# Is Every Rational Number an Integer?

Is every rational number an integer?

Every integer is a rational number but a rational number need not be an integer.

We know that 1 = 1/1, 2 = 2/1, 3 = 3/1, 4 = 4/1 and so on ……. .

also, -1 = -1/1, -2 = -2/1, -3 = -3/1, -4 = -4/1 and so on …….. .

In other words, any integer a can be written as a = a/1, which is a rational number.

Thus, every integer is a rational number.

Clearly, 3/2,-5/3, etc. are rational numbers but they are not integers.

Hence, every integer is a rational number but a rational number need not be an integer.

Let us determine whether the following rational numbers are integers or not:

(i) 2/5

2/5 is not an integer. Since we cannot express 2/5 without a fractional or decimal component

(ii) 8/4

8/4 is an integer. Since if we simplify 8/4 to its lowest term we get 2/1 = 2, which is an integer.

(iii) -5/-5

-5/-5 is an integer. Since if we simplify -5/-5 to its lowest term we get 1/1 = 1, which is an integer.

(iv) -15/2

-15/2 is not an integer. Since we cannot express -15/2 without a fractional or decimal component

(v) -32/8

-32/8 is an integer. Since if we simplify -32/8 to its lowest term we get -4, which is an integer.

(vi) 49/-9

49/-9 is not an integer. Since we cannot express 49/-9 without a fractional or decimal component

(vii) -75/-20

-75/-20 is not an integer. Since if we simplify -75/-20 to its lowest term we get 15/4 and we cannot express 15/4 without a fractional or decimal component

(viii) 500/-10

500/-10 is an integer. Since if we simplify 500/-10 to its lowest term we get 50/-1 = -50, which is an integer.

So, from the above explanation we conclude that every rational number is not an integer.

Rational Numbers

What is Rational Numbers?

Is Every Rational Number a Natural Number?

Is Zero a Rational Number?

Is Every Rational Number an Integer?

Is Every Rational Number a Fraction?

Positive Rational Number

Negative Rational Number

Equivalent Rational Numbers

Equivalent form of Rational Numbers

Rational Number in Different Forms

Properties of Rational Numbers

Lowest form of a Rational Number

Standard form of a Rational Number

Equality of Rational Numbers using Standard Form

Equality of Rational Numbers with Common Denominator

Equality of Rational Numbers using Cross Multiplication

Comparison of Rational Numbers

Rational Numbers in Ascending Order

Representation of Rational Numbers on the Number Line

Addition of Rational Number with Same Denominator

Addition of Rational Number with Different Denominator

Properties of Addition of Rational Numbers

Subtraction of Rational Number with Different Denominator

Subtraction of Rational Numbers

Properties of Subtraction of Rational Numbers

Simplify Rational Expressions Involving the Sum or Difference

Multiplication of Rational Numbers

Properties of Multiplication of Rational Numbers

Rational Expressions Involving Addition, Subtraction and Multiplication

Division of Rational Numbers

Rational Expressions Involving Division

Properties of Division of Rational Numbers

To Find Rational Numbers

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Divisibility Rules | Divisibility Test|Divisibility Rules From 2 to 18

Apr 12, 24 04:32 PM

To find out factors of larger numbers quickly, we perform divisibility test. There are certain rules to check divisibility of numbers. Divisibility tests of a given number by any of the number 2, 3, 4…

2. ### Even and Odd Numbers Between 1 and 100 | Even and Odd Numbers|Examples

Apr 12, 24 04:22 PM

All the even and odd numbers between 1 and 100 are discussed here. What are the even numbers from 1 to 100? The even numbers from 1 to 100 are:

3. ### Prime and Composite Numbers | Prime Numbers | Composite Numbers

Apr 12, 24 04:07 PM

What are the prime and composite numbers? Prime numbers are those numbers which have only two factors 1 and the number itself. Composite numbers are those numbers which have more than two factors.

4. ### Methods of Prime Factorization | Division Method | Factor Tree Method

Apr 12, 24 03:43 PM

In prime factorization, we factorise the numbers into prime numbers, called prime factors. There are two methods of prime factorization: 1. Division Method 2. Factor Tree Method

5. ### Worksheet on Factors and Multiples | Find the Missing Factors | Answer

Apr 11, 24 02:19 PM

Practice the questions given in the worksheet on factors and multiples. 1. Find out the even numbers. 27, 36, 48, 125, 360, 453, 518, 423, 54, 58, 917, 186, 423, 928, 358 2. Find out the odd numbers.

Rational Numbers - Worksheets

Worksheet on Rational Numbers

Worksheet on Lowest form of a Rational Number

Worksheet on Standard form of a Rational Number

Worksheet on Equality of Rational Numbers

Worksheet on Comparison of Rational Numbers

Worksheet on Representation of Rational Number on a Number Line

Worksheet on Properties of Addition of Rational Numbers

Worksheet on Rational Expressions Involving Sum and Difference

Worksheet on Multiplication of Rational Number

Worksheet on Division of Rational Numbers

Worksheet on Finding Rational Numbers between Two Rational Numbers

Worksheet on Word Problems on Rational Numbers

Objective Questions on Rational Numbers