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
Is Every Rational Number a Natural Number?
Is Every Rational Number an Integer?
Is Every Rational Number a Fraction?
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
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
Properties of Multiplication of Rational Numbers
Rational Expressions Involving Addition, Subtraction and Multiplication
Reciprocal of a Rational Number
Rational Expressions Involving Division
Properties of Division of Rational Numbers
Rational Numbers between Two Rational Numbers
8th Grade Math Practice
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● Rational Numbers - Worksheets
Worksheet on Equivalent Rational Numbers
Worksheet on Lowest form of a Rational Number
Worksheet on Standard form of a Rational Number
Worksheet on Equality of Rational Numbers
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