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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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**Algebraic Operations**Simplest Form Adding / Sub Fractions Multiple / Divide Fractions www.mathsrevision.com Subject of Formula Harder Subject of Formula www.mathsrevision.com**1. Simplify the following fractions :**Starter Questions www.mathsrevision.com**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**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**Examples**Fraction in Simplest form 1 1 3 1 1 1 1 1 www.mathsrevision.com**Examples**Fraction in Simplest form 1 1 1 1 Exercise 1 Page 186 www.mathsrevision.com**What Goes In The Box ?**Simplify the following square roots: www.mathsrevision.com**1. Simplify the following fractions :**Starter Questions www.mathsrevision.com**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**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.**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.**Adding Algebraic Fractions**Example 1a Example 1b 3d d + 4 2 + d2 8 ÷d ÷2 4d ÷d ÷2 d2 www.mathsrevision.com**Adding Algebraic Fractions**Example 1a Example 1b 15 8 - 3m p - 20 pm www.mathsrevision.com**What Goes In The Box ?**Simplify the following square roots: www.mathsrevision.com**Adding / Subtracting Algebraic Fractions**Exercise 2 Page 200 www.mathsrevision.com**Starter Questions**Calculate the following : www.mathsrevision.com**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**Algebraic Fractions**Multiplication and division Example 1b Example 1a 1 1 1 a 2 2 www.mathsrevision.com**Algebraic Fractions**Multiplication and division Example 2b Example 2a 1 2 1 3 www.mathsrevision.com**What Goes In The Box ?**Simplify the following square roots: www.mathsrevision.com**Algebraic Fractions**Multiplication and division Exercise 3 Page 200 www.mathsrevision.com**Starter Questions**Calculate the following : www.mathsrevision.com**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**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**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**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**Starter Questions**Calculate the following : www.mathsrevision.com**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**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**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**What Goes In The Box ?**Change the subject to x. www.mathsrevision.com**Algebraic Fractions**The Subject of a Formula Exercise 6 Page 204 www.mathsrevision.com**Surds**S5 Int2 Simplifying a Surd Rationalising a Surd Conjugate Pairs www.mathsrevision.com**Starter Questions**S5 Int2 Use a calculator to find the values of : = 6 = 12 = 3 = 2 www.mathsrevision.com**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**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**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**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**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**Have a go !**Think square numbers S5 Int2 45 32 72 = 9 x 5 = 16 x 2 = 4 x 18 = 35 = 42 = 2 x 9 x 2 = 2 x 3 x 2 = 62 www.mathsrevision.com**What Goes In The Box ?**S5 Int2 Simplify the following square roots: (2) 27 (3) 48 (1) 20 = 25 = 33 = 43 (6) 3200 (4) 75 (5) 4500 = 305 = 402 = 53 www.mathsrevision.com**Starter Questions**S5 Int2 Simplify : = 2√5 = 3√2 = ¼ = ¼ www.mathsrevision.com**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**Second Rule**S5 Int2 Examples www.mathsrevision.com**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**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**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**Rationalising Surds**S5 Int2 Let’s try this one : Remember multiply top and bottom by root you are trying to remove www.mathsrevision.com**Rationalising Surds**S5 Int2 Rationalise the denominator www.mathsrevision.com**What Goes In The Box ?**S5 Int2 Rationalise the denominator of the following : www.mathsrevision.com

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