Fractions and Equations

Transcription

1 Frctios d Eqtios Remider of frctios We he sed frctios with mers efore: Add or strct: Chge to commo deomitor + chge oth frctios to commo deomitor of Mltipl: Ccel dow, if o c, the mltipl tops (mertors), mltipl ottoms (deomitors). ccel dow 9 8 mltipl Diide: Iert (tr pside dow) the secod frctio, chge sig to mltipl. 0 iert d frctio d chge sig to mltipl Now tret s mltiplictio. Ccel dow. mltipl: 7 0 Mied mers: If ddig or strctig, del with whole mer prts seprtel. whole mer prt first: + the s preiosl, sig commo deomitor of ow del with frctio: 6 0 +

2 Mied mers: If mltiplig or diidig, YOU MUST CHANGE THE MIXED NUMBERS TO IMPROPER (Top He) FRACTIONS. chge to improper frctios: 7 Ccel dow, where o c. 7 d mltipl 7 chge to improper frctios: iert d chge to mltipl: mltipl Chgig from frctio to mied mer: To chge improper (top he) frctio to mied mer: Diide the top (mertor) the ottom (deomitor) 9 ecse: 7 ecse: Chgig from mied mer to frctio: To chge mied mer to improper (top he) frctio: Mltipl the whole mer prt the deomitor d dd o the mertor. 8 ecse: ecse: = =

3 Algeric Frctios: Simplifig frctios: Diide the mertor d deomitor commo fctor so, 0 More emples: diide commo fctor diide commo fctor 6 6 diide commo fctor 6 diide commo fctor Tkig ot commo fctor first: m + 6 tke ot commo fctor ( m + ) ( m + ) m + + tke ot commo fctor ( + ) + + ( ) More ioled fctors ( + )( ) ( ) diide commo fctor ( ) ( + ) ( ) ( ) + ( t )( t + ) ( t + )( t ) diide commo fctor ( t + ) ( t ) ( t + ) t ( t + ) ( t ) t

4 Frther fctoristio: fctorise top ( + ) + ccel ( + ) + d + d d + fctorise top d( d + ) d + ccel d ( d + ) d + d t + t + fctorise ( t + ) ( t + ) ccel ( t + ) ( t ) + m m m fctorise m( m ) ( m ) ccel m ( m ) ( m ) m Usig differece of two sqres: fctorise ( + )( ) ccel ( + ) ( ) + m 9 m + fctorise ( m + )( m ) m + ccel ( m + ) m + ( m ) m Tr these: (coer p the swers o the right first) ( + ) + 0 ( + ) ( )( ) + d d + d + d ( + ) ( + ) d d d d d d d + ( + ) +

5 Algeric Frctios: Mltiplictio: The sme rles ppl s with mers: Ccel dow, if o c, the mltipl tops (mertors), mltipl ottoms (deomitors). m p othig will ccel so mltipl r m pr t ccel the mltipl t t k ccel the mltipl k k ccel the mltipl ccel the mltipl Diisio: The sme rles ppl s with mers: Iert (tr pside dow) the secod frctio, chge sig to mltipl. iert, ccel, mltipl iert, ccel, mltipl iert, ccel, mltipl iert, ccel, mltipl iert, ccel, mltipl iert, ccel, mltipl

6 Tr these: (coer p the swers o the right first) z z z 6 m m p r p r p t t t t t m m m p q p q p q pq q p t 7 t 7 t

7 Algeric Frctios: Additio d strctio: The sme rles ppl s with mers: Chge to commo deomitor + se commo deomitor of se commo deomitor of + se commo deomitor of se commo deomitor of m m m m m m m m m m + + se commo deomitor of 6 + ( + ) ( ) se commo deomitor of se commo deomitor of se commo deomitor of ( ) ( ) ( ) ( ) ( ) p p + se commo deomitor of p( p + ) ( + ) + ( ) ( ) ( ) p + p p p 7 p p p + p + p p p + p p + p p +

8 Eqtios with Frctios: A method: Remoe frctios Remoe rckets Use these rles: dd or strct the sme mer o ech side mltipl or diide ech side the sme mer. = mltipl oth sides 6 (l.c.m. of d ) 6 = 6 = which we c sole: = = = ( ) mltipl oth sides = ( ) ( ) = which we c sole: = = = = mltipl oth sides = = 0 which we c sole: = 0 = = mltipl oth sides = 6 ( ) = 0 9 = 0 = 9 = = mltipl oth sides = ( ) ( ) = = 8 + = 8 = = ( + ) = mltipl oth sides ( + ) = ( ) 9 + = 9 = = = 6 =

9 Some Pst Pper Qestios: Algeric Frctios. Epress s sigle frctio i its simplest form, 0. Epress s sigle frctio i its simplest form +, 0. Epress s sigle frctio i its simplest form, 0 or ( ) Soltios: ( ) ( ) ( ) ( ) ( ) More pst pper qestios o et pge

10 Some Pst Pper Qestios: Frctio Eqtios. Sole the eqtio. Sole the eqtio + = + + =, where is rel mer.. Sole lgericll the eqtio ( + ) =. Sole the eqtio + =. Sole this eqtio for : = 6. Sole lgericll, the eqtio 7. Sole lgericll, the eqtio ( ) + = ( ) m m = Soltios:... + = mltipl throghot ( + ) = = + + = mltipl throghot 6 ( + ) ( + ) = 6 = + = mltipl throghot 6 = 6 = 8. + = mltipl throghot 6 ( ) + ( ) = =. = mltipl throghot ( ) 6 = = 6. + = mltipl throghot 6 ( + ) = = 6 7. m m = mltipl throghot m = m m = 8