Get strted 25 Algeri frtions This unit will help you to work with lgeri frtions nd solve equtions. AO1 Flueny hek 1 Ftorise 2 2 5 2 25 2 6 5 d 2 2 6 2 Simplify 2 6 3 rs r s 2 d 8 2 y 3 6 y 2 3 Write s single frtion 3 5 1 4 2 1 6 1 3 2 4 Solve 2 2 15 0 2 2 5 1 0 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 1 2 3 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. 1 2 3 Simplify 2 3 4 2 12 Add 4 1 Solve 2 5 2 2 How onfident re you? Unit 2 Algeri frtions 7
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 2 2 3 2 4 3 Ftorise the numertor nd ftorise the denomintor. 2 2 3 2 4 3 ( )( 1) ( )( 1) Cnel identil epressions in the numertor nd denomintor. _ ( 3)( 1) Why? ( 3)( 1) Write without rkets. 3 3 1 Simplify 4 8 4( ) 2 2 ( 1) ( 1) 1 2 3 ( ) 2 Simplify 2 2 8 2 3 2 3 Simplify fully 2 16 2 5 4 Hint Ftorise, then nel. 2 2 3 2 2 2 10 25 2 5 2 5 5 ( ) 5 4 Simplify 2 2 6 8 2 1( 2) 12 4 2 2 15 Em-style question 5 Simplify fully 2 2 9 5 2 4 5 (3 mrks) Reflet How is simplifying lgeri frtions similr to simplifying numeril frtions? 8 Unit 2 Algeri frtions
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. _ 3 6 1 Ftorise 3( 2) 1 1 1 ( 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 3 1 ( ) 1 ( ) ( 1)( ) ( )( 3) 4 2 Hint 2 ( 4) 2 2 Hint LCM ( 1)( 3) 3 1 2 Write s single frtion. 2 5 1 2 ( ) 1 ( ) ( 5)( ) ( )( 1) 4 1 3 2 Unit 2 Algeri frtions 9
Skills oost 3 Simplify _ 3 3 1 2 4 5 8 2 3 3 1 d 5 4 1 2 2 4 Write s single frtion. _ 4 2 3 _ 5 10 2 6 Hint Ftorise first. 5 Add these frtions. 5 2 3 1 3 6 Sutrt these frtions. 3 2 1 2 1 2 5 3 2 1 d 4 1 1 Hint Epnd the rkets in the finl denomintor, to simplify. Em-style question 7 Write s single frtion in its simplest form. 2 1 2 3 (4 mrks) Reflet How is dding lgeri frtions similr to dding numeril frtions? 10 Unit 2 Algeri frtions
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 1 3 3 1 1 Worked em question Write the LHS s single frtion: 4 8 1 ( 3)( 1) Multiply oth sides y the denomintor. ( 3) ( 1) (4 8) ( )( ) ( 3) ( 1) Epnd the rkets. 4 8 2 2 3 Rerrnge so one side is 0. 0 2 6 5 See skills oost 2 Q3 Get rid of the denomintor. ( 3)( 1) 2 3 3 2 h 3 Solve y ftorising (or use the qudrti formul). 0 ( )( ) 5 or 1 Ftorise. Give oth solutions. 1 Solve 7 3 ( 1)( 3) 1 4 2 ( 2)( 3) 3 7 3 Hint Ftorise nd solve. 7 3 2 0 2 2 Solve 2 6 6 1 2 2 1 2 Give your nswer to 2 d.p. Hint Use the qudrti formul. Em-style question 3 Solve 9 2 _ 3 2 2 (4 mrks) Reflet Why do these equtions eh hve two possile solutions? Unit 2 Algeri frtions 11
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. _ 2 1 4 4 A B C D 4 8 4 (2 1)( 4) 2 1 4( 4) (2 1)( 4) 4 2 1 (2 1)( 4) 4 8 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 2 1 2(2 1) 3( ) ( 1)(2 1) 4 2 ( 1)(2 1) 2 Simplify fully 2 4 4 2 5 2 4 5 _ 3 4 2 2 49 2 6 7 5 5 2( ) (3 4)( 5) d 2 3 2 6 Em-style question 3 Simplify fully 5 2 25 (3 mrks) 4 Write s single frtion in its simplest form. 2 3 2 3 6 5 1 Em-style questions 5 Simplify fully 2 2 11 21 _ 2 6 7 6 Write s single frtion 2 5 3 2 1 7 Solve this eqution 7 2 4. Give your nswer to 2 deiml ples. 1 (4 (3 mrks) (4 mrks) mrks) 12 Unit 2 Algeri frtions
Get k on trk Prolem-solve! Em-style question 1 Simplify fully 2 3 ( 3) 2 (2 mrks) 2 Simplify these epressions, where possile. 5 25 8 3 10 2 y 3y y 2 d 4 2 2 8 3 Write s single frtion 1 1 e 4 2 9 2 2 3 1 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 1 3 2 1 2 Give your nswer in surd form. 5 2 6 Solve the eqution 3 7 7 Solve 2 6 2 9 14 21 (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