cannot be zero because division by zero is undefined. For example, 6/15 is not in lowest form because both terms share 3, whereas 2/5 is in lowest form because 2 and 5 have HCF 1. The signs of the integers do not change this coprime condition.
Frequently asked questions
What is the correct answer to this question?
They are coprime
Why is this the correct answer?
The governing concept is the lowest or simplest form of a rational number. A rational number is written as p/q with q not equal to zero, and the fraction is in lowest form when p and q have no common factor greater than 1. Equivalently, their highest common factor is 1, so p and q are coprime. Therefore option A is correct. They do not have to be both even; in fact, if both were even, the fraction could be reduced further. They also need not both equal 3, and the denominator cannot be zero because division by zero is undefined. For example, 6/15 is not in lowest form because both terms share 3, whereas 2/5 is in lowest form because 2 and 5 have HCF 1. The signs of the integers do not change this coprime condition.
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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