Before you study this concept, you are adviced to read:
What are Positive Rational Numbers ?
What are Negative Rational Numbers ?
What are Positive Integers ?
What are Negative Integers ?
How to convert rational number in standard form ?
Positive Rational Number is of following types:
Positive Rational Numbers with Positive Integer
Positive Rational Numbers with 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 of positive and negative rational numbers, you will find following situation:
Multiplication of Positive Rational Number (with positive Integers) and Negative Rational Numbers (with Negative Numerator)
Example: (1/7) X (-2/3)
Multiplication of Positive Rational Number (with positive Integers) and Negative Rational Numbers (with Negative Denominator)
Example: (5/2) X (3/-7)
Multiplication of Positive Rational Number (with negative Integers) and Negative Rational Numbers (with Negative Numerator)
Example: (-10/-11) X (-1/3)
Multiplication of Positive Rational Number (with negative Integers) and Negative Rational Numbers (with Negative Denominator)
Example: (-3/-5) X (2/-7s)
Situation 1: Multiplication of Positive Rational Number (with positive Integers) and Negative Rational Numbers (with 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 (1/7) and (-2/3)
Solution: Write the given rational numbers in Multiplication expression and we get:
(1/7) X (-2/3)
Multiplication of numerators, divided by, multiplication of denominators; of the given rational numbers and we get:
= (1 X -2) / (7 X 3)
Multiply the integer in the brackets.
Numerator has one positive integer and one negative integer, so follow process of multiplication of positive and negative integers
Denominator has positive integers, so follow process of multiplication of positive integers
And we get:
= (-2/21)
Hence, (1/7) X (-2/3) = (-2/21)
Situation 2: Multiplication of Positive Rational Number (with positive Integers) and Negative Rational Numbers (with Negative Denominator)
Steps are as follows -
Multiplication of numerators, divided by, multiplication of denominators; of the given rational numbers
For multiplication follow the process of multiplication of integers
And In last, since denominator has negative integer so will convert it into standard form.
Example 2: Multiply (5/2) and (3/-7)
Solution: Write the given rational numbers in Multiplication expression and we get:
(5/2) X (3/-7)
Multiplication of numerators, divided by, multiplication of denominators; of the given rational numbers and we get:
= (5 X 3) / (2 X -7)
Multiply the integer in the brackets.
Numerator has positive integers, so follow process of multiplication of positive integers
Denominator has one positive integer and one negative integer, so follow process of multiplication of positive and negative integers
And we get:
= (15/-14)
Since denominator has negative integer so convert it into standard form and we get:
= (-15/14)
Hence, (5/2) X (3/-7) = (-15/14)
Situation 3: Multiplication of Positive Rational Number (with negative Integers) and Negative Rational Numbers (with Negative Numerator)
Multiplication of numerators, divided by, multiplication of denominators; of the given rational numbers
For multiplication follow the process of multiplication of integers
And In last, since denominator has negative integer so will convert it into standard form.
Example 3: Multiply (-10/-11) and (-1/3)
Solution: Write the given rational numbers in Multiplication expression and we get:
(-10/-11) X (-1/3)
Multiplication of numerators, divided by, multiplication of denominators; of the given rational numbers and we get:
= (-10 X -1) / (-11 X 3)
Multiply the integer in the brackets.
Numerator has negative integers, so follow process of multiplication of negative integers
Denominator has one positive integer and one negative integer, so follow process of multiplication of positive and negative integers
And we get:
= (10/-33)
Since denominator has negative integer so convert it into standard form and we get:
= (-10/33)
Hence, (-10/-11) X (-1/3) = (-10/33)
Situation 4: Multiplication of Positive Rational Number (with negative Integers) and Negative Rational Numbers (with Negative Denominator)
Steps are as follows -
Multiplication of numerators, divided by, multiplication of denominators; of the given rational numbers
For multiplication follow the process of multiplication of integers
And In last, since denominator has negative integer so will convert it into standard form.
Example 4: Multiply (-3/-5) and (2/-7)
Solution: Write the given rational numbers in Multiplication expression and we get:
(-3/-5) X (2/-7)
Multiplication of numerators, divided by, multiplication of denominators; of the given rational numbers and we get:
= (-3 X 2) / (-5 X -7)
Multiply the integer in the brackets.
Numerator has one positive integer and one negative integer, so follow process of multiplication of positive and negative integers
Denominator has negative integers, so follow process of multiplication of negative integers
And we get:
= (-6/35)
Hence, (-3/-5) X (2/-7) = (-6/35)
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