Addition & Subtraction with Algebraic Fractions (SQA National 5 Maths): Revision Note

Adding & subtracting algebraic fractions

How do I add (or subtract) two algebraic fractions?

• The rules for adding and subtracting algebraic fractions are the same as they are for fractions with numbers

• STEP 1
  Find the lowest common denominator (LCD)

  • Sometimes the LCD can be found by multiplying the denominators together

    • E.g. The LCD for the fractions and is

    • Similarly, with numbers, the LCD of and is 2 × 5 = 10

  • Although multiplying the denominators will always give you a common denominator, it is not necessarily the lowest common denominator

    • E.g. The LCD for the fractions and is (not ) as both terms already include an

    • Similarly, with numbers, the LCD of and is just 4, not 2 × 4 = 8

  • Other examples include:

    • The LCD of and is

    • The LCD of and is

    • The LCD of and is

• STEP 2

  Write each fraction over the lowest common denominator

  Multiply the numerator of each fraction by the same amount as the denominator

  • E.g.

• STEP 3

  Write as a single fraction over the lowest common denominator and simplify the numerator

  • Do this by adding or subtracting the numerators

    • Take particular care with minus signs if subtracting

  • E.g.

• STEP 4

  Check at the end to see if the top factorises and the fraction can be simplified

  • E.g. , the top factorises but there are no common factors so it is in its most simple form