Question

If $p$ and $q$ are positive integers, then $\frac{p}{q}$ is a ______ rational number and $-\frac{p}{q}$ is a ______ rational number.

• A. positive
• B. negative

Answer 1

Positive and negative rational number

Rational numbers :A rational number is defined as any number which can be represented in the form of $\frac{p}{q}$ where $q\ne 0$.

The set of rational numerals include positive, negative numbers, and zero.

Condition for positive rational numbers:

1. If both the numerator and denominator are of the same signs.
2. All are greater than 0
3. All are less than 0.
4. Examples of positive rational numbers: $\frac{12}{17},\frac{3}{9},\frac{5}{4}$

Condition for Negative rational numbers:

1. If the rational number takes the form $-\left(\frac{p}{q}\right)$, then either $p$ or $q$takes the negative value. It means that $-\left(\frac{p}{q}\right)=\frac{\left(-p\right)}{q}=\frac{p}{\left(-q\right)}$
2. If numerator and denominator are of opposite signs.
3. All are less than 0.
4. Examples of negative rational numbers: $-\frac{2}{17},\frac{9}{-11},\frac{-1}{5}$

Hence, $\frac{p}{q}$ is a positive rational number and $-\frac{p}{q}$ is a negative rational number.