In this chapter we will learn the concept of positive rational numbers with examples.

To understand the chapter, we will first start with the revision of the basics of rational number.

## What are rational numbers ?

The number which can be **arranged in the form of P / Q **are called **rational numbers**.

Numbers like \mathtt{\frac{2}{3} ,\ \frac{7}{5} \ ,\ \frac{11}{13}} are some examples of rational number.

If you want to learn about **rational numbers in detail**, click the red link.

## Positive rational numbers

A rational number is positive when **both the sign of numerator and denominator is same**.

That is, **the positive rational number has**;

(i) either both positive numerator and denominator, or;

(ii) both negative numerator and denominator.

Hence, numbers like \mathtt{\frac{5}{3} ,\ \frac{-11}{-13} \ ,\ \frac{2}{7}} are examples of positive rational number.

### Why rational number with negative numerator and denominator is positive ?

The rational number with negative sign in numerator and denominator** cancel out each other to produce positive rational number**.

## Are all natural numbers example of positive integers ?

Let us first classify the natural numbers.

All positive integers like 1, 2, 3, 4, 5 . . . . are the** natural numbers**.

These **natural numbers are also positive rational numbers** because;

(i) By inserting denominator 1, we can** represent in the form of P / Q**.

(ii) Both **numerator and denominator are positive**.**For example;**

Consider the natural number 22.

Insert 1 in the denominator so that it get represented in the form of P / Q.

\mathtt{22\ \Longrightarrow \ \frac{22}{1}}

You can see that \mathtt{\ \frac{22}{1}} contains numerator and denominator of same sign.

Hence, the **number 22 is a positive rational number**.**Conclusion**

All the natural numbers are part of positive rational numbers.

### Are all negative integers part of positive rational number ?

Let us first understand the negative integers.

The numbers less than 0 which are neither fraction or decimal are **negative integers**.

Numbers like -1, -2, -3, -4, -5 . . . etc. are **example of negative integers.**

These **negative integers are also negative rational numbers** since;

(i) They can be **represented in the form of P / Q** by inserting denominator 1.

(ii) Here **numerator is negative number & denominator is positive**, so the rational number is non positive.

**For example;**

Consider the negative integer -50.

Insert 1 in denominator to represent in the form of P / Q.

\mathtt{-50\ \Longrightarrow \ \frac{-50}{1}}

You can see that the rational number is negative since the numerator and denominators are of different signs.

I hope you understood the above concept. Let us now practice some questions.

## Positive Rational Number – Solved examples

Among the given numbers, identify the positive rational numbers.

( i ) \mathtt{\frac{7}{11}}

Since both numerator and denominator have the same sign, the given rational number is** positive rational number**.

(ii) \mathtt{\frac{-2}{15}}

Here the numerator and denominator have different signs, hence the **rational number is not positive.**

(iii) \mathtt{\ \frac{-33}{-19}}

Here both the numerator an denominator have same sign. Hence the given **rational number is positive**.

(iv) \mathtt{\ \frac{50}{3}}

Both numerator & denominator have same sign. Hence, the given number is **positive rational number.**

(v) \mathtt{\frac{70}{-13}}

Here numerator is positive number and denominator is negative number.

Since both numerator and denominator have different sign, the **given rational number is not positive**.