Comparison of Positive Negative Rational Numbers at Algebra Den

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Home >> Numbers >> Real Numbers >> Rational Numbers >> Compare Rational Numbers >> Comparison of Positive Negative Rational Numbers >>

Comparison of Positive Negative Rational Numbers

Comparison of Positive Rational Numbers Comparison of Negative Rational Numbers Comparison of Positive Negative Rational Numbers

Before you study this concept, you are advice to read:

What are Positive Rational Numbers ?
What are Negative Rational Numbers ?

Negative Rational Numbers are of following two types:

Negative Rational Numbers having Negative Numerator
Negative Rational Numbers having Negative Denominator

Positive Rational Numbers are of two types:

Positive Rational Numbers having positive integers
Positive Rational Numbers having negative integers

Because of the above classification of negative rational number and positive rational number, you can observe following situation while comparing one negative rational number and one positive rational number:

Comparison of Negative Rational Numbers (having Negative Numerator) with Positive Rational Numbers (with positive integers)

Example 1: Compare -15/4, 10/8
Answer: 10/8 > -15/4

Comparison of Negative Rational Numbers (having Negative Denominator) with Positive Rational Numbers (with positive integers)

Example 2: 8/-19, 2/3
Solution: 2/3 > 8/-19

Comparison of Negative Rational Numbers (having Negative Numerator) with Positive Rational Numbers (with negative integers)

Example 3: Compare -5/3, -10/-11
Solution: 10/-11 > -5/3

Comparison of Negative Rational Numbers (having Negative Denominator) with Positive Rational Numbers (with negative integers)

Example 4 : Compare 21/-100, -33/-17
Solution: -33/-17 21/-100

Now you can observe one common thing in all the above examples i.e. positive rational numbers are greater than negative rational number (irrespective of above classifications).

Also, if you put the rational numbers on number line, from above example, you will observe that positive rational numbers lie on right hand side of number line; while negative rational numbers lie on the left side of number line. And we know that on number line; numbers which are on the right hand side of other numbers are always greater.

Hence, this concludes that positive rational numbers are always greater than negative rational numbers (same as positive integers are always greater than negative integers)