Addition of Negative Rational Numbers with Same Denominator

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

Before you understand this topic, you are adviced to read: What are Negative Rational Numbers ? How to add Negative Integers ? How to convert rational number into standard form ? Negative Rational Number is of two types: Rational Number with Negative Numerator Rational Number with Negative Denominator Addition of Negative Rational Numbers having Negative Numerator and whose denominators are same Steps of addition under this situation are: Step 1: Since the denominators are same; so we keep the denominator same (i.e. common denominator) Step 2: Add the numerators. The numerators are negative integers, so we will add numerators as we add negative integers. Example 1: Add -1/10 and -5/10 Solution: Add the given rational numbers and we get: -1 10 + -5 10 Since the denominators are same; so we keep the denominator same (i.e. common denominator) as shown below (-1) + (-5) 10 Add numerators as we add negative integers and we get: -6 10 Divide both numerator and denominator by 2 and convert the resultant rational number into standard form. So we get: -3 5 Hence, (-1/10) + (-5/10) = (-3/5) Addition of Negative Rational Numbers having Negative Denominator and whose denominators are same Steps of addition under this situation are: Step 1: Since the denominators are negative, so firstly we convert the given rational numbers in standard form. Step 2: Also since the denominators are same; so we keep the denominator same (i.e. common denominator) Step 3: Add the numerators. The numerators are negative integers, so we will add numerators as we add negative integers. Example 2: Add 10/-15 and 2/-15 Solution: Since the denominators are negative, so firstly we convert the given rational numbers in standard form and we get: -10 15 , -2 15 Add the rational numbers and we get: -10 15 + -2 15 Since the denominators are same; so we keep the denominator same (i.e. common denominator) as shown below: (-10) + (-2) 15 Add numerators as we add negative integers and we get: -12 10 Divide both numerator and denominator by 2 and convert the resultant rational number into standard form. So we get: -6 5 Hence, (10/-15) + (2/-15) = (-6/5) Addition of Negative Rational Numbers having same denominators, where one rational number have negative numerator and other have negative denominator Steps of addition under this situation are: Step 1: Convert the rational numbers, with negative denominator, into standard form Step 2: Also since the denominators are same; so we keep the denominator same (i.e. common denominator) Step 3: Add the numerators. The numerators are negative integers, so we will add numerators as we add negative integers. Example 3: Add -7/8 and 6/-8 Solution: Convert the rational numbers (6/-8) in standard form, so we get:

-6 8

Add the rational numbers and we get:

-7 8

+

-6 8

Since the denominators are same; so we keep the denominator same (i.e. common denominator) as shown below:

(-7) + (-6) 8

Add numerators as we add negative integers and we get:

-13 8

Hence, (-7/8) + (6/-8) = (-13/8)


Above examples 1, 2 & 3 under three different situations, must have given you the clarity how to add two negative rational numbers having same denominator. Now, in the following example you can now learn to add more than two rational numbers with same denominator.


Example 4: Add -9/19, -8/19, -13/19
Solution: Since the denominators are same; so we keep the denominator same (i.e. common denominator) as shown below:

(-9) + (-8) + (-13) 19

Add numerators as we add negative integers and we get:

-30 19

Hence, (-9/19) + (-8/19) + (-13/19) = (-30/19)


Example 5: Add 20/-7, 2/-7, 11/-7, 8/-7
Solution : Since the denominators are negative, so firstly we convert the given rational numbers in standard form, so we get:

-20 7

,

-2 7

,

-11 7

,

-8 7

Add the rational numbers and we get:

(-20) 7

+

(-2) 7

+

(-11) 7

,

(-8) 7

Since the denominators are same; so we keep the denominator same (i.e. common denominator) as shown below:

(-20) + (-2) + (-11) + (-8) 7

Add numerators as we add negative integers and we get:

-41 7

Hence, (20/-7) + (2/-7) + (11/-7) + (8/-7) = (-41/7)

Example 6: Add -11/15, 5/-15, -21/15, -16/15, 4/-15
Solution: In the given rational numbers there are some rational numbers which have negative denominator. So firstly, convert such rational numbers in standard form and we get:

-11 15

,

-5 15

,

-21 15

,

-16 15

,

-4 15

Add the rational numbers and we get:

(-11) 15

+

(-5) 15

+

(-21) 15

+

(-16) 15

+

(-4) 15

Since the denominators are same; so we keep the denominator same (i.e. common denominator) as shown below:

(-11) + (-5) + (-21) + (-16) + (-4) 15

Add numerators as we add negative integers and we get:

-57 15

Divide both numerator and denominator by 2 and convert the resultant rational number into standard form, So we get:

-19 15

Hence, (-11/15) + (5/-15) + (-21/15) + (-16/15) + (4/-15) = (-19/15)