ALGEBRAIC OPERATIONS. A. Reducing algebraic fractions to their simplest form

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1 ALGEBRAIC OPERATIONS A. Reducing lgebric frctions to their simplest form Students should be shown the method for Ôcncelling downõ vulgr frction, then frctions with letters cn be introduced. * Before this eercise some revision of fctoristion my be necessry. Emple Simplify / Emple Simplify / / / 7 / / y Emple Simplify p pq Emple Simplify p y y y y p pq p(p q) p p p q Note the fctoristion in the numertor! Eercise Questions nd my now be ttempted. The following two emples could be used to illustrte the need for fctorising the numertor nd/or denomintor before cncelling. Emple Simplify v Emple Simplify v v v (v )(v ) v v ( )( ) ( )( ) ( ) ( ) Eercise Question my now be ttempted. B. Applying the four rules to lgebric frctions The following eight emples cn be used to illustrte the four rules. It my be tht dditionl emples will be required to be shown to the clss in order to reinforce the method. Emple Simplify Emple Simplify b 8 b b 8 b b b contd. Mthemtics Support Mterils: Mthemtics (Int ) Stff Notes

2 Emple Simplify Emple Simplify c c d d c c d d c d d c / (by cncelling) c (by cncelling) Eercise Questions nd my now be ttempted. Emple Simplify Emple Simplify 8 / / Emple 7 Simplify r s Emple 8 Simplify r s v 8r s w 8r s w v v w v w Eercise Questions nd my now be ttempted. Emple Simplify ( ) 8 7 ( ) Eercise Question my now be ttempted. This emple should be followed by the simplifiction of Mthemtics Support Mterils: Mthemtics (Int ) Stff Notes

3 ALGEBRAIC OPERATIONS A. Reducing lgebric frctions to their simplest form Eercise. Simplify these frctions: () (b) (c) 8 (d) 0 00 p p v w rs rt (j) b c (k) d (l) m m (m) (n) 8z z (o) (p) d d (q) (r) v w (s) 8y (t) b (u) pq p (v) b b (w) yz z () ef 7ef (y) pq pq (z) 8y y () (b) - -. Fctorise either the numertor or the denomintor, then simplify: 8 () (b) (c) y (j) - pq p p (k) v v v. Fctorise the numertor nd/or the denomintor, then simplify: c () (b) (c) d - c d - (d) (l) (d) g g g y y p q 7p 7q - w - w - y 8-8y - - (j) y - y (k) - - (l) w w - 0 (m) - (n) v -v- v - (o) y y- y y- (p) - -8 Mthemtics Support Mterils: Mthemtics (Int ) Student Mterils

4 B. Multiplying, dividing, dding nd subtrcting lgebric frctions Eercise. Simplify these frctions by multiplying: () (b) (c) (d) c b d (j) v (k) m m (l) b y w n n b (m) (n) (o) (p) n 7 (q) (r) d (s) c (t) c n. Chnge these divisions to multiplictions nd simplify: () (b) 8 (c) (d) d d m m 8 0 (j) (k) (l) b b r r b b (m) (n) (o) (p) d d w w y d (q) b b (r) d d. Do the following dditions nd subtrctions: () (b) (c) (d) 7 (j) (k) (l) 8 7 c d (m) e h (n) m n (o) k (p) u w 8 (q) r s (r) d (s) (t) y u Mthemtics Support Mterils: Mthemtics (Int ) Student Mterils

5 . By finding common denomintor with letters, work out these dditions/subtrctions: () (b) (c) (d) y b c d p q 7 8 v w g h k n y. Add or subtrct these frctions: () (b) (c) (d) C. Chnging the subject of formul Eercise A This eercise hs mied selection of formule. Chnge the subject of ech formul to the letter shown in the brckets. ALL WORKING nd ALL STEPS SHOULD BE SHOWN.. c (). c (). p q (). p q (). / (). / 7 () 7. / y () 8. / p m (). / r s (). 0 (). (). g h (). n t (). (). b (). c b () 7. c b () 8. p q r (). v w y () 0. D S T (S). C pd (d). (). y (). A pr (r). T D / S (S). A y (y) 7. P pr (p) 8. P pr (r). h p q 0. h p q (p). h p q. h p q (p). b c () Eercise B. Chnge the subject of ech formul to h. () g hf (b) e g h (c) k h /f(d) e g h. Chnge the subject of ech formul to r. () Q r (b) N pr (c) M pr (d) P pr w Mthemtics Support Mterils: Mthemtics (Int ) Student Mterils

6 ANSWERS Algebric opertions Eercise. () / (b) / (c) / (d) / / / / v /w s /t (j) b /c (k) /d (l) /m (m) / (n) 8 /z (o) (p) /d (q) / (r) v / w (s) y (t) / b (u) q / (v) /b (w) y () / 7 (y) / q (z) /y () /( ) (b) /( ). () (b) (c) (d) y (j) q (k) v (l). () (b) (c) / (d) g / / 7 /8 (j) y (k) (l) v y /(w ) (m) (n) v (o) y (p) Eercise. () / (b) / (c) / (d) 7 / / c /bd (j) v /yw (k) m (l) (m) (n) (o) (p) (q) n 7 /d (r) (s) (t). () / (b) / (c) / (d) / / / (j) b / (k) r / (l) (m) d (n) / w (o) / (p) d / y (q) (r) /. () 7 / (b) / (c) / 0 (d) 8 / / / 7 / / / 8 (j) / (k) (l) c d (m) e h (n) m n (o) k 8 (p) u w (q) 8r s (r) d (s) y (t) 8u 0. () y (b) b (c) d c (d) q p y b cd pq w v Mthemtics Support Mterils: Mthemtics (Int ) Student Mterils

7 h g gh 7n k kn y 8 y. () (b) 0 (c) 7 (d) 8 7 Eercise A. c. c. q p. q p y 8. mp. rs.. /. h /g. t /n.. b. b c 7. b c 8. r p q. y v w 0. S D /T. d C /p. or. Öy or Öy. r Ö( A /p). S D /T. y ÖA (or ÖA) 7. p P /r 8. r Ö( P /p). h q p 0. p h q. h q p. p h q. b c Eercise B. () h g /f (b) h e g (c) h kf (d) h g e. () r ÖQ (b) r Ö( N /p) (c) r Ö( M /p) (d) r Ö( P /pw). () M A /kl (b) m B /K (c) m c /pr (d) m /pd. () p q (b) s r (c) (s r) / (d) (r ) /7 (m ) / m n p q. () P QR (b) s /t (c) Q Ö( P /M) (d) w v z f e /d n K /mt s Ö( 7 /r) Ö(c b ). () T V / (d) (b) r /(p q) (c) c /( b) (d) r /(m ) w (v v) / ( ) r (p ) Eercise. () Ö (b) Ö (c) Ö (d) Ö Ö Ö7 Ö Ö Ö (j) Ö (k) Ö (l) Ö (m) Ö (n) 7Ö (o) Ö (p) Ö (q) 0Ö (r) Ö Mthemtics Support Mterils: Mthemtics (Int ) Student Mterils 0