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