| Arithmetic Additive Identity
Arithmetic Progression
Associative Property
Averages
Brackets
Closure Property
Commutative Property
Conversion of Measurement Units
Cube Root
Decimal
Distributivity of Multiplication over Addition
Divisibility Principles
Equality
Exponents
Factors
Fractions
Fundamental Operations
H.C.F / G.C.D
Integers
L.C.M
Multiples
Multiplicative Identity
Multiplicative Inverse
Numbers
Percentages
Profit and Loss
Ratio and Proportion
Simple Interest
Square Root
Unitary Method
Algebra Cartesian System
Order Relation
Polynomials
Probability
Standard Identities & their applications
Transpose
Geometry Basic Geometrical Terms
Circle
Curves
Angles
Define Line, Line Segment and Rays
Non-Collinear Points
Parallelogram
Rectangle
Rhombus
Square
Three dimensional object
Trapezium
Triangle
Quadrilateral
Trigonometry Trigonometry Ratios
Data-Handling Arithmetic Mean
Frequency Distribution Table
Graphs
Median
Mode
Range
Videos
Solved Problems
|
Home >> Numbers >> Real Numbers >> Rational Numbers >> Addition of Rational Number & Integer >> Addition of Rational Number & Integer
Before you study this concept, you are advice to read:
What are Rational Numbers ?
What are Integers ?
How to add Integers ?
Integers are of following two types:
Positive Integers
Negative Integers
So, with above mentioned types of integers, we get:
Addition of Rational Number and Positive Integer
Addition of Rational Number and Negative Integer
Addition of Rational Number and Positive Integers is similar to addition of Rational Number and Natural Number which you can read at
Addition of Rational Number and Natural Number
Under Addition of Rational Number and Negative Integer you will find the following situations
Addition of Positive Rational Number (with positive integers) and Negative Integer
Example: (1/5) + (-2)
Addition of Positive Rational Number (with negative integers) and Negative Integer
Example: (-3/-2) + (-2)
Addition of Negative Rational Number (with negative numerator) and Negative Integer
Example: (-2/7) + (-5)
Addition of Negative Rational Number (with negative denominator) and Negative Integer
Example: (10/-11) + (-9)
Situation 1: Addition 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 addition operation in numerator as we do addition of positive and negative integers.
Example 1: Add (1/5) and (-2)
Solution: Add the given rational number & integer and we get:
(1/5) + (-2)
Convert the integer into rational number by putting 1 as its denominator and we get:
= (1/5) and (-2/1)
Find LCM of denominators of 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 addition operation in numerator as we do addition of positive and negative integers & we get:
= (-9/5)
Hence, (1/5) + (-2) = (-9/5)
Situation 2: Addition 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 addition operation in numerator as we do addition of positive and negative integers.
Example 2: Add (-3/-2) and (-2)
Solution: Since the denominator of rational number (-3/-2) is negative, so firstly we convert the given 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)
Add the above rational numbers from statement 1 & 2 and 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 addition operation in numerator as we do addition of positive and negative integers & we get:
= (-1/4)
Hence, (-3/-2) + (-2) = (-1/4)
Situation 3: Addition 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 addition operation in numerator as we do addition of negative integers.
Example 3: Add(-2/7) and (-5)
Solution: Add the given rational number & integer and we get:
(-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 addition operation in numerator as we do addition of negative integers.
= (-37/7)
Hence, (-2/7) + (-5) = (-37/7)
Situation 4: Addition 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 addition operation in numerator as we do addition 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)
Add the above rational numbers from statement 1 & 2 and 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 addition operation in numerator as we do addition of negative integers.
= (-109/11)
Hence, (-10/11) + (-9) = (-109/11)
|
|
