 # Positive and Negative Rational Numbers

Positive and Negative Rational Numbers, in Mathematics, are classified under the concept of rational numbers for Class 7 students. A rational number is a number that can be expressed in the form of numerator and denominator, such as P/Q, where P and Q are both integers and Q is not equal to zero. For example, ¾, 8/9, etc., are rational numbers.

Now, these rational numbers are again divided into three groups such as:

1. Positive rational numbers
2. Zero
3. Negative rational numbers

Also, check: Properties of Rational Numbers

Zero is a neutral value, it is neither a negative nor positive rational number. Let us learn here what are positive and negative rational numbers, along with examples.

 Facts: All the positive rational numbers are greater than zero All the negative rational numbers are smaller than zero

## What are Positive rational numbers?

A rational number is said to be positive if its numerator and denominator are both positive. Or we say, if the numerator and denominator of a rational number are both positive integers or both are negative integers, then it is called a positive rational number.

Examples of positive rational numbers are:

 3/8 5/7 2/9 (-3/-7) (-1/-5)

In the above examples, we can see, both the numerators and denominators of the rational numbers are positive integers or both are negative integers.

Even if the numerator and denominator of the rational numbers are negative, then we can multiply both top and bottom by -1. Since, the product of two negative signs is equal to a positive sign, hence, again we get positive integers in both the numerator and denominator.

## What are Negative rational numbers?

A rational number is said to be negative, if any of its numerator or denominator is negative.

So, if either the numerator or denominator of a rational number is a negative integer, then it is a negative rational number.

Examples of negative rational numbers are:

 -3/8 5/(-7) (-2)/9 (-3)/7 1/(-5)

In the above examples, we can see, either the numerator or denominator of the rational numbers is a negative integer.

If the denominator is having a negative integer, then we can multiply the numerator and denominator both by -1, to bring the minus sign at the top. Let us see an example.

Example: Is 8/-3 a negative rational number?

We can multiply and divide 8/-3 by (-1), to get;

8/(-3) x (-1)/(-1) = -8/3

Thus, 8/-3 is a negative rational number.

## Solved Examples

Q.1: Is 6 a positive rational number?

Solution: 6 can be expressed in the form of ratio, such that,

6 = 6/1

Where both numerator and denominator, i.e. 6 and 1 are positive integers.

Therefore, 6 is a positive rational number.

Q.2: List any five positive rational numbers.

Solution: The positive rational numbers are: ⅔, ⅗, -2/-5, 9/5, 5/7.

Q.3: Is -3/-5 a positive or negative rational number?

Solution: Given, -3/-5 is a rational number.

Both numerator and denominator have negative signs. Thus, we can multiply and divide both top and bottom of rational numbers by -1, to get;

(-3/-5) x (-1/-1)

= ⅗ [Since, (- ) x (-) = (+)]

Therefore, -3/-5 is a positive rational number.

Q.4: Which of the following are negative rational numbers?

(i) -⅔

(ii) 5/7

(iii) 3/-5

(iv) 0

(v) 6/11

(vi) -2/-9

Solution: The negative rational numbers are:

(i) -⅔

(iii) 3/-5

### Practice Questions

1. List any five negative rational numbers.

2. Represent on the number line any two positive and negative integers.

3. Reduce -45/50 into standard form and find if it is a positive or negative rational number.

## Frequently Asked Questions on Positive and Negative Rational Numbers

### What is a positive rational number? Give an example

A positive rational number has its numerator and denominator either both positive or negative. For example, ¾ and -3/-4, both are positive rational numbers.

### What is a negative rational number? Give an example.

A negative rational number has either its numerator or denominator, negative. For example, -2/7 and 2/-7 are both negative rational numbers.

### Zero is neither positive nor a negative rational number. True or False?

True. Zero is neither positive nor a negative rational number.

### Is 1/-3 a negative rational number?

Yes, 1/-3 is a negative rational number. It can be also expressed as -⅓.

### Is 1/-7 a positive rational number?

1/-7 has a negative sign on its denominator. Thus, it can be a positive rational number but a negative rational number.