Invert and multiply. Fractions express a ratio of two quantities. For example, the fraction

Transcription

1 Appendi E: Mnipuling Fions Te ules fo mnipuling fions involve lgei epessions e el e sme s e ules fo mnipuling fions involve numes Te fundmenl ules fo omining nd mnipuling fions e lised elow Te uses of ese ules e illused moe ompleel le in is ppendi ) Adding fions d + + d d Suing fions d d d ) Mulipling fions d d d) Dividing fions d d d Inve nd mulipl Numeo nd denomino Fions epess io of wo quniies Fo emple, e fion epesses e io of quni o quni Te quni ppes on e op of e fion is lled e numeo In is se, e numeo is Te quni ppes on e oom of e fion is lled e denomino In is se, e denomino is Finding ommon denomino Adding nd suing fions usull equies ommon denomino, is, ll of e fions involved ve e sme denomino Emple E Find ommon denominos fo e following olleions of fions Epess e fions using is ommon denomino

2 ),, ), Soluion: ) Te ommon denomino is Te wo fions n e epessed mulipling o numeo nd denomino (op nd oom) weve fo is needed o onve e denomino o e ommon denomino A ommon denomino n lws e oined jus mulipling e of e denominos ogee A possile ommon denomino is ( ) Epessing e wo fions using is ommon denomino: Noe, oweve, ( ) Te signifine of is osevion is sine led s e denominos of o nd s fos So, is led ommon denomino fo o of ese fions nd ould e used insed of ) One w o oin ommon denomino is o jus mulipl e denominos of e wo fions, ogee Howeve, + + ( + ) Sine + is fo of + +, + + n e used s ommon denomino Epessing e wo fions using e ommon denomino + + : + +

3 Te dvnge of using + + s ommon denomino (e n, s, e moe ovious ( + ) ( + + ) ) is e fions ou oin using e ommon denomino e usull e simples possile Adding nd suing fions Fions n onl e dded nd sued wen e wo fions ve e sme denomined If e wo fions do no ve e sme denomino, en ommon denomino mus e found efoe e fions n e dded o sued Te neessi of finding ommon denomino is w e podu of e wo denominos (ie d) ppes in e ules epessed elow Epessed using lgei smols, e ules fo dding nd suing funions e: d d d d d d d d + d d d d Emple E Evlue nd simplif e of e lgei epessions ) + + ) d) Soluion: ) ( ) + ve e sme denomino) (Te wo fions led

4 ) ( + ) + ( + ) ( + ) ( + ) d) ( + ) + ( + ) ( + )( + ) ( + ) + ( + ) ( + ) ( + ) ( + ) Some fue simplifiions e possile in P (d) Fo emple, ou ould mulipl ou ll of e kes Te impon poin in P (d), oweve, is using e simples (o les ) ommon denomino, e lgei fom of e esul will e s simple s possile In e se of P (d), e simples ommon denomino is ( + )( + )( + ), e n e moe ovious ommon denomino ( + )( + )( + )( + ) Mulipling fions Mulipling wo fions is peps e mos sig-fowd of ll opeions You simpl mulipl e numeos nd mulipl e denominos Epessed using lgei smols, is ule is: d d Emple E Evlue nd simplif e following fions s mu s possile ) sin θ os θ sin θ os θ + θ θ Soluion: ) + + ( + ) + + / sin θ os θ sin θ os θ sin θ sin θ os θ os θ + θ θ θ Dividing fions Mn people ememe e ule fo dividing one fion noe ememeing ou mus inve e denomino nd mulipl Epessed s lgei smols, e ule is:

5 d d d Emple E4 Evlue o simplif e of e fions given elow ) + 4 / ) + + Soluion: ) / / ) Simplifing omplied fions Someimes, fions will ve oe fions in ei numeo o denomino (o o) To simplif nd evlue omplied fions, evlue e numeo nd denomino sepel, nd en divide e wo Emple E5 Simplif e of e omplied fions s mu s possile

6 ) + / ) Soluion: ) ( + ) ( + ) ( + ) / ( + ) / ( + ) + + ) ( + + ) ( 9 ) ( + ) Eeises fo Appendi E Fo Polems -0, evlue e quni wiou using lulo

7 z z Fo Polems -0, pefom e opeion indied Simplif ou nswes s mu s possile L+ w+ L L+ w ( ) q q + q /

8 sin θ os θ sin θ os θ + + Fo Polems -5, deide wee e of e semens e ue o flse Answes o Eeises fo Appendi E / /6 /4 4 (6 + )/(4) 5 (4 - )/(7) 6 ()/(6 7 7/( ) 8 / 9 (z)/ 0 /( - ) (L + wl + w + L)/(L + w)

9 ( - /( - 4 ( + )/(7 + ) 5 (q - )/(q + ) 6 (9-8)/(7-8) 7 ( + / + -/ )/( - ) 8 / 9 / 0 sin(θ ) + os(θ) Flse Tue Flse 4 Flse 5 Flse