Before you study this concept, you are advice to read:
What are Negative Integers ?
How to Compare Fractions ?
While comparing two negative rational numbers, you find following situations:
Both have Negative Numerator:
Both have Negative Denominator
One have Negative Numerator and other have Negative Denominator
Both have Negative Numerator:
This situation arises when you have to compare two negative rational numbers, both having negative numerator. For example: -2/5, -1/3
This is further classified into:
1. Same Denominator : In this situation you are asked to compare two negative rational numbers having negative numerators and whose denominators are same. The Steps of conversion are as follows:
Step 1: Ignore the negative operators
Step 2: Compare them as we compare like fractions (Read in details How to Compare Like Fractions ? )
Step 3: After comparison, put negative operators (as given) and reverse the order of comparison.
(Note: Order of comparison is reversed, when integers are converted from positive to negative. The same principle applies to Rational Numbers also. Read this in detail Compare Integers on Number Line)
Example 1: Compare -7/9, -11/9
Solution: Ignore the negative operators and we get:
7/9, 11/9
Now, we can compare them as we compare like fractions and we get:
Put negative operators (as given) and reverse the order of comparison & we get:
2) Same Numerator : In this situation you are asked to compare two negative rational numbers having negative numerators and whose numerators are same. The steps of conversion are as follows:
Step 1: Ignore the negative operators
Step 2: Compare them as we compare unlike fractions having same numerator (Read in detail Compare Unlike Fractions with Same Numerator)
Step 3: After comparison, put negative operators (as given) and reverse the order of comparison.
(Note: Order of comparison is reversed, when integers are converted from positive to negative. The same principle applies to Rational Numbers also. Read this in detail Compare Integers on Number Line ? )
Example 2: Compare -15/6, -15/8
Solution: Ignore the negative operators and we get:
15/6, 15/8
Now, we can compare them as we compare unlike fraction having same numerator and we get
Put negative operators (as given) and reverse the order of comparison & we get:
3) Different Numerator and Denominator :In this situation you are asked to compare two negative rational numbers having negative numerators and whose numerators & denominators are different. The steps of conversion are as follows:
Step 1: Ignore the negative operators
Step 2: Compare them as we compare unlike fraction having different numerators (Read in detail Compare Unlike Fractions with Different Numerator)
Step 3: After comparison, put negative operators (as given) and reverse the order of comparison.
(Note: This is already explained earlier that order of comparison is reversed, when integers are converted from positive to negative. The same principle applied to Rational Numbers also. Read this in detail Compare Integers on Number Line ? )
Example 3: Compare -1/3, -2/5
Solution: Ignore the negative operators and we get:
1/3, 2/5
Now, we can compare them as we compare unlike fractions having different numerators & we get:
Put negative operators (as given) and reverse the order of comparison & we get:
Both have Negative Denominator
This situation arises when you have to compare two negative rational numbers, both having negative denominator. For example: 9/-10, 12/-13
This is further classified into:
1) Same Denominator In this situation you are asked to compare two negative rational numbers having negative denominators and whose denominators are same. The steps of conversion are as follows:
Step 1: Ignore the negative operators
Step 2: Compare them as we compare like fractions (Read in details How to Compare Like Fractions ? )
Step 3: After comparison, put negative operators (as given) and reverse the order of comparison.
(Note: Order of comparison is reversed, when integers are converted from positive to negative. The same principle applies to Rational Numbers also. Read this in detail Compare Integers on Number Line ? )
Example 4: Compare 24/-87, 10/-87
Solution: Ignore the negative operators and we get:
24/87, 10/87
Now, we can compare them as we compare like fractions and we get:
Put negative operators (as given) and reverse the order of comparison & we get:
2) Same Numerator : In this situation you are asked to compare two negative rational numbers having negative denominators numbers and whose numerators are same. The steps of conversion are as follows:
Step 1: Ignore the negative operators
Step 2: Compare them as we compare unlike fractions having same numerator (Read in detail Compare Unlike Fractions with Same Numerator)
Step 3: After comparison, put negative operators (as given) and reverse the order of comparison.
(Note: Order of comparison is reversed, when integers are converted from positive to negative. The same principle applies to Rational Numbers also. Read this in detail Compare Integers on Number Line )
Example 5: 9/-8, 9/-2
Solution: Ignore the negative operators and we get:
9/8, 9/2
Now, we can compare them as we compare unlike fraction having same numerator and we get
Put negative operators (as given) and reverse the order of comparison & we get:
3) Different Numerator and Denominator : In this situation you are asked to compare two negative rational numbers having negative denominators and whose numerators & denominators are different. The steps of conversion are as follows:
Step 1: Ignore the negative operators
Step 2: Compare them as we compare unlike fraction having different numerators (Read in detail Compare Unlike Fractions with Different Numerator)
Step 3: After comparison, put negative operators (as given) and reverse the order of comparison.
(Note: This is already explained earlier that order of comparison is reversed, when integers are converted from positive to negative. The same principle applies to Rational Numbers also. Read in detail Compare Integers on Number Line )
Example 6: Compare 7/-6, 1/-15
Solution: Ignore the negative operator and we get:
7/6, 1/15
Now, we can compare them as we compare unlike fractions having different numerators & we get:
Put negative operators (as given) and reverse the order of comparison & we get:
One have Negative Numerator and other have Negative Denominator
This situation arises when you have to compare two negative rational numbers, in which one rational number has negative numerator and other rational has negative denominator. For example: compare 4/-5 and -6/7 or compare -10/11 and 12/-13
This is further classified into:
1) Same Denominator : In this situation you are asked to compare two negative rational numbers, in which one rational number has negative numerator and other rational has negative denominator. And also whose denominators are same. The steps of conversion are as follows:
Step 1: Ignore the negative operators
Step 2: Compare them as we compare like fractions (Read in details How to Compare Like Fractions ? )
Step 3: After comparison, put negative operators (as given) and reverse the order of comparison.
(Note: Order of comparison is reversed, when integers are converted from positive to negative. The same principle applies to Rational Numbers also. Read this in detail from link provided on the top Compare Integers on Number Line )
Example 7: Compare 23/-10, -13/10
Solution: Ignore the negative operators and we get:
23/10, 13/10
Now, we can compare them as we compare like fractions and we get:
Put negative operators (as given) and reverse the order of comparison & we get:
2) Same Numerator : In this situation you are asked to compare two negative rational numbers, in which one rational number has negative numerator and other rational has negative denominator. And also whose numerators are same. The steps of conversion are as follows:
Step 1: Ignore the negative operators
Step 2: Compare them as we compare unlike fractions having same numerator (Read in detail Compare Unlike Fractions with Same Numerator)
Step 3: After comparison, put negative operators (as given) and reverse the order of comparison.
(Note: Order of comparison is reversed, when integers are converted from positive to negative. The same principle applies to Rational Numbers also. Read this in detail from link provided on the top Compare Integers on Number Line )
Example 8: -77/32, 77/-23
Solution: Ignore the negative operators and we get:
77/32, 77/23
Now, we can compare them as we compare unlike fraction having same numerator and we get
Put negative operators (as given) and reverse the order of comparison & we get:
3. Different Numerator and Denominator : In this situation you are asked to compare two negative rational numbers, in which one rational number has negative numerator and other rational has negative denominator. And whose numerators & denominators are different. The steps of conversion are as follows:
Step 1: Ignore the negative operators
Step 2: Compare them as we compare unlike fraction having different numerators (Read in detail Compare Unlike Fractions with Different Numerator)
Step 3: After comparison, put negative operators (as given) and reverse the order of comparison.
(Note: This is already explained earlier that order of comparison is reversed, when integers are converted from positive to negative. The same principle applies to Rational Numbers also. Read in detail Compare Integers on Number Line )
Example 9: Compare 7/-10, -3/4
Solution: Ignore the negative operator and we get:
7/10, 3/4
Now, we can compare them as we compare unlike fractions having different numerators & we get:
Put negative operators (as given) and reverse the order of comparison & we get:
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