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Home >> Numbers >> Real Numbers >> Rational Numbers >> Division of Rational Numbers >> Division of Positive Rational Number by Positive Rational Number >> Division of Positive Rational Number by Positive Rational Number
Before you study this concept, you are adviced to read:
What are Positive Rational Numbers ?
What are Negative Rational Numbers ?
What is Multiplication of Rational Numbers ?
What is Reciprocal of Rational Number ?
How to convert Rational Number in Standard Form ?
What is Divisor and Dividend ?
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:
Division of Negative Rational Numbers (with Negative Numerator) by Positive Rational Number (with positive Integers)
Example: (-7/2) ÷ (1/11)
Division of Negative Rational Numbers (with Negative Denominator) by Positive Rational Number (with positive Integers)
Example: (5/-7) ÷ (1/9)
Division of Negative Rational Numbers (with Negative Numerator) by Positive Rational Number (with negative Integers)
Example: (-1/4) ÷ (-1/-9)
Division of Negative Rational Numbers (with Negative Denominator) by Positive Rational Number (with negative Integers)
Example: (3/-10) ÷ (-11/-7)
Note: Division of a negative Rational number and a positive rational number always leads to negative rational number only.
Situation 1: Division of Negative Rational Numbers (with Negative Numerator) by Positive Rational Number (with positive 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: Divide (-7/2) by (1/11)
Solution: Write the given rational number in division expression and we get:
(-7/2) ÷ (1/11)
Find the reciprocal of divisor (1/11) and we get;
Reciprocal of divisor (1/11) = (11/1)
Multiply the dividend (-7/2) with the reciprocal of divisor (calculated above and we get:
= (-7/2) X (11/1)
Follow the process of multiplication of rational number we get:
= (-7 X 11) / (2 X 1)
Solve Brackets and follow process of multiplication of integers and we get:
= (-77/2)
Since denominator has negative integer so convert it into standard form i.e. divide both numerator and denominator with (-1) and we get:
= (-3/14)
Hence, (-7/2) ÷ (1/11) = (-77/2)
Situation 2: Division of Negative Rational Numbers (with Negative Denominator) by Positive Rational Number (with positive 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: Divide (5/-7) by (1/9)
Solution: Write the given rational number in division expression and we get:
(5/-7) ÷ (1/9)
Find the reciprocal of divisor (1/9) and we get;
Reciprocal of divisor (1/9) = (9/1)
Multiply the dividend (5/-7) with the reciprocal of divisor (calculated above and we get:
= (5/-7) X (9/1)
Follow the process of multiplication of rational number we get:
= (5 X 9) / (-7 X 1)
Solve Brackets and follow process of multiplication of integers and we get:
= (45/-7)
Since denominator has negative integer so convert it into standard form i.e. divide both numerator and denominator with (-1) and we get:
= (-45/7)
Hence, (5/-7) ÷ (1/9) = (-45/7)
Situation 3: Division of Negative Rational Numbers (with Negative Numerator) by Positive Rational Number (with 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: Divide (-1/4) by (-1/-9)
Solution: Write the given rational number in division expression and we get:
(-1/4) ÷ (-1/-9)
Find the reciprocal of divisor (-1/-9) and we get;
Reciprocal of divisor (-1/-9) = (-9/-1)
Multiply the dividend (-1/4) with the reciprocal of divisor (calculated above and we get:
= (-1/4) X (-9/-1)
Follow the process of multiplication of rational number we get:
= (-1 X -9) / (4 X -1)
Solve Brackets and follow process of multiplication of integers and we get:
= (9/-4)
Since denominator has negative integer so convert it into standard form i.e. divide both numerator and denominator with (-1) and we get:
= (-9/4)
Hence, (-1/4) ÷ (-1/-9) = (-9/4)
Situation 4: Division of Negative Rational Numbers (with Negative Denominator) by Positive Rational Number (with 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: Divide (3/-10) by (-11/-7)
Solution: Write the given rational number in division expression and we get:
(3/-10) ÷ (-11/-7)
Find the reciprocal of divisor (-11/-7) and we get;
Reciprocal of divisor (-11/-7) = (-7/-11)
Multiply the dividend (3/-10) with the reciprocal of divisor (calculated above and we get:
= (3/-10) X (-7/-11)
Follow the process of multiplication of rational number we get:
= (3 X -7) / (-10 X -11)
Solve Brackets and follow process of multiplication of integers and we get:
= (-21/110)
Hence, (3/-10) ÷ (-11/-7) = (-21/110)
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