I. Addition of Fractions

  1. Adding fractions with the same denominator:

  • Add the numerators and keep the same denominator.

          display style a over m plus b over m equals fraction numerator a plus b over denominator m end fraction    left parenthesis m not equal to 0 right parenthesis

    • Formula:  display style 8 over 5 plus 7 over 5 equals fraction numerator 8 plus 7 over denominator 5 end fraction equals 15 over 5 equals 3

     2. Adding fractions with different denominators:

    • Convert them to have a common denominator, then add the numerators.

    • Example:

II. Properties of Fraction Addition

  • Commutative Property:

  • Associative Property:

    display style open parentheses a over b plus c over d close parentheses plus p over q equals a over b plus open parentheses c over d plus p over q close parentheses

  • Additive Identity (Adding 0):

III. Opposite of a Fraction

  • Two fractions are opposites if their sum is zero.

  • The opposite of display style a over b plus open parentheses negative a over b close parentheses equals 0​.

  • Note: The opposite of 0 is still 0.

IV. Subtraction of Fractions

  1. Subtracting fractions with the same denominator:

    • Subtract the numerators, keep the same denominator.

    • Formula:

  2. Subtracting fractions with different denominators:

    • Convert them to the same denominator, then subtract the numerators.

  3. Alternative method (Using opposites):

    • Subtraction can be turned into addition of the opposite:

      display style 1 over 6 minus 1 half equals 1 over 6 plus open parentheses negative 1 half close parentheses equals fraction numerator 1 plus left parenthesis negative 3 right parenthesis over denominator 6 end fraction equals fraction numerator negative 2 over denominator 6 end fraction equals negative 1 third
Last modified: Wednesday, 28 May 2025, 8:01 PM