1. www.mathsrevision.com Nat 5 www.mathsrevision.com Equivalent and Simplifying Fractions Adding & Subtracting Fractions Algebraic Fractions Multiplication & Division of Fractions Factorising and Simplifying Fractions Exam Type Questions

2. www.mathsrevision.com Nat 5 15-Aug-15Compiled by Mr. Lafferty Maths Dept. S3 Starter Questions www.mathsrevision.com

3. Nat 5 www.mathsrevision.com Learning Intention Success Criteria 1.We are learning how to simplify algebraic fractions. 1.Understand term Highest Common Factor. Algebraic Fractions 2.Simplify algebraic fractions by identifying HCF.

4. www.mathsrevision.com Nat 5 www.mathsrevision.com Equivalent Fractions We already know how to create an equivalent fraction for numerical fractions. The exact same process is used for algebraic fractions. Numerical Fraction Algebraic Fraction Multiply top and bottom by any number Multiply top and bottom by any number or letter

5. www.mathsrevision.com Nat 5 www.mathsrevision.com Equivalent Fractions Numerical Fraction Algebraic Fraction Common Denominator for 2 fractions

6. www.mathsrevision.com Nat 5 www.mathsrevision.com We can sometimes reduce fractions to a simpler form if the numerator and denominator have a number or letter in common. Examples HCF = 3 HCF = Y Algebraic Fractions

7. www.mathsrevision.com Nat 5 www.mathsrevision.com Examples 3 1 1 1 1 1 1 1 3 1 1 1 1 6 1 1 1 1 Algebraic Fractions We can only simplify if fraction is a product of factors.

8. www.mathsrevision.com Nat 5 www.mathsrevision.com Examples 1 1 1 1 Algebraic Fractions We can only simplify if fraction is a product of factors. 1 1

9. www.mathsrevision.com Nat 5 www.mathsrevision.com Examples Algebraic Fractions We can only simplify if fraction is a product of factors. 1 1 1 1 3 4

10. www.mathsrevision.com What Goes In The Box ? Nat 5 Factorise first

11. www.mathsrevision.com Now try N5 TJ Ex 9.1 Ch9 (page 90) Nat 5 Algebraic Fractions

12. www.mathsrevision.com Nat 5 15-Aug-15Compiled by Mr. Lafferty Maths Dept. Starter Questions In pairs, write down the three types of factorising and show an example of each.

13. www.mathsrevision.com Nat 5 www.mathsrevision.com Learning Intention Success Criteria 1.We are learning how to simplify algebraic fractions by first factorising. 1.Know the three types of factorisations. Algebraic Fractions 2.Simplify algebraic fractions by first factorising.

14. www.mathsrevision.com Nat 5 www.mathsrevision.com Type 1 3 1 Algebraic Fractions 1 1

15. www.mathsrevision.com Nat 5 www.mathsrevision.com Type 2 1 1 Algebraic Fractions 1 1

16. www.mathsrevision.com Nat 5 www.mathsrevision.com Type 3 1 1 Algebraic Fractions 1 1

17. www.mathsrevision.com Now try N5 TJ Ex 9.2 Ch9 (page 92) Nat 5 Algebraic Fractions

18. www.mathsrevision.com 15-Aug-15Compiled by Mr. Lafferty Maths Dept. Starter Questions Q1.Explain why 4 + 6 x 5 = 34 and not 50 Q2.Calculate Q3. Does x 2 – 121 factorise to (x – 11) (x - 11) Q4. The cost of an iPod is £80 including VAT. How much is the iPod BEFORE VAT. Nat 5

19. www.mathsrevision.com Nat 5 www.mathsrevision.com Learning Intention Success Criteria 1.We are learning how to add & subtract algebraic fractions. 1.Know how to add and subtract algebraic fractions using equivalent fractions. Algebraic Fractions Addition

20. www.mathsrevision.com Example 1 + 4 2 1 + 3 d Nat 5 Addition Algebraic Fractions LCM = 4 4 LCM = d d

21. www.mathsrevision.com Example 8 - 20 15 p - 3m pm Nat 5 Subtraction Algebraic Fractions LCM = 20 20 LCM = pm pm

22. www.mathsrevision.com Example x2x2 + 4x 12 x(x - 1) + 3(x + 1) (x - 1)(x + 1) 3x + 3 + x 2 – x (x - 1)(x + 1) Nat 5 Addition Algebraic Fractions x 2 + 2x + 3 (x - 1)(x + 1) 4x 12 + x 2 4x (x - 1)(x + 1) LCM = 4x LCM = (x-1)(x+1)

23. www.mathsrevision.com Example fg - 5g 15 x - 3(x + 5) x(x + 5) Nat 5 Subtraction Algebraic Fractions x-3x + 15 x(x + 5) 2x + 15 x(x + 5) LCM = 5g LCM = x(x+5) 5g 15 - fg 5g x(x + 5)

24. www.mathsrevision.com What Goes In The Box ? Nat 5

25. www.mathsrevision.com What Goes In The Box ? Nat 5

26. www.mathsrevision.com Now try N5 TJ Ex 9.3 Q1...Q9 Ch6 (page 93) Nat 5 Addition & Subtraction Algebraic Fractions

27. 15-Aug-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Fraction Equations Nat 5 + 5 = 8 x + 2 4 (x 4) x + 2 + 20 = 32 x + 22 = 32 - 22 x = 10 Multiply EVERY term to get rid of fractional term. and then apply ‘Balancing Method’ Example Tidy Up !

28. 15-Aug-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com MTH 3-15a MTH 4-15a (x 6) 18x 22x - 36 = 96 (÷ 22) x = 6 (2x – 4) + x = 16 3 2 2 3 (2x – 4) + x = 96 9 4 22x = 132 - 36 + 4x = 96 Example Tidy Up ! + 36 Fraction Equations

29. www.mathsrevision.com Now try N5 TJ Ex 9.3 Q10 Ch6 (page 94) Nat 5 Addition & Subtraction Algebraic Fractions

30. www.mathsrevision.com Nat 5 15-Aug-15Compiled by Mr. Lafferty Maths Dept. Starter Questions

31. www.mathsrevision.com Nat 5 www.mathsrevision.com Learning Intention Success Criteria 1.We are learning how to multiply and divide algebraic fractions. 1.Know rules for multiplying and dividing fractions. 2.Apply knowledge to algebraic fractions. Algebraic Fractions Multiplication & Division

32. www.mathsrevision.com Numerical fraction Algebraic Fraction Algebraic Fractions Nat 5 10 3 2 15 1 Multiplication & Division Remember you can simplify top and bottom and diagonally first to make things easier

33. www.mathsrevision.com Numerical Fraction Algebraic Fraction Algebraic Fractions Nat 5 1 1 15 8 Multiplication & Division Be careful !!! ONLY at the multiplication stage can you simplify to make things easier

34. www.mathsrevision.com Example 2 Example 3 Algebraic Fractions 1 11 1 Nat 5 Multiplication & Division Remember you can simplify top and bottom and diagonally first to make things easier

35. www.mathsrevision.com Algebraic Fractions Nat 5 4 3 Example 2 Example 3 Multiplication & Division Be careful !!! ONLY at the multiplication stage can you simplify to make things easier

36. www.mathsrevision.com Algebraic Fractions Nat 5 1 1 Example 4 1 1 1 1 Multiplication & Division Be careful !!! ONLY at the multiplication stage can you simplify to make things easier

37. www.mathsrevision.com What Goes In The Box ? Nat 5 Multiplication & Division

38. www.mathsrevision.com What Goes In The Box ? Nat 5 Multiplication & Division

39. www.mathsrevision.com Now try N5 TJ Ex 9.4 Ch9 (page 95) Nat 5 Multiplication & Division Algebraic Fractions