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Home >> Numbers >> Real Numbers >> Rational Numbers >> Division of Rational Numbers >> Division of Negative Rational Numbers >> Division of Negative Rational Numbers
Before you study this concept, you are advice to read:
What are Negative Rational Numbers ?
What is Reciprocal of Rational Number ?
How to divide Rational Numbers ?
How to divide Integers ?
Negative Rational Number is of following types:
Negative Rational Numbers with Negative Numerator
Negative Rational Numbers with Negative Denominator
Base on above classification, you will find following situation:
Division of Negative Rational Numbers by another Negative Rational Number (both having Negative Numerator)
Example: (-1/2) ÷ (-3/5)
Division of Negative Rational Numbers by another Negative Rational Number (both having Negative Denominator)
Example: (2/-7) ÷ (3/-11)
Division of Negative Rational Numbers (having negative numerator) by another Negative Rational Number (having Negative Denominator)
Example: (-8/7) ÷ (3/-4)
Note: Division of negative Rational number by another negative rational number always leads to positive rational number only.
Situation 1: Division of Negative Rational Numbers by another Negative Rational Number (both having Negative Numerator)
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 1: Divide (-1/2) by (-3/5)
Solution: Write the given rational number in division expression and we get:
(-1/2) ÷ (-3/5)
Find the reciprocal of divisor (-3/5) and we get;
Reciprocal of divisor (-3/5) = (5/-3)
Multiply the dividend (-1/2) with the reciprocal of divisor (calculated above and we get:
= (-1/2) X (5/-3)
Follow the process of multiplication of rational number we get:
= (-1 X 5) / (2 X -3)
Solve Brackets and follow process of multiplication of integers and we get:
= (-5/-6)
Since denominator has negative integer so convert it into standard form i.e. divide both numerator and denominator with (-1) and we get:
= 5/6
Hence, (-1/2) ÷ (-3/5 = 5/6
Situation 2: Division of Negative Rational Numbers by another Negative Rational Number (both having Negative Denominator)
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 2: Divide (2/-7) by (3/-11)
Solution: Write the given rational number in division expression and we get:
(2/-7) ÷ (3/-11)
Find the reciprocal of divisor (3/-11) and we get;
Reciprocal of divisor (3/-11) = (-11/3)
Multiply the dividend (2/-7) with the reciprocal of divisor (calculated above and we get:
= (2/-7) X (-11/3)
Follow the process of multiplication of rational number we get:
= (2 X -11) / (-7 X 3)
Solve Brackets and follow process of multiplication of integers and we get:
= (-22/-21)
Since denominator has negative integer so convert it into standard form i.e. divide both numerator and denominator with (-1) and we get:
= 22/21
Hence, (2/-7) ÷ (3/-11) = 22/21
Situation 3: Division of Negative Rational Numbers (having negative numerator) by another Negative Rational Number (having Negative Denominator)
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 3: Divide (-8/7) by (3/-4)
Solution: Write the given rational number in division expression and we get:
(-8/7) ÷ (3/-4)
Find the reciprocal of divisor (3/-4) and we get;
Reciprocal of divisor (3/-4) = (-4/3)
Multiply the dividend (-8/7) with the reciprocal of divisor (calculated above and we get:
= (-8/7) X (-4/3)
Follow the process of multiplication of rational number we get:
= (-8 X -4) / (7 X 3)
Solve Brackets and follow process of multiplication of integers and we get:
= 32/21
Hence, (-8/7) ÷ (3/-4) = 32/21
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