1. Revision - Algebraic Fractions Numerical and Algebraic Fraction Operations. By I Porter Addition & Subtraction

2. Card2 Numerical Operation Revision Addition a) Find a common denominator. 3 x 5 = 15 easiest. Same denominator, add the numerators. Reduce the fraction. Subtraction b) Find a common denominator. 6 x 4 = 24 easiest. Same denominator, subtract the numerators. But if we factorise the two denominators, 6 = 2 x 3 and 4 = 2 x 2, they have a common factor 2. This gives the L.C.M as 2 x 3 x 2 = 12 Hence, multiply each fraction by So that the denominators are the same.

3. Card3 Simple Algebraic Fractions Simplify the following a) Find L.C.M. of denominators. Factorise the two denominators, 6b = 2 x 3 x b and 4c = 2 x 2 x c, they have a common factor 2. So that the denominator are equal. Add the numerators. The L.C.M. is 2 x 3 x 2 x b x c = 12bc. Hence, multiply the first fraction by the second fraction by

4. Card4 b) Find L.C.M. of denominators. Factorise the two denominators, they have a common factor 3c. So that the denominator are equal. Subtract the numerators. Simplify the following The L.C.M. is 6ac. Hence, multiply the first fraction by second fraction by

5. Card5 Simplification of Addition and Subtraction of Algebraic Fractions. Factorise the numerator and denominator FIRST Find the common denominator L.C.M. Convert each fraction to the same denominator by a suitable multiplier. Examples: Simplify a) Factorise top and bottom. LCM = (x+2)(x-2) Leave denominator & numerator in factoise form. Convert to same denominator. Multiply the second fraction by

6. Card6 b) Factorise top and bottom. LCM = x(x+2)(x-2) Leave denominator & numerator in factoise form. Examples: Simplify Convert to same denominator. multiply the first fraction by multiply the second fraction by

7. Card7 Your Example: Simplify the following Factorise denominators as (x-2)(x-3) and (x-2)(x+4) The LCM is (x-2)(x-3)(x+4). Rearrange, some student would write down the next line of working. Write as a single denominator, expand the numerator(s) Clean up the numerator. Multiply first fraction by and second fraction by [Click the mouse button for hints]

8. Card8 Exercise: Simplify the following