Before you study this concept, you are adviced to read:
What are Positive Rational Numbers ?
What are Positive Integers ?
What are Negative Integers ?
Positive Rational Number is of following types:
Positive Rational Numbers with Positive Integer
Positive Rational Numbers with Negative Integer
Base on above classification, you will find following situation:
Multiplication of Positive Rational Numbers with positive Integers
Example: (4/5) X (6/2)
Multiplication of Positive Rational Numbers with Negative Integers
Example: (-2/-3) X (-4/-5)
Multiplication of Positive Rational Numbers, where one Rational Number has positive integer and other rational number has Negative Integers
Example: (1/2) X (-5/-7)
Situation 1: Multiplication of Positive Rational Numbers with positive Integers
Example 1: Multiply (4/5) and (6/2)
Multiplication under this situation is similar to multiplication of fraction and you can read the details at :
How to multiply two & more fractions
Situation 2: Multiplication of Positive Rational Numbers with Negative Integers
This is done in the following way:
Multiplication of numerators, divided by, multiplication of denominators; of the given rational numbers
Since both numerators and denominator of given rational numbers are negative integers, so we follow the process of multiplication of negative integers
Example 2: Multiply (-2/-3) and (-4/-5)
Solution: Write the given rational numbers in Multiplication expression and we get:
(-2/-3) X (-4/-5)
Multiplication of numerators, divided by, multiplication of denominators; of the given rational numbers and we get:
= (-2 X -4) / (-3 X -5)
Multiply the integer in the brackets, as we multiply negative integers and we get:
= 8/15
Hence, (-2/-3) X (-4/-5) = 8/15
Situation 3: Multiplication of Positive Rational Numbers, where one Rational Number has positive integer and other rational number has Negative Integers
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 (1/2) and (-5/-7)
Solution: Write the given rational numbers in Multiplication expression and we get:
(1/2) X (-5/-7)
Multiplication of numerators, divided by, multiplication of denominators; of the given rational numbers and we get:
= (1 X -5) / (2 X -7)
Multiply the integer in the brackets, as we multiply positive and negative integers & we get:
= (-5/-14)
Since denominator has negative integer, so convert into standard form and we get:
= (5/14)
Hence, (1/2) X (-5/-7) = (5/14)
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