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Year 8 – Algebraic Fractions

ζ. Dr Frost. Year 8 – Algebraic Fractions. Objectives: Be able to add and subtract algebraic fractions. Starter. (Click your answer). Are these algebraic steps correct?. 40 - x 3. 40 3. = x + 4. = 2x + 4. . Fail.  . Win!. 2(4) = 5x - 2. 2(4 – 2x) = 3x - 2. . Fail.  .

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Year 8 – Algebraic Fractions

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  1. ζ Dr Frost Year 8 – Algebraic Fractions Objectives: Be able to add and subtract algebraic fractions.

  2. Starter (Click your answer) Are these algebraic steps correct? 40 - x 3 40 3 = x + 4 = 2x + 4  Fail  Win! 2(4) = 5x - 2 2(4 – 2x) = 3x - 2  Fail  Win! √2 = 3x + 2 √(2 - x) = 2x + 3  Fail  Win!

  3. Starter (Click your answer) Are these algebraic steps correct? (x+3)2 x2 + 32  Fail  Win! (3x)2 32x2 9x2  Fail  Win!

  4. Starter (Click your answer) To cancel or not to cancel, that is the question? y2 + x 2 + x s(4 + z) s √(x2 + 2) = y + 2  Fail Win!  Fail  Win!  Fail  Win!  1 + r 2 pq(r+2) + 1 pq (2x+1)(x – 2) x – 2 - 1  Fail  Win!  Fail  Win! Fail  Win! 

  5. Adding algebraic fractions What’s our usual approach for adding fractions? ? The same principle can be applied to algebraic fractions. ?

  6. The Wall of Algebraic Fraction Destiny ? ? ? ? “To learn the secret ways of the ninja, simplify fraction you must.”

  7. Exercises ? 1 9 ? 15 ? 2 ? 16 ? ? 10 ? 3 17 ? 11 ? ? 4 ? 18 ? ? 12 5 ? 19 ? 13 ? 6 ? 14 7 ? 20 ? ? 21 ? 8 ?

  8. More Difficult Algebraic Fractions For most of the examples so far, we’ve considered numerators that don’t contain variables. But when we have variables, the principle is the same! Lowest Common Multiple of 3 and 4? 12 ? Lowest Common Multiple of 2x and 3x2? 6x2 ? Lowest Common Multiple of x and y? xy ? Lowest Common Multiple of x and x+1? x(x+1) ?

  9. Example Step 2: Whatever we multiplied the denominator by, we have to do the same to the numerator. ? ? ? ? Step 1: Identify the Lowest Common Multiple.

  10. Example Step 2: Whatever we multiplied the denominator by, we have to do the same to the numerator. ? ? ? ? Step 1: Identify the Lowest Common Multiple.

  11. Examples ? ? ? ? ? ?

  12. Exercises ? 1 ? 7 ? 2 ? 8 ? 3 9 ? ? 4 10 ? ? 5 11 ? ? 6

  13. Multiplying and Dividing Brackets y2 2 x 3 xy2 6 ? z2 4 x 3 3z2 4x ? × =  = ( )= x3 2 2 x6 4 ? x+1 3 x+2 4 4(x+1) 3(x+2) ?  =

  14. Exercises y3 2 x y xy2 2 ( ) ( ) ( ) ( ) ( ) ( ) 3x2y3 2z4 x+1 3y x+1 3y 3x y 2q5 z3 x y2 2 2 2 2 2 3 (x+1)2 9y2 (x+1)2 9y2 x2 y4 27x6y9 8z12 4q10 z6 9x2 y2 ? ? ? 1 = 7 = = = = = = 13 × x 2y x y x2 2y2 ? 8 ? 14 ? 2 = × 15 ? ? 9 x+1 x2 x y x+1 xy ? 3 = × 16 2x y z q 2qx yz 10 ? ? ? 4  = 17 x+1 y z+1 q q(x+1) y(z+1) ? 11 ? ? 5  = 18 q2 y+1 x q q3 x(y+1) 12 6 ? ? ?  =

  15. Head to Head vs Head Table 8 9 Rear Table 2 7 10 15 3 6 11 14 4 5 12 13

  16. Question 1 Answer:

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  18. Question 3 Answer:

  19. Question 4 Answer:

  20. Question 5 Answer:

  21. Question 6 Answer:

  22. Question 7 Answer:

  23. Question 8 Answer:

  24. Question 9 Answer:

  25. Question 10 Answer:

  26. Question 11 Answer:

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