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Algebraic Operations

Algebraic Operations. Simplest Form. Adding / Sub Fractions. Multiple / Divide Fractions. www.mathsrevision.com. Subject of Formula. Harder Subject of Formula. 1. Simplify the following fractions :. Starter Questions. Algebraic Operations. Learning Intention. Success Criteria.

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Algebraic Operations

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  1. Algebraic Operations Simplest Form Adding / Sub Fractions Multiple / Divide Fractions www.mathsrevision.com Subject of Formula Harder Subject of Formula www.mathsrevision.com

  2. 1. Simplify the following fractions : Starter Questions www.mathsrevision.com

  3. Algebraic Operations Learning Intention Success Criteria • To explain how to simplify algebraic fractions. • Understand term • Highest Common Factor. • 2. Simplify algebraic fractions by identifying HCF. www.mathsrevision.com www.mathsrevision.com

  4. We can sometimes reduce fractions to a simpler form if the numerator and denominator have a number or letter in common. Fraction in Simplest form Examples HCF = Y HCF = 3 www.mathsrevision.com

  5. Examples Fraction in Simplest form 1 1 3 1 1 1 1 1 www.mathsrevision.com

  6. Examples Fraction in Simplest form 1 1 1 1 Exercise 1 Page 186 www.mathsrevision.com

  7. What Goes In The Box ? Simplify the following square roots: www.mathsrevision.com

  8. 1. Simplify the following fractions : Starter Questions www.mathsrevision.com

  9. Algebraic Operations Learning Intention Success Criteria • To explain how to add and subtract algebraic fractions. • Know how to add and sub simple fractions • 2. Apply same knowledge to add and sub algebraic fractions. www.mathsrevision.com www.mathsrevision.com

  10. Harder Fractions Step 1 : Do the smile Step 2 : Do the kiss 4 2 + 8 Example 1 Step 3 : Add/Subtract the numerator and simplify ÷2 ÷2 Compiled by Mr. Lafferty Maths Dept.

  11. Harder Fractions Step 1 : Do the smile Step 2 : Do the kiss 25 6 - 30 Example 1 Step 3 : Add/Subtract the numerator and simplify Compiled by Mr. Lafferty Maths Dept.

  12. Adding Algebraic Fractions Example 1a Example 1b 3d d + 4 2 + d2 8 ÷d ÷2 4d ÷d ÷2 d2 www.mathsrevision.com

  13. Adding Algebraic Fractions Example 1a Example 1b 15 8 - 3m p - 20 pm www.mathsrevision.com

  14. What Goes In The Box ? Simplify the following square roots: www.mathsrevision.com

  15. Adding / Subtracting Algebraic Fractions Exercise 2 Page 200 www.mathsrevision.com

  16. Starter Questions Calculate the following : www.mathsrevision.com

  17. Algebraic Operations Multiplication and division Learning Intention Success Criteria • To explain how to multiply and divide by algebraic fractions. • Know rules for multiplication and division of simple fractions. • 2. Apply knowledge to algebraic fractions. www.mathsrevision.com www.mathsrevision.com

  18. Algebraic Fractions Multiplication and division Example 1b Example 1a 1 1 1 a 2 2 www.mathsrevision.com

  19. Algebraic Fractions Multiplication and division Example 2b Example 2a 1 2 1 3 www.mathsrevision.com

  20. What Goes In The Box ? Simplify the following square roots: www.mathsrevision.com

  21. Algebraic Fractions Multiplication and division Exercise 3 Page 200 www.mathsrevision.com

  22. Starter Questions Calculate the following : www.mathsrevision.com

  23. Algebraic Operations The Subject of a Formula Learning Intention Success Criteria • To explain how to change the subject of a formula using • “change side change sign” • method. • Know change sign change sign for solving equations. • 2. Apply knowledge to change subject of a formula. www.mathsrevision.com www.mathsrevision.com

  24. Algebraic Fractions The Subject of a Formula The formula below is used to work out the circumference of a circle Since the formula works out C , then C is called the subject of the formula. www.mathsrevision.com

  25. Algebraic Fractions The Subject of a Formula We can make D the subject of the formula by using the rule “ change side change side “ www.mathsrevision.com

  26. What Goes In The Box ? Make y the subject of the formulae below : -x + 2y = 2 x + y = 8 y = 8- x x = 4( y + 1 ) x = y - 9 y = x + 9 Exercise 4 Page 202 www.mathsrevision.com

  27. Starter Questions Calculate the following : www.mathsrevision.com

  28. Algebraic Operations The Subject of a Formula Learning Intention Success Criteria • To explain how to change the subject of a formula containing square and square root terms. • Know change sign change sign for solving equations. • 2. Apply knowledge to change subject of harder formulae including square and square root terms. www.mathsrevision.com www.mathsrevision.com

  29. Algebraic Fractions The Subject of a Formula Example : The force of the air against a train is given by the formula below. Make the speed (S) the subject of the formula. www.mathsrevision.com

  30. Algebraic Fractions The Subject of a Formula Example : The thickness of a rope T cm to lift a weight W tonnes can be worked out by the formula below. Make W the subject of the formula. www.mathsrevision.com

  31. What Goes In The Box ? Change the subject to x. www.mathsrevision.com

  32. Algebraic Fractions The Subject of a Formula Exercise 6 Page 204 www.mathsrevision.com

  33. Surds S5 Int2 Simplifying a Surd Rationalising a Surd Conjugate Pairs www.mathsrevision.com

  34. Starter Questions S5 Int2 Use a calculator to find the values of : = 6 = 12 = 3 = 2 www.mathsrevision.com

  35. The Laws Of Surds S5 Int2 Learning Intention Success Criteria • To explain what a surd is and to investigate the rules for surds. • Learn rules for surds. • Use rules to simplify surds. www.mathsrevision.com www.mathsrevision.com

  36. What is a Surd S5 Int2 = 12 = 6 The above roots have exact values and are called rational These roots do NOT have exact values and are called irrational OR Surds www.mathsrevision.com

  37. Adding & Subtracting Surds Note : √2 + √3 does not equal √5 S5 Int2 Adding and subtracting a surd such as 2. It can be treated in the same way as an “x” variable in algebra. The following examples will illustrate this point. www.mathsrevision.com

  38. First Rule S5 Int2 Examples List the first 10 square numbers 1, 2, 4, 9, 16, 25, 36, 49, 64, 81, 100 www.mathsrevision.com

  39. Simplifying Square Roots S5 Int2 Some square roots can be broken down into a mixture of integer values and surds. The following examples will illustrate this idea: To simplify 12 we must split 12 into factors with at least one being a square number. 12 = 4 x 3 Now simplify the square root. = 2 3 www.mathsrevision.com

  40. Have a go ! Think square numbers S5 Int2  45  32  72 = 9 x 5 = 16 x 2 = 4 x 18 = 35 = 42 = 2 x 9 x 2 = 2 x 3 x 2 = 62 www.mathsrevision.com

  41. What Goes In The Box ? S5 Int2 Simplify the following square roots: (2)  27 (3)  48 (1)  20 = 25 = 33 = 43 (6)  3200 (4)  75 (5)  4500 = 305 = 402 = 53 www.mathsrevision.com

  42. Starter Questions S5 Int2 Simplify : = 2√5 = 3√2 = ¼ = ¼ www.mathsrevision.com

  43. The Laws Of Surds S5 Int2 Learning Intention Success Criteria • To explain how to rationalise a fractional surd. • Know that √a x √a = a. • 2. To be able to rationalise the numerator or denominator of a fractional surd. www.mathsrevision.com

  44. Second Rule S5 Int2 Examples www.mathsrevision.com

  45. Rationalising Surds S5 Int2 You may recall from your fraction work that the top line of a fraction is the numerator and the bottom line the denominator. Fractions can contain surds: www.mathsrevision.com

  46. Rationalising Surds S5 Int2 If by using certain maths techniques we remove the surd from either the top or bottom of the fraction then we say we are “rationalising the numerator” or “rationalising the denominator”. Remember the rule This will help us to rationalise a surd fraction www.mathsrevision.com

  47. Rationalising Surds S5 Int2 To rationalise the denominator multiply the top and bottom of the fraction by the square root you are trying to remove: ( 5 x 5 =  25 = 5 ) www.mathsrevision.com

  48. Rationalising Surds S5 Int2 Let’s try this one : Remember multiply top and bottom by root you are trying to remove www.mathsrevision.com

  49. Rationalising Surds S5 Int2 Rationalise the denominator www.mathsrevision.com

  50. What Goes In The Box ? S5 Int2 Rationalise the denominator of the following : www.mathsrevision.com

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