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Home >> Numbers >> Real Numbers >> Rational Numbers >> Subtraction of Rational Number & Integer >> Subtraction of Rational Number & Integer
Before you study this concept, you are advice to read:
What are Rational Numbers ?
What are Integers ?
How to Subtract Integers ?
How to find LCM ?
How to convert Rational Number in Standard Form ?
Subtraction of Rational Number and Natural Number
Integers are of following two types:
Positive Integers
Negative Integers
So, with above mentioned types of integers, we get:
Subtraction of Rational Number and Positive Integer
Subtraction of Rational Number and Negative Integer
Subtraction of Rational Number and Positive Integers is similar to subtraction of Rational Number and Natural Number which you can study at
Under the Subtraction of Rational Number and Negative Integer you will find the following situations:
Subtraction of Positive Rational Number (with positive integers) and Negative Integer
Example: (1/5) - (-2)
Subtraction of Positive Rational Number (with negative integers) and Negative Integer
Example: (-3/-2) - (-2)
Subtraction of Negative Rational Number (with negative numerator) and Negative Integer
Example: (-2/7) - (-5)
Subtraction of Negative Rational Number (with negative denominator) and Negative Integer
Example: (10/-11) - (-9)
Situation 1: Subtraction of Positive Rational Number (with positive integers) and Negative Integer
Step 1: Convert the natural number into rational number by putting 1 as its denominator
Step 2: Find LCM of denominators of rational numbers
Step 3: LCM = common denominator of resultant rational number
Step 4: Divide common denominator by the denominator and multiply the quotient with the numerator of given respective rational numbers
Step 5: Solve subtraction operation in numerator as we do subtraction of positive and negative integers.
Example 1: Solve (1/5) - (-2)
Solution: As given in the question:
(1/5) - (-2)
Convert the integer (-2) into rational number by putting 1 as its denominator and we get:
= (1/5) and (-2/1)
Find LCM of denominators of above rational numbers and we get:
LCM of 5 and 1 = 5
LCM = common denominator of resultant rational number
And divide common denominator by the denominator and multiply the quotient with the numerator of given respective rational numbers; as shown below:
= (1 X 1) - (-2 X 5) / 5
Solve the multiplication expression in the brackets and we get;
= 1 - (-10) / 5
Solve subtraction operation in numerator as we do subtraction of positive and negative integers & we get:
= (11/5)
Hence, (1/5) - (-2) = (11/5)
Situation 2: Subtraction of Positive Rational Number (with negative integers) and Negative Integer
Step 1: Since the denominator is negative, so firstly we convert the given rational numbers in standard form.
Step 2: Convert the natural number into rational number by putting 1 as its denominator
Step 3: Find LCM of denominators of rational numbers
Step 4: LCM = common denominator of resultant rational number
Step 5: Divide common denominator by the denominator and multiply the quotient with the numerator of given respective rational numbers
Step 6: Solve subtraction operation in numerator as we do subtraction of positive and negative integers.
Example 2: Solve (-3/-2) - (-2)
Solution: Since the denominator of rational number (-3/-2) is negative, so firstly we convert this rational numbers in standard form and we get:
(3/2) ..... (Statement 1)
Convert the integer (-2) into rational number by putting 1 as its denominator and we get:
(-2/1) ..... (Statement 1)
From statement 1 & 2, subtraction operation we get:
(3/2) - (-2/1)
Find LCM of denominators of above rational numbers and we get:
LCM of 2 and 1 = 2
LCM = common denominator of resultant rational number
And divide common denominator by the denominator and multiply the quotient with the numerator of given respective rational numbers; as shown below:
= (3 X 1) - (-2 X 2) / 4
Solve the multiplication expression in the brackets and we get;
= 3 - (-4) / 4
Solve subtraction operation in numerator as we do subtraction of positive and negative integers & we get:
= (7/4)
Hence, (-3/-2) - (-2) = (7/4)
Situation 3: Subtraction of Negative Rational Number (with negative numerator) and Negative Integer
Step 1: Convert the natural number into rational number by putting 1 as its denominator
Step 2: Find LCM of denominators of rational numbers
Step 3: LCM = common denominator of resultant rational number
Step 4: Divide common denominator by the denominator and multiply the quotient with the numerator of given respective rational numbers
Step 5: Solve subtraction operation in numerator as we do subtraction of negative integers.
Example 3: Solve (-2/7) - (-5)
Solution: As given in the question:
(-2/7) - (-5)
Convert the integer (-5) into rational number by putting 1 as its denominator and we get:
= (-2/7) - (-5/1)
Find LCM of denominators of above rational numbers and we get:
LCM of 7 and 1 = 7
LCM = common denominator of resultant rational number
And divide common denominator by the denominator and multiply the quotient with the numerator of given respective rational numbers; as shown below:
= (-2 X 1) - (-5 X 7) / 7
Solve the multiplication expression in the brackets and we get;
= (-2) - (-35) / 7
Solve subtraction operation in numerator as we do subtraction of negative integers.
= (-33/7)
Hence, (-2/7) - (-5) = (33/7)
Situation 4: Subtraction of Negative Rational Number (with negative denominator) and Negative Integer
Step 1: Since the denominator is negative, so firstly we convert the given rational numbers in standard form.
Step 2: Convert the natural number into rational number by putting 1 as its denominator
Step 3: Find LCM of denominators of rational numbers
Step 4: LCM = common denominator of resultant rational number
Step 5: Divide common denominator by the denominator and multiply the quotient with the numerator of given respective rational numbers
Step 6: Solve subtraction operation in numerator as we do subtraction of negative integers.
Example: (10/-11) + (-9)
Solution: Since the denominator of rational number (10/-11) is negative, so firstly we convert the given rational numbers in standard form and we get:
(-10/11) ..... (Statement 1)
Convert the integer (-9) into rational number by putting 1 as its denominator and we get:
(-9/1) ..... (Statement 1)
From statement 1 & 2, subtraction operation we get:
(-10/11) - (-9/1)
Find LCM of denominators of above rational numbers and we get:
LCM of 11 and 1 = 11
LCM = common denominator of resultant rational number
And divide common denominator by the denominator and multiply the quotient with the numerator of given respective rational numbers; as shown below:
= (-10 X 1) - (-9 X 11) / 11
Solve the multiplication expression in the brackets and we get;
= (-10) - (-99) / 11
Solve subtraction operation in numerator as we do subtraction of negative integers.
= (89/11)
Hence, (-10/11) - (-9) = (89/11)
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