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Home >> Numbers >> Real Numbers >> Rational Numbers >> Addition of Rational & Natural Number >>

Addition of Rational Number & Natural Number

Equivalent Rational Numbers Positive Rational Numbers Negative Rational Numbers Rational Numbers in Standard Form Compare Rational Numbers
Addition of Rational Numbers Addition of Rational & Natural Number Addition of Rational Number & Integer Subtraction of Rational Numbers Subtraction of Rational Number & Integer
Multiplication of Rational Numbers Multiplication of Rational & Natural Number Multiplication of Rational Number & Integer Reciprocal of a Rational Number Division of Rational Numbers

This concept can also be referred to as addition of rational numbers and positive integers

Before you understand this concept, you are advice to read:

What are Positive Rational Numbers ?
What are Negative Rational Numbers ?
What are Natural Numbers ?
How to find LCM ?
How to convert Rational Number into Standard Form ?
How to add Integers ?

During addition of rational number and natural, you will face following situations:

  • Addition of Positive Rational Number (with positive integers) and Natural Number
    Example: (1/5) + 2

  • Addition of Positive Rational Number (with negative integers) and Natural Number
    Example: (-3/-5) + 1

  • Addition of Negative Rational Number (with negative numerator) and Natural Number
    Example: (-7/6) + 2

  • Addition of Negative Rational Number (with negative denominator) and Natural Number
    Example: (1/-2) + 4

    Situation 1: Addition of Positive Rational Number (with positive integers) and Natural Number

    Example 1: Add (2/3) + 5
    Solution : Addition under situation is exactly same to addition of fraction and whole number and you can read that details at
    Addition of Fraction and whole Number

    Situation 2: Addition of Positive Rational Number (with negative integers) and Natural Number

    Steps of addition under this situation are:
    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

    Example 2: Add (-3/-5) and 3
    Solution: Since the denominator of given rational number (-3/-5)is negative, so convert this rational numbers in standard form and we get:
    (3/5) .....(Statement 1)

    Convert the natural number (3) into rational number by putting 1 as its denominator and we get:
    (3/1) ..... (Statement 2)

    Add the above rational number from statement 1 & 2 and we get:
    = (3/5) + (3/1)

    Since the denominator of given rational number is negative, so convert the given rational numbers in standard form and we get:
    = (3/5) + (3/1)

    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:
    = (3 X 1) + (3 X 5) / 5

    Solve the multiplication expression in the brackets and we get;
    = 3 + 15 / 5

    Solve addition operation in numerator and we get:
    = 18/5

    Hence, (-3/-5) + 3 = 18/5

    Situation 3: Addition of Negative Rational Number (with negative numerator) and Natural Number

    Steps of addition under this situation are:
    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 3: Add (-7/6) and 2
    Solution: Add the given rational number & natural number and we get:
    (-7/6) + 2

    Convert the natural number into rational number by putting 1 as its denominator and we get:
    = (-7/6) + (2/1)

    Find LCM of denominators of rational numbers and we get:
    LCM of 6 and 1 = 6

    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:
    = (-7 X 1) + (2 X 6) / 6

    Solve the multiplication expression in the brackets and we get;
    = (-7) + 12 / 6

    Solve addition operation in numerator as we do addition of positive and negative integers & we get:
    = 5/6

    Hence, (-7/6) + (2/1) = 5/6

    Situation 4: Addition of Negative Rational Number (with negative denominator) and Natural Number

    Steps of addition under this situation are:
    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 4: Add (1/-2) and 4
    Solution: Since the denominator of given rational number (1/-2) is negative, so convert this rational numbers in standard form and we get
    = (-1/2) ..... (Statement 1)

    Convert the natural number (4) into rational number by putting 1 as its denominator and we get:
    = (1/-2) ..... (Statement 2)

    Add the given rational number & natural number and we get:
    = (1/-2) + 4

    Find LCM of denominators of 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:
    = (-1 X 1) + (4 X 2) / 2

    Solve the multiplication expression in the brackets and we get;
    = (-1) + 8 / 2

    Solve addition operation in numerator as we do addition of positive and negative integers & we get:
    = 7/2
    Hence, (1/-2) + (4/1) = 7/2

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