C 3 Chapter 1 Algebraic Fractions Dr J

C 3 Chapter 1 Algebraic Fractions Dr J Frost (jfrost@tiffin. kingston. sch. uk) www. drfrostmaths. com Last modified: 30 th August 2015

RECAP: Terminology dividend ? quotient ? 7 = 2 + 3 divisor ? 1 3 remainder ?

1 Simplify the following fractions. ? 6 2 ? ? ? 7 ? 3 4 5 ? ? 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 Exercise 1 A 1 a ? 1 j ? 1 g ? 1 i ? ? 1 k ? 1 o 1 i 1 j 1 b 1 c 1 g Exercise 1 B 1 g Exercise 1 C ? ? 1 n ? ? 1 k ? 1 l ? ? 1 n ? 1 o 1 l ? ? 1 q ? ? ?

RECAP: Algebraic Division 2 6 x x + 5 - 2 x + 3 6 x 3 + 28 x 2 – 7 x + 15 3 2 6 x + 30 x 2 – 2 x – 7 x – 2 x 2 – 10 x 3 x + 15 0 The Anti-Idiot Test: You can check your solution by expanding (x+5)(6 x 2 – 2 x + 3)

Test Your Understanding 2 2 x + 3 x – 4 x - 4 2 x 3 – 5 x 2 – 16 x + 10 3 2 2 x – 8 x Find the 2 3 x – 16 x remainder. 3 x 2 – 12 x -4 x + 10 Q: Is (x-4) a factor of -4 x + 16 2 x 3 – 5 x 2 – 16 x + 10? -6

Alternative Method: Remainder Theorem RECAP ? ? ?

Alternative Method: Remainder Theorem Q ?

Test Your Understanding Q ?

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