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Home >> Numbers >> Real Numbers >> Rational Numbers >> Multiplication of Rational Numbers >> Positive Rational Numbers >>

Multiplication of Positive Rational Numbers

Positive Rational Numbers Negative Rational Numbers Negative and Positive Rational Numbers

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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