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Home >> Numbers >> Real Numbers >> Rational Numbers >> Division of Rational Numbers >> Division of Positive Rational Numbers >> Division of Positive Rational Numbers
Before you study this concept, you are adviced to read:
What are Positive Rational Numbers ?
How to multiply Rational Numbers ?
How to multiply Integers ?
How to convert rational Number in Standard Form ?
What is Reciprocal of Rational Number
Positive Rational Number is of following types:
Positive Rational Numbers with Positive Integer
Positive Rational Numbers with Negative Integers
Base on above classification, you will find following situation:
Division of Positive Rational Number by another positive rational (both having positive Integers)
Example: (4/5) ÷ (3/2)
Division of Positive Rational Number by another positive rational (both having Negative Integers)
Example: (-2/-3) ÷ (-7/-5)
Division of Positive Rational (having positive integer) and by another Positive rational number having (Negative Integers)
Example: (1/2) ÷ (-3/-11)
Note: Division of positive rational numbers by another positive rational number always leads to positive rational number only
Situation 1: Division of Positive Rational Number by another positive rational (both having positive Integers)
Example 1: Divide (4/5) by (3/2)
Division under this situation is similar to Division of fraction and you can read the details at
Division of Fraction by Fraction
Situation 2: Division of Positive Rational Number by another positive rational (both having Negative Integers
Step of division under this situation:
Step 1: Find the Reciprocal of divisor
Step 2: Multiply dividend with the reciprocal of divisor (calculated in step 1)
Step 3: Multiply rational numbers
Example 2: Divide (-2/-3) by (-3/-5)
Solution: Write the given rational number in division expression and we get:
(-2/-3) ÷ (-7/-5)
Find the reciprocal of divisor (-7/-5) and we get;
Reciprocal of divisor (-7/-5) = (-5/-7)
Multiply the dividend (-2/-3) with the reciprocal of divisor (calculated above and we get:
= (-2/-3) X (-5/-7)
Follow the process of multiplication of rational number we get:
= (-2 X -5) / (-3 X -7)
Solve Brackets
Follow process of multiplication of integers and we get:
= 10/21
Hence, (-2/-3) ÷ (-7/-5) = 10/21
Situation 3: Division of Positive Rational (having positive integer) and by another Positive rational number having (Negative Integers)
Step of division under this situation:
Step 1: Find the Reciprocal of divisor
Step 2: Multiply dividend with the reciprocal of divisor (calculated in step 1)
Step 3: Multiply rational numbers
Step 4: Since denominator has negative integer so convert it into standard form.
Example 3: Divide (1/2) by (-3/-11)
Solution: Write the given rational number in division expression and we get:
(1/2) ÷ (-3/-11)
Find the reciprocal of divisor (-3/-11) and we get;
Reciprocal of divisor (-3/-11) = (-11/-3)
Multiply the dividend (1/2) with the reciprocal of divisor (calculated above and we get:
= (1/2) X (-11/-3)
Follow the process of multiplication of rational number we get:
= (1 X - 11) / (2 X -3)
Solve Brackets
Follow process of multiplication of integers and we get:
= (-11/-6)
Since denominator has negative integer so convert it into standard form and we get
= 11/6
Hence, (1/2) ÷(-3/-11) = 11/6
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