Before you study this concept, you are advice to read:
What are Negative Rational Numbers ?
What are Positive Integers ?
What are Negative Integers ?
Negative Rational Number is of following types:
Negative Rational Numbers with Negative Numerator
Negative Rational Numbers with Negative Denominator
Base on above classification, you will find following situation:
Multiplication of Negative Rational Numbers having Negative Numerator
Example: (-1/2) X (-3/2)
Multiplication of Negative Rational Numbers having Negative Denominator
Example: (2/-7) X (10/-11)
Multiplication of Negative Rational Numbers, where one has Negative Numerator and other Rational Number has Negative Denominator
Example: (-8/7) X (3/-4)
Situation 1: Multiplication of Negative Rational Numbers having Negative Numerator
This is done in the following way:
Multiplication of numerators, divided by, multiplication of denominators; of the given rational numbers
For multiplication follow the process of multiplication of integers
Example 1: Multiply (-1/2) and (-3/2)
Solution: Write the given rational numbers in Multiplication expression and we get:
(-1/2) X (-3/2)
Multiplication of numerators, divided by, multiplication of denominators; of the given rational numbers and we get:
= (-1 X -3) / (2 X 2)
Multiply the integer in the brackets.
Numerator has negative integer, so follow process of multiplication of negative integers
Denominator has positive integer, so follow process of multiplication of positive integers
And we get:
= (3/4)
Hence, (-1/2) X (-3/2) = (3/4)
Situation 2: Multiplication of Negative Rational Numbers having Negative Denominator
This is done in the following way:
Multiplication of numerators, divided by, multiplication of denominators; of the given rational numbers
For multiplication follow the process of multiplication of integers
Example 2: Multiply (2/-7) and (10/-11)
Solution: Write the given rational numbers in Multiplication expression and we get:
(2/-7) X (10/-11)
Multiplication of numerators, divided by, multiplication of denominators; of the given rational numbers and we get:
= (2 X 10) / (-7 X -11)
Multiply the integer in the brackets.
Numerator has positive integer, so follow process of multiplication of positive integers
Denominator has negative integer, so follow process of multiplication of negative integers
And we get:
= (20/77)
Hence, (2/-7) X (10/-11) = (20/77)
Situation 3: Multiplication of Negative Rational Numbers, where one has Negative Numerator and other Rational Number has Negative Denominator
This is done in the following way:
Multiplication of numerators, divided by, multiplication of denominators; of the given rational numbers
For multiplication follow the process of multiplication of positive and negative integers
And In last, since denominator has negative integer so will convert it into standard form.
Example 3: Multiply (-1/7) and (3/-2)
Solution: Write the given rational numbers in Multiplication expression and we get:
(-1/7) X (3/-2)
Multiplication of numerators, divided by, multiplication of denominators; of the given rational numbers and we get:
= (-1 X 3) / (7 X -2)
Multiply the integer in the brackets.
For multiplication follow the process of multiplication of positive and negative integers and we get:
= (-3/-14)
Since denominator has negative integer so convert it into standard form and we get:
= (3/14)
Hence, (-1/7) X (3/-2) = (3/14)
|
