Berechnung einer Bruchrechnung

Question

(3Ganze4/5-1Ganze2/3)x5/8+4Ganze5/6-(2Ganze1/9+1Ganze7/12)x6/19

Answer 1

(3Ganze4/5-1Ganze2/3)x5/8+4Ganze5/6-(2Ganze1/9+1Ganze7/12)x6/19

= (3Ganze12/15-1Ganze10/15)x5/8+4Ganze5/6-(2Ganze 4/36+1Ganze21/36)x6/19

= (2Ganze 2/15) x5/8+4Ganze5/6-(3Ganze 25/36)x6/19

= ( 32/15) x5/8+4Ganze5/6-(133/36)x6/19

= ( 32/3) x1/8+4Ganze5/6-(133/6)x1/19 

= ( 4/3) x1/1+4Ganze5/6-(7/6)x1/1

=  4/3 +4Ganze5/6-    7/6

=  8/6 +4Ganze5/6-    7/6

=  1/6 +4Ganze5/6  

= 5Ganze.

Answer 2

(3Ganze4/5-1Ganze2/3)x5/8+4Ganze5/6-(2Ganze1/9+1Ganze7/12)x6/19

Ganze umrechnen:

(19/5 - 5/3) • 5/8 + 29/6 - (19/9 + 19/12) • 6/19

Klammern auflösen:

95/40 - 25/24 + 29/6 - 6/9 - 6/12

Kürzen:

19/8 - 25/24 + 29/6 - 2/3 - 1/2

Hauptnenner 24:

(57 - 25 + 116 - 16 - 12) / 24   = 120/24  = 5

Gruß Wolfgang