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

Introduction of 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

Rational Numbers in Descending Order

Representation of Rational Numbers on the Number Line

Rational Numbers on the Number Line

Addition of Rational Number with Same Denominator

Addition of Rational Number with Different Denominator

Addition of Rational Numbers

Properties of Addition of Rational Numbers

Subtraction of Rational Number with Same Denominator

Subtraction of Rational Number with Different Denominator

Subtraction of Rational Numbers

Properties of Subtraction of Rational Numbers

Rational Expressions Involving Addition and Subtraction

Simplify Rational Expressions Involving the Sum or Difference

Multiplication of Rational Numbers

Product of Rational Numbers

Properties of Multiplication of Rational Numbers

Rational Expressions Involving Addition, Subtraction and Multiplication

Reciprocal of a Rational  Number

Division of Rational Numbers

Rational Expressions Involving Division

Properties of Division of Rational Numbers

Rational Numbers between Two Rational Numbers

To Find Rational Numbers

8th Grade Math Practice

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