Year 8: Algebraic Fractions

Year 8: Algebraic Fractions Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 11th 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  Win!  Fail  Win!

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

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

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!

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 !) 

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. ? ?

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.

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

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

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

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 .

Test Your Understanding ? ? ? ? ? ? ? ?

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

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) ? ?  =

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 ?

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 ? ? ?  =

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

Question 1 Answer:

Year 8: Algebraic Fractions