Subtraction of Negative Rational Number with Different Denominator

Positive Rational Numbers with Same Denominator	Positive Rational Numbers with Different Denominator	Negative Rational Number with Same Denominator	Negative Rational Number with Different Denominator	Positive & Negative Rational Numbers with Same Denominator
Positive & Negative Rational Numbers with Different Denominator

Before you understand this topic, you are advice to read: What are Negative Rational Numbers ? How to subtract Integers ? How to convert rational number into standard form ? How to find LCM ? Negative Rational Number is of two types: Rational Number with Negative Numerator Rational Number with Negative Denominator Based on above classification, you will find the following three situations: Subtraction of Negative Rational Numbers having Negative Numerator and whose denominators are different. Example 1: Add (-4/6), (-5/8) Subtraction of Negative Rational Numbers having Negative Denominator and whose denominators are different. Example 2: Add (8/-9), (7/-3) Subtraction of Negative Rational Numbers having different denominators, where one rational number have negative numerator and other have negative denominator. Example 3: Add (2/-9) and (-7/6) Situation 1: Subtraction of Negative Rational Numbers having Negative Numerator and whose denominators are different. Steps of subtraction under this situation are: Step 1: Find LCM of denominators of given rational numbers Step 2: LCM = common denominator of resultant rational number Step 3: Divide common denominator by the denominator and multiply the quotient with the numerator of given respective rational numbers Step 4: Do subtraction of the numerators. The numerators are negative integers, so we do subtraction as we do subtraction of integers. Example 1: Subtract (-5/8) from (-4/6) Solution: Subtract the given rational numbers and we get: = (-4/6) - (-5/8) Find LCM of denominators of given rational numbers and we get: LCM of 6 and 8 = 24 LCM = common denominator of resultant rational number And divide common denominator by the denominator and multiply the quotient with the numerator of given respective rational numbers; as shown below: = (-4 X 4) - (-5 X 3) / 24 Solve the multiplication expression in the brackets and we get; = (-16) - (-15) / 24 Do subtraction of the numerators. The numerators are negative integers, so we do subtraction as we do subtraction of integers. = (-1/24) Hence, (-4/6) - (-5/8) = (-1/24) Situation 2: Subtraction of Negative Rational Numbers having Negative Denominator and whose denominators are different. Steps of subtraction under this situation are: Step 1: Since the denominators are negative, so firstly we convert the given rational numbers in standard form. Step 2: Find LCM of denominators of given rational numbers Step 3: LCM = common denominator of resultant rational number Step 4: Divide common denominator by the denominator and multiply the quotient with the numerator of given respective rational numbers Step 5: Do subtraction of the numerators. The numerators are negative integers, so we do subtraction as we do subtraction of integers. Example 2: Subtract (7/-3) from (8/-9) Solution: Since the denominators are negative, so firstly we convert the given rational numbers in standard form and we get: = (-8/9), (-7/3) Subtract the rational numbers and we get: = (-8/9) - (-7/3) Find LCM of denominators of given rational numbers and we get: LCM of 9 and 3 = 9 LCM = common denominator of resultant rational number And divide common denominator by the denominator and multiply the quotient with the numerator of given respective rational numbers; as shown below: = (-8 X 1) - (-7 X 3) / 9 Solve the multiplication expression in the brackets and we get; = (-8) - (-21) / 9 Do subtraction of the numerators. The numerators are negative integers, so we do subtraction as we do subtraction of integers. = (13/9) Hence, (8/-9) - (7/-3) = (13/9) Situation 3: Subtraction of Negative Rational Numbers having different denominators, where one rational number have negative numerator and other have negative denominator. Steps of subtraction under this situation are: Step 1: Firstly we convert the rational numbers with negative denominator in standard form. Step 2: Find LCM of denominators of given rational numbers Step 3: LCM = common denominator of resultant rational number Step 4: Divide common denominator by the denominator and multiply the quotient with the numerator of given respective rational numbers Step 5: Do subtraction of the numerators. The numerators are negative integers, so we do subtraction as we do subtraction of integers. Example 3: Subtract (-7/6) from (2/-9) Solution: Convert the rational numbers (2/-9) in standard form and we get: = (-2/9) Subtract the rational numbers and we get: = (-2/9) - (-7/6) Find LCM of denominators of given rational numbers and we get: LCM of 9 and 6 = 18 LCM = common denominator of resultant rational number And divide common denominator by the denominator and multiply the quotient with the numerator of given respective rational numbers; as shown below: = (-2 X 2) - (-7 X 3) / 18 Solve the multiplication expression in the brackets and we get; = (-4) - (-21) / 18 Do subtraction of the numerators. The numerators are negative integers, so we do subtraction as we do subtraction of integers. = (17/18) Hence, (2/-9) + (-7/6) = (17/18)