Architecture

# Are Negative Numbers Rational Or Irrational ? Is A Negative Number An Irrational Number

A rational number is said to be negative if its numerator and denominator are of opposite signs such that, one of them is positive integer and another one is a negative integer.

In other words, a rational number is negative, if its numerator and denominator are of the opposite signs.

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Each of the rational numbers -1/6, 2/-7, -30/11, 13/-19, -15/23 are negative rationals, but -11/-18, 2/5, -3/-5, 1/3 are not negative rationals.

1. Is every negative integer a negative rational number?

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

In other words, any negative integer n can be written as n = n/1, here n is negative and 1 is positive.

Hence, every negative integer is a negative (-ve) rational number.

Note: The rational number 0 is neither positive nor negative.

2. Determine whether the following rational numbers are negativesor not:

(i) 3/(-8)

3/(-8) is a negativerational. Since both the numerator and denominator are of the opposite sign.

(ii) (-1)/(-5)

(-1)/(-5) is not a negativerational. Since both the numerator and denominator are of the same sign.

(iii) 11/29

11/29 is not a negativerational. Since both the numerator and denominator are of the same sign.

(iv) 11/(-15)

11/(-15) is a negativerational. Since both the numerator and denominator are of the opposite sign.

(v) (-71)/(-9)

(-71)/(-9) is not a negativerational. Since both the numerator and denominator are of the same sign.

(vi) (-33)/7

(-33)/7 is a negativerational. Since both the numerator and denominator are of the opposite sign.

(vii) 21/22

21/22 is not a negativerational. Since both the numerator and denominator are of the same sign.

(viii) (-14)/39

(-14)/39 is a negativerational. Since both the numerator and denominator are of the opposite sign.

So, from the aboveexplanation we conclude that a rational number is negative, if its numeratorand denominator are of the opposite sign.

● 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 Numberson 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

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