All integers are rational numbers ?

The question is, are all integers part of rational numbers ?

To understand the explanation, you should have basic understanding of the concept of integers and rational numbers.

Let us revise both the concepts.

What are Integers ?

All the numbers that are not fraction or decimals are known as integers.

Numbers like -4, 8, 13, -26, 106 etc. are the examples of integers.

Note that integers also contain negative numbers.

If you want to understand about integers in detail, click the red link.

What are rational numbers ?

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

Where, P & Q are integers.

The numbers like \mathtt{\frac{7}{3} ,\ \frac{5}{6} ,\ \frac{40}{8}} are all examples of rational numbers.

Note that the rational numbers can be in form of integers or decimals.

If you want to understand the concept of rational number in detail, click the red link.

Is every integer a rational number ?

The answer is YES !!

We can express any given integer in the form of P / Q by inserting 1 as denominator.

For example;
Consider integer number 7

If we insert denominator 1, the number will remain unchanged.

\mathtt{7\ \Longrightarrow \ \frac{7}{1}}

Since, we have expressed the integer in form of P / Q, it is a part of rational number.

Every integer possible is also a rational number.

All integers are rational number – solved examples

Given below are some examples for your further understanding.

(i) -22

-22 is an integer which can also be written as \mathtt{\frac{-22}{1}}

Since the number can be expressed in form of P / Q, the given number is also a rational number.

(ii) 913

Inserting 1 in the denominator will not change the number.

\mathtt{913\ \Longrightarrow \ \frac{913}{1}}

Since the number is expressed in form of P/Q, it is a rational number.

Leave a Comment

Your email address will not be published. Required fields are marked *

You cannot copy content of this page