Before you understand this topic, you are adviced to read:
What are Negative Rational Numbers ?
What are Positive Rational Numbers ?
How to convert rational number in standard form ?
Subtraction of Positive and Negative Integer
Positive Rational Numbers are of two types:
Positive Rational Numbers with Positive Numerator and Denominator
Positive Rational Numbers with Negative Numerator and Denominator
Negative Rational Number is of two types:
Rational Number with Negative Numerator
Rational Number with Negative Denominator
Based on above classification, you will find following situations:
Subtraction of Positive Rational Number (with positive numerator and denominator) and Negative Rational Number (with Negative Numerator), having same denominator
Example: Subtract (-5/3) from (2/3)
Subtraction of Positive Rational Number (with positive numerator and denominator) and Negative Rational Number (with Negative Denominator), having same denominator
Example: Subtract (7/-5) from (8/5)
Subtraction of Positive Rational Number (with negative numerator and denominator) and Negative Rational Number (with Negative Numerator), having same denominator
Example: Subtract (-6/4) from (-1/-4)
Subtraction of Positive Rational Number (with negative numerator and denominator) and Negative Rational Number (with Negative Denominator), having same denominator
Example: Subtract (4/-9) from (-3/-9)
Situation 1: Subtraction of Positive Rational Number (with positive numerator and denominator) and Negative Rational Number (with Negative Numerator), having same denominator
Steps of subtraction under this situation are:
Step 1: Since the denominators are same; so we keep the denominator same (i.e. common denominator)
Step 2: Do subtraction of the numerators. The numerators are negative integers, so we do subtraction as we do subtraction of integers.
Example 1: Subtract (-5/3) from (2/3)
Solution: Subtract the given rational numbers and we get:
(2/3) - (-5/3)
Since the denominators are same; so we keep the denominator same (i.e. common denominator) as shown below:
= (2) - (-5) / 3
Do subtraction of the numerators. The numerators are negative integers, so we do subtraction as we do subtraction of integers.
= 7/3
Hence, (2/3) - (-5/3) = (7/3)
Situation 2: Subtraction of Positive Rational Number (with positive numerator and denominator) and Negative Rational Number (with Negative Denominator), having same denominator
Steps of subtraction under this situation are:
Step 1: Firstly we convert the rational numbers with negative denominator in standard form.
Step 2: Since the denominators are same; so we keep the denominator same (i.e. common denominator)
Step 3: Do subtraction of the numerators. The numerators are negative integers, so we do subtraction as we do subtraction of integers.
Example 2: Subtract (7/-5) from (8/5)
Solution: In the given rational numbers there is one rational numbers which have negative denominator i.e. (8/-5).
So firstly, convert this rational numbers in standard form and we get:
(Read in detail from the link Rational Numbers in Standard Form)
= (-8/5)
Now, Subtract the rational numbers and we get:
(3/5) - (-8/5)
Since the denominators are same; so we keep the denominator same (i.e. common denominator) as shown below:
= (3) - (-8) / 5
Do subtraction of the numerators.
The numerators are negative integers, so we do subtraction as we do subtraction of integers.
= (11/5)
Hence, (3/5) - (7/-5) = (11/5)
Situation 3: Subtraction of Positive Rational Number (with negative numerator and denominator) and Negative Rational Number (with Negative Numerator), having same denominator
Steps of subtraction under this situation are:
Step 1: Firstly we convert the rational numbers with negative denominator in standard form.
Step 2: Since the denominators are same; so we keep the denominator same (i.e. common denominator)
Step 3: Do subtraction of the numerators. The numerators are negative integers, so we do subtraction as we do subtraction of integers.
Example 3: Subtract (-6/4) from (-1/-4)
Solution: In the given rational numbers there is one rational numbers which have negative denominator i.e. (-1/-4). So firstly, convert this rational numbers in standard form and we get:
= (1/4)
Now, subtract the rational numbers and we get:
(1/4) - (-6/4)
Since the denominators are same; so we keep the denominator same (i.e. common denominator) as shown below:
= (1) - (-6) / 4
Do subtraction of the numerators. The numerators are negative integers, so we do subtraction as we do subtraction of integers.
= (7/4)
Hence, (-1/-4) - (-6/4) = (7/4)
Situation 4: Subtraction of Positive Rational Number (with negative numerator and denominator) and Negative Rational Number (with Negative Denominator), having same denominator
Steps of subtraction under this situation are:
Step 1: Firstly we convert the rational numbers with negative denominator in standard form.
Step 2: Since the denominators are same; so we keep the denominator same (i.e. common denominator)
Step 3: Do subtraction of the numerators. The numerators are negative integers, so we do subtraction as we do subtraction of integers.
Example 4: Subtract (4/-9) from (-3/-9)
Solution: In the given rational numbers both rational numbers have negative denominators. So firstly, convert this rational numbers in standard form and we get:
= (3/9), (-4/9)
Now, subtract the rational numbers and we get:
(3/9) - (-4/9)
Since the denominators are same; so we keep the denominator same (i.e. common denominator) as shown below:
= (3) - (-4) / 9
Do subtraction of the numerators. The numerators are negative integers, so we do subtraction as we do subtraction of integers.
= (7/9)
Hence, (-3/-9) + (4/-9) = (7/9)
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