Positive and negative rational numbers are part maths. A rational number is any number that can be written as $p%2Fq$ , where $p$ and $%20q%20$ are integers and $%20q%20$ is not zero. Examples are $%203%2F4$ , $%E2%88%925%2F6$ , and $7%2F2$ . If both $p$ and $q$ have the same sign, the number is positive. If they have different signs, it is negative. Positive numbers are to the right of zero, and negative numbers are to the left.

Now, these rational numbers are divided into three groups:

Positive Rational Numbers
Negative Rational Numbers
Zero Rational Numbers
Solved Examples

Also check: Properties of Rational Numbers.

Zero is neither positive or negative. Let’s learn positive and negative rational numbers with examples.

Facts:

All positive rational numbers are greater than 0.
All negative rational numbers are less than 0.

Positive Rational Number

A rational number is said to be positive if its numerator and denominator have the same sign, i.e. if its numerator and denominator both are either positive or negative integers.

For example, ⁹⁄₁₃, ²⁄₃, ⁻¹⁄_−8, etc. are positive rational numbers.

Negative Rational Number

A rational number is said to be negative if its numerator and denominator have opposite signs i.e. if the numerator is a positive integer and denominator is a negative integer or if the numerator is a negative integer and the denominator is a positive integer.

For example, ⁻⁶⁄₁₁, ⁴⁄₋₇, and ⁻¹⁄₅ are negative rational numbers.

Note: Zero is a rational number which is neither positive or negative.

Know more about related topics:

Zero Rational Numbers

Zero is a rational number that is neither positive nor negative. It can be written as ⁰⁄₁, ⁰⁄₂, ⁰⁄₃, etc. No matter what positive or negative integer is in the denominator, if the numerator is 0, the value of the rational number is always 0. Therefore, zero does not fall in the category of either positive or negative rational numbers.

Example: Is ⁰⁄₅ a positive or negative rational number?

Solved Examples

Example 1: Is ⁷⁄₉ a positive or negative rational number?

Solution: The numerator is 7 (positive), and the denominator is 9 (positive). Since both the numerator and denominator have the same sign (both positive),

⁷⁄₉ is a positive rational number.

Example 2: Is ⁻⁵⁄₋₁₁ a positive or negative rational number?

Solution: The numerator is −5 (negative), and the denominator is −11 (negative). Since both the numerator and denominator have the same sign (both negative),

⁻⁵⁄₋₁₁ is a positive rational number.

Example 3: Is ³⁄₋₈ a positive or negative rational number?

Solution: The numerator is 3 (positive) and the denominator is −8 (negative). Since the numerator and denominator have opposite signs,

³⁄₋₈ is a negative rational number.

Example 4: Is ⁻⁴⁄₁₃ a positive or negative rational number?

Solution: The numerator is −4 (negative), and the denominator is 13 (positive). Since the numerator and denominator have opposite signs,

⁻⁴⁄₁₃ is a negative rational number.

Frequently Asked Questions on Positive and Negative Rational Numbers

1. Is −3/−5 a positive or negative rational number?

−3/−5 is a positive rational number. Since both the numerator (−3) and the denominator (−5) are negative, they have the same sign. We can multiply both by −1 to get ³⁄₅, which is clearly positive. So, −3/−5 = ³⁄₅, a positive rational number.

2. Are all integers rational numbers?

Yes, all integers are rational numbers. Any integer ‘n’ can be written in the form ⁿ⁄₁, where the denominator is 1 (not zero). For example, −7 = ⁻⁷⁄₁, 4 = ⁴⁄₁. Since they can be expressed in the form ^p⁄_q where q ≠ 0, all integers are rational numbers.

3. What is the product of two negative rational numbers?

The product of two negative rational numbers is always a positive rational number. This is because the product of two negative signs gives a positive sign. For example, (⁻²⁄₃) × (⁻⁴⁄₅) = ⁸⁄₁₅, which is positive.

4. Is 1/−7 a positive or negative rational number?

1/−7 is a negative rational number. The numerator (1) is positive and the denominator (−7) is negative. Since they have opposite signs, the rational number is negative. It can also be written as ⁻¹⁄₇.

5. Are all whole numbers positive rational numbers?

No, not all whole numbers are positive rational numbers. Whole numbers include 0, 1, 2, 3, 4, … and so on. Among these, 0 is neither positive nor negative. Only the natural numbers (1, 2, 3, …), which are whole numbers except 0, are positive rational numbers. Therefore, all whole numbers except 0 are positive rational numbers.

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Positive and Negative Rational Numbers