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C3 Chapter 1 Algebraic Fractions Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 13 th May 2014

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

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? ? ? ? ? 1 2 3 4 5 6 7 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. ? ? ?

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Test Your Understanding ? ? ? ?

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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 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

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x + 56x 3 + 28x 2 – 7x + 15 6x 2 6x 3 + 30x 2 – 2x 2 – 7x - 2x – 2x 2 – 10x 3x + 15 + 3 3x + 15 0 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

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x - 42x 3 – 5x 2 – 16x + 10 2x 2 2x 3 – 8x 2 3x 2 – 16x + 3x 3x 2 – 12x -4x + 10 – 4 -4x + 16 -6 Find the remainder. Q: Is (x-4) a factor of 2x 3 – 5x 2 – 16x + 10? Test Your Understanding

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Alternative Method: Remainder Theorem RECAP ? ? ? ? ?

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Alternative Method: Remainder Theorem ? Q

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Test Your Understanding Q ?

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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 ? ? ? ? ?

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4. Check that the answer is reduced: The numerator and denominator should not have any common factors besides 1. When the GCF of the numerator and denominator.

4. Check that the answer is reduced: The numerator and denominator should not have any common factors besides 1. When the GCF of the numerator and denominator.

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