Algebraic fractions. This unit will help you to work with algebraic fractions and solve equations. rs r s 2. x x.

Transcription

1 Get strted 25 Algeri frtions This unit will help you to work with lgeri frtions nd solve equtions. AO1 Flueny hek 1 Ftorise d Simplify rs r s 2 d 8 2 y 3 6 y 2 3 Write s single frtion Solve Key points An lgeri frtion is frtion with letter terms in the numertor or the denomintor or oth. You n simplify, dd, sutrt, multiply nd divide lgeri frtions using the sme methods s with numer frtions. These skills oosts will help you to work with lgeri frtions nd solve equtions. Simplifying lgeri frtions Adding nd sutrting lgeri frtions Solving equtions involving lgeri frtions You might hve lredy done some work on lgeri frtions. Before strting the first skills oost, rte your onfidene using eh onept Simplify Add 4 1 Solve How onfident re you? Unit 2 Algeri frtions 7

2 Skills oost 1 Simplifying lgeri frtions To simplify n lgeri frtion: ftorise the numertor nd ftorise the denomintor divide the numertor nd denomintor y ny ommon ftors. Guided prtie _ Simplify Ftorise the numertor nd ftorise the denomintor ( )( 1) ( )( 1) Cnel identil epressions in the numertor nd denomintor. _ ( 3)( 1) Why? ( 3)( 1) Write without rkets Simplify 4 8 4( ) 2 2 ( 1) ( 1) ( ) 2 Simplify Simplify fully Hint Ftorise, then nel ( ) 5 4 Simplify ( 2) Em-style question 5 Simplify fully (3 mrks) Reflet How is simplifying lgeri frtions similr to simplifying numeril frtions? 8 Unit 2 Algeri frtions

3 Skills oost 2 Adding nd sutrting lgeri frtions To dd or sutrt lgeri frtions: ftorise if possile find the lowest ommon multiple (LCM) of the denomintors write equivlent frtions with this LCM s denomintor. Guided prtie Write s single frtion in its simplest form. _ Ftorise 3( 2) ( 1) 3( 2 )( 1) 3( 2 ) 1 3( 2 )( 1) Epnd the rkets 3( 2 )( 1) 3 3( 2 )( 1) Add 4 7 3( 2 )( 1) Find the LCM of the denomintors: 3( 2)(h h) Write equivlent frtions with this LCM s the denomintor. Why? 1 3( 2 )( 1) 3( 2) 3( 2 )( 1) 3( 2) _ 1 1 Write s single frtion in its simplest form ( ) 1 ( ) ( 1)( ) ( )( 3) 4 2 Hint 2 ( 4) 2 2 Hint LCM ( 1)( 3) Write s single frtion ( ) 1 ( ) ( 5)( ) ( )( 1) Unit 2 Algeri frtions 9

4 Skills oost 3 Simplify _ d Write s single frtion. _ _ Hint Ftorise first. 5 Add these frtions Sutrt these frtions d Hint Epnd the rkets in the finl denomintor, to simplify. Em-style question 7 Write s single frtion in its simplest form (4 mrks) Reflet How is dding lgeri frtions similr to dding numeril frtions? 10 Unit 2 Algeri frtions

5 Skills oost 3 Solving equtions involving lgeri frtions To solve equtions involving lgeri frtions: write frtion lultions s single frtion multiply oth sides y the denomintor solve the resulting eqution. Guided prtie Solve Worked em question Write the LHS s single frtion: ( 3)( 1) Multiply oth sides y the denomintor. ( 3) ( 1) (4 8) ( )( ) ( 3) ( 1) Epnd the rkets Rerrnge so one side is See skills oost 2 Q3 Get rid of the denomintor. ( 3)( 1) h 3 Solve y ftorising (or use the qudrti formul). 0 ( )( ) 5 or 1 Ftorise. Give oth solutions. 1 Solve 7 3 ( 1)( 3) ( 2)( 3) Hint Ftorise nd solve Solve Give your nswer to 2 d.p. Hint Use the qudrti formul. Em-style question 3 Solve 9 2 _ (4 mrks) Reflet Why do these equtions eh hve two possile solutions? Unit 2 Algeri frtions 11

6 Get k on trk Prtise the methods Answer this question to hek where to strt. Chek up Write s single frtion Tik the orret working. _ A B C D (2 1)( 4) 2 1 4( 4) (2 1)( 4) (2 1)( 4) (2 1)( 4) If you tiked A go to Q2. If you tiked B, C or D go to Q1 for more prtie. 1 Write s single frtion (2 1) 3( ) ( 1)(2 1) 4 2 ( 1)(2 1) 2 Simplify fully _ ( ) (3 4)( 5) d Em-style question 3 Simplify fully (3 mrks) 4 Write s single frtion in its simplest form Em-style questions 5 Simplify fully _ Write s single frtion Solve this eqution Give your nswer to 2 deiml ples. 1 (4 (3 mrks) (4 mrks) mrks) 12 Unit 2 Algeri frtions

7 Get k on trk Prolem-solve! Em-style question 1 Simplify fully 2 3 ( 3) 2 (2 mrks) 2 Simplify these epressions, where possile y 3y y 2 d Write s single frtion 1 1 e Sustitute your nswer from prt into 1 1 then, y tking the reiprol of oth sides, find. Em-style questions 4 Sory uses the formul 1 R T 1 R 1 1 R 2 to find the totl resistne R T of iruit when two resistors R 1 nd R 2 re onneted in prllel. Mke R T the sujet of the formul. Mke R 2 the sujet of the formul. 5 Solve the eqution Give your nswer in surd form Solve the eqution Solve (2 mrks) (2 mrks) (4 mrks) (4 mrks) (5 mrks) Now tht you hve ompleted this unit, how onfident do you feel? 1 Simplifying 2 Adding nd sutrting 3 lgeri frtions lgeri frtions Solving equtions involving lgeri frtions Unit 2 Algeri frtions 13