1 / 29

Year 8: Algebraic Fractions

Year 8: Algebraic Fractions. Dr J Frost (jfrost@tiffin.kingston.sch.uk). Last modified: 11 th June 2013. 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.  .

edana
Download Presentation

Year 8: Algebraic Fractions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Year 8: Algebraic Fractions Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 11th June 2013

  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!  Fail  Win!

  3. Starter (Click your answer) Are these algebraic steps correct?  Fail  Win!

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

  5. Starter To cancel or not to cancel, that is the question? (Click your answer) y2 + x 2 + x s(4 + z) s  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!

  6. What did we learn? Bro Tip #1: You can’t add or subtract a term which is ‘trapped’ inside a bracket, fraction or root.  Bro Tip #2: In a fraction, we can only divide top and bottom by something, not add/subtract. (e.g. is not the same as !) 

  7. Adding/Subtracting Fractions What’s our usual approach for adding fractions? ? Sometimes we don’t need to multiply the denominators. We can find the Lowest Common Multiple of the denominators. ? ?

  8. Adding/Subtracting Algebraic Fractions The same principle can be applied to algebraic fractions. ! ? ? Bro Tip: Notice that with this one, we didn’t need to times x and x2 together: x2 is a multiple of both denominators.

  9. Further Examples ? ? ? Bro Tip: Be careful with your negatives!

  10. Test Your Understanding ? ? ? ? ? “To learn the secret ways of the ninja, add fractions you must.”

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

  12. Harder Questions We can do a cross-multiplication type thing just as before. ? ? ? If were to add say, then we could use 6 as the denominator because is divisible by both 2 and 3. This gives us a clue what we could use as a denominator .

  13. Test Your Understanding ? ? ? ? ? ? ? ?

  14. Exercise 2 ? 1 ? 7 ? 2 ? 8 ? 3 9 ? ? 4 ? 10 ? 5 ? N1 6 ? ? N2

  15. Multiplying and Dividing The same rules apply as with normal fractions. y2 2 x 3 xy2 6 ? z2 4 x 3 3z2 4x ? × =  = x+1 3 x+2 4 4(x+1) 3(x+2) ? ?  =

  16. Test Your Understanding 2x+1 3 y+4 5 5(2x+1) 3(y+4) ? x2 2 4 3x 2x 3 ?  = × = ( )= x2y3 z5 3 x6y9 z15 ?

  17. Exercise 3 y3 2 x y xy2 2 ( ) ( ) ( ) ( ) ( ) ( ) 3x2y3 2z4 x+1 3y x+1 3y 3x y 2q5 z3 x y2 2 2 2 3 2 2 (x+1)2 9y2 (x+1)2 9y2 x2 y4 9x2 y2 27x6y9 8z12 4q10 z6 ? ? ? 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 ? ? ?  =

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

  19. Question 1 Answer:

  20. Question 2 Answer:

  21. Question 3 Answer:

  22. Question 4 Answer:

  23. Question 5 Answer:

  24. Question 6 Answer:

  25. Question 7 Answer:

  26. Question 8 Answer:

  27. Question 9 Answer:

  28. Question 10 Answer:

  29. Question 11 Answer:

More Related