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A rational number turns out to be NEGATIVE. What must be true about and ?

Class 7Rational NumbersRational Numbers
  • ABoth p and q are negative
  • BBoth p and q are positive
  • Cp is 0
  • Dp and q have opposite signs

Step-by-Step Solution

A rational is negative exactly when numerator and denominator carry OPPOSITE signs — as in and . If both are negative the two minus signs cancel and the number is POSITIVE, e.g. ; that is the trap in "both negative". And gives 0, which is neither positive nor negative.
Answer: D) p and q have opposite signs

Key idea: Rationals on the number line

Every rational number has a place on the number line. Negative rationals on the left of 0, positive on the right. Between any two rationals, you can always find another rational (in fact, infinitely many) — this is called **density**.

Example: between 1/3 and 1/2, the average (1/3 + 1/2)/2 = 5/12 sits in the middle. Between 1/3 and 5/12 there's another rational, and so on, forever.

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