Algebraic Fractions Mastery for Year 8: Tips and Practice

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Explore algebraic fractions with Dr. J. Frost in this comprehensive guide for Year 8 students. Learn common mistakes to avoid and essential strategies for success in adding/subtracting algebraic expressions. Test your understanding and enhance your skills in working with fractions.

  • Algebraic Fractions
  • Year 8
  • Add/Subtract Fractions
  • Educational Resources
  • Mathematics Learning
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  1. Year 8: Algebraic Fractions Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 30th August 2015

  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 = 3? + 2 2 ? = 2? + 3 Fail Win!

  3. Starter (Click your answer) Are these algebraic steps correct? ?2? ? + ? ?? ? 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 ?2+ 2 = ? + 2 Fail Win! Win! Fail Win! 1 + r 2 pq(r+2) + 1 pq (2x+1)(x 2) x 2 Fail - 1 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. 2 ? ? = 2? + 1 2 ? = 3? + 1 Bro Tip #2: In a fraction, we can only divide top and bottom by something, not add/subtract. (e.g. 5 ?+? ?+? ? ? 7 is not the same as 6 8!)

  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. ? 3 ?+ ? 1=3 ? 1 + 2? ? ? 1 2 5? 3 ? ? 1 ? = ? If were to add 1 use 6 as the denominator because 2 3 = 6 is divisible by both 2 and 3. 2+1 3 say, then we could This gives us a clue what we could use as a denominator .

  13. Test Your Understanding ? + 12 ?2 ? ? + 1 ? + 1 ? ? 2? + 1 ? ? + 1 ? + 1= = ? ? 2 ?+ ? + 1=2 ? + 1 + 3? ?(? + 1) 3 5? + 2 ?(? + 1) = ? ? 1 ? + 3=1 ? + 3 3(? 1) (? 1)(? + 3) 3 2? + 6 (? 1)(? + 3) ? ? ? 1 = ? 1=1 1 1 ? ? ? 1 + 1+ ? 1= ? 1

  14. Exercise 2 1 +1 =? + 1 2?2 ?2 1 1 ? ? ? ? ? ? + 1+ ? 1 = ? 7 1 ?+1 =? + ? ?? 2 ? ? 3 =4? 7 ? 1 ? 8 4 ? 1 3 ?+? =6 + ?? 2? 3 ? 2 =?2+ ? ?2 ?(? + 1) ? ? ? 9 ? ? + 1 1 1 2 ? 4 ? + 1 ? 1 = ? 1 ? + 2 ? 2 10 (? + 1)(? 1) ? ? + 1 = ? + 1 ? 1 1 1 2? + 3 ? + 1 ? + 2 ? 5 ? + 1+ ? + 2 = 3?2+ 6? + 2 ?(? + 1)(? + 2) ? 1 ?+ 1 1 1 ? + 1+ ? + 2 = 2 1 ? + 12 ? + 4 ? 4 ? 6 ? 4 ? + 4 = 1 1 ? + 2 ? + 110 2 ? ? + 110+ ? + 19 =

  15. Extra Practice ? 2+? + 1 =5? + 2 1 ? 3 6 2 ? =6 ? 2 3 ? 3 ? + 1 2 5 3? 2 ? ? + 1 3 ? ? = ? 2 2 3 ? + 4 ? ? 2 4 ? ? = =?2+ ? + 4 2 ? + 1 ? 2+ 2 5 ? ? + 1 6 5 ?? 3 =5? + 5 3?? ?? ? + 1 ? ? + 1

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

  17. Test Your Understanding x2 2 4 3x =2x 2? + 1 3 ? + 4 =5 2? + 1 3 ? + 4 ? ? 3 5 3 ?2?3 ?5 = ???? ????

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

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

  20. Question 1 1 ?+3 ? Answer: 4 ?

  21. Question 2 ? 2+? 4 Answer: 3? 4

  22. Question 3 2 3+? + 1 9 Answer: ?+7 9

  23. Question 4 ? ?+? + 1 ?2 Answer: ??+?+1 ?2

  24. Question 5 1 ?+? ? Answer: ?+?2 ??

  25. Question 6 1 ?+ 1 ? + 2 Answer: 2?+2 ?(?+2) ?? 2?+2 ?2+2?

  26. Question 7 1 ?+1 ?+1 ? Answer: ??+??+?? ???

  27. Question 8 1 ? 3 Answer: 1 3?

  28. Question 9 2 1 ?2 Answer: 2?2

  29. Question 10 1 ? 1 ?2? Answer: ??

  30. Question 11 2 ? ?3 Answer: ?2 ?6

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