C3 Chapter 1 Algebraic Fractions Dr J Frost Last modified: 13 th May 2014

7 3 = dividend divisor quotient remainder RECAP: Terminology dividend divisor quotientremainder ? ? ??

? ? ? ? ? Simplify the following fractions. 8 Bro Tip: When you have a fraction within a fraction, multiply the top and bottom of the outer fraction by the denominator of the inner one. ? ? ?

Test Your Understanding ? ? ? ?

Exercises 1g 1i 1j 1l 1n Exercise 1B Exercise 1A 1a 1g 1i 1j 1k 1o Exercise 1C 1b 1c 1g 1k 1l 1n 1o 1q ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

x + 56x x 2 – 7x x 2 6x x 2 – 2x 2 – 7x - 2x – 2x 2 – 10x 3x x The Anti-Idiot Test: You can check your solution by expanding (x+5)(6x 2 – 2x + 3) The Anti-Idiot Test: You can check your solution by expanding (x+5)(6x 2 – 2x + 3) RECAP: Algebraic Division

x - 42x 3 – 5x 2 – 16x x 2 2x 3 – 8x 2 3x 2 – 16x + 3x 3x 2 – 12x -4x + 10 – 4 -4x Find the remainder. Q: Is (x-4) a factor of 2x 3 – 5x 2 – 16x + 10? Test Your Understanding

Alternative Method: Remainder Theorem RECAP ? ? ? ? ?

Alternative Method: Remainder Theorem ? Q

Test Your Understanding Q ?

Exercise 1D Express the following improper fractions in ‘mixed’ number form by: i) Using long division ii) Using the remainder theorem. a c e g h ? ? ? ? ?