Simplify algebraic fractions into the lowest terms

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Presentation transcript:

Simplify algebraic fractions into the lowest terms Objective Simplify algebraic fractions into the lowest terms Terms and Conditions: To the best of the producer's knowledge, the presentation’s academic content is accurate but errors and omissions may be present and Brain-Cells: E.Resources Ltd cannot be held responsible for these or any lack of success experienced by individuals or groups or other parties using this material. The presentation is intended as a support material for GCSE maths and is not a comprehensive pedagogy of all the requirements of the syllabus. The copyright proprietor has licensed the presentation for the purchaser’s personal use as a teaching and learning aid and forbids copying or reproduction in part or whole or distribution to other parties or the publication of the material on the internet or other media or the use in any school or college that has not purchased the presentation without the written permission of Brain-Cells: E.Resouces Ltd.

12 15 What do we mean by ‘write in the lowest terms’ or ‘simplify’? You can see that 12/15 is equal to 4/5 Here is how to do this with numbers

What do we mean by ‘write in the lowest terms’ or ‘simplify’? 12 15  4 x 3 5 x 3 Cancel out common factors Factorise top and bottom

The remaining numbers give the fraction in its lowest terms What do we mean by ‘write in the lowest terms’ or ‘simplify’? 12  4 x 3 15 5 x 3  4 5 The remaining numbers give the fraction in its lowest terms

We can use the same method to simplify algebraic fractions into the lowest terms. x2 2x3  x x x 2 x x x x x x  1 2x This gives… Factorise… Cancel common terms…

Simplify these algebraic fractions  y 4 2a2 a3  2 a 8h 4h2  2 h 3t3 6t  t2 2

x2 + 3x – 10 5 x -2 = -10 5 + -2 = 3 (x + 5)(x – 2) x2 + 3x x(x + 3) Sometimes, the fractions will have quadratics as the numerator and/or denominator. You will need to factorise these and to refresh your memory, below are examples of how three different types of quadratic are factorised. x2 + 3x – 10 5 x -2 = -10 5 + -2 = 3 (x + 5)(x – 2) x2 + 3x x(x + 3) x2 - 16 (x + 4)(x – 4) Common factor of x Difference between two squares Finding two numbers that have a product of -10 and sum of +3

x2 + 2x x2 - 4 x(x + 2) (x + 2)(x - 2) x (x – 2)   Here is an example of how to simplify the algebraic fraction below: Cancel common terms The top terms have a common factor of x x2 + 2x x2 - 4 x(x + 2) (x + 2)(x - 2) x (x – 2)   The bottom is the difference between two squares This is the fraction in its lowest terms

x2 - 9 x2 + x - 6 (x + 3)(x – 3) (x + 3)(x - 2) x - 3 x - 2   Another example of how to simplify a slightly more difficult the algebraic fraction: The top is the difference between two squares Cancel common terms x2 - 9 x2 + x - 6 (x + 3)(x – 3) (x + 3)(x - 2) x - 3 x - 2   Factorise the bottom by finding two numbers that have a product of -6 and sum of 1 This give the fraction in its lowest terms

Write these algebraic fraction in the simplest terms: 1. x2 + 4x x2 - 16 2. x2 - 9 x2 – 3x 3. x2 + 5x + 6 x2 + 3x 4. x2 + 5x x2 - 25 5. x2 - 16 x2 – 3x - 4 6. x2 - x - 12 x2 – 9 7. x2 + 7x + 10 x2 - 2x - 8 8. x2 + x - 6 x2 + 8x + 15 9. x2 - 5x - 6 x2 – 4x - 12

Here are the answers: 1. x x - 4 2. x + 3 x 3. x + 2 x 4. x x - 5 5. x + 4 x + 1 6. x - 4 x – 3 7. x + 5 x - 4 8. x - 2 x + 5 9. x + 1 x + 2