5 a ) ( - 3 / 4 ) + ( - 4 / 21 ) : ( 8 / 42 ) =
= - 3 / 4 + ( - 4 / 21 ) × 42 / 8 =
= - 3 / 4 - ( 4 / 8 ) x ( 42 / 21 ) =
= - 3 / 4 - 2 / 2 =
= - 3 / 4 - 4 / 4 =
= - 7 / 4 =
= - 1 intreg si 3 / 4 = - 1,75
________________________
b) [ ( - 8 / 14 ) + ( - 3 / 35 ) : ( - 9 / 25 ) ] : ( - 2 / 7 ) =
= [ - 4 / 7 + ( - 3 / 35 ) × ( - 25 / 9 ) ] × ( - 7 / 2 ) =
= ( - 4 / 7 + 5 / 21 ) × ( - 7 / 2 ) =
= ( - 12 / 21 + 5 / 21 ) × ( - 7 / 2 ) =
= ( - 7 / 21 ) × ( - 7 / 2 ) =
= 7/ 6
_______________________
6 a )
( - 8 / 15 + 3 / 10 ) : ( - 14 / 15 ) + ( - 2 / 9 + 1 / 12 ) : ( - 5 / 9 ) = 1 / 2
= ( - 16 / 30 + 9 / 30 ) × ( - 15 / 14 ) + ( - 8 / 36 + 3 / 36 ) × ( - 9 / 5 ) =
= ( - 7 / 30 ) × ( - 15 / 14 ) + ( - 5 / 36 ) × ( - 9 / 5 ) =
= 1 / 4 + 1 / 4 =
= 2 / 4 =
= 1 / 2
Obs.:
→ aflu cmmmc al numerelor 15 si 10 :
15 = 3 x 5
10 = 2 x 5
_____________
cmmmc al numitorilor 15 si 10 = 2 x 3 x 5 = 30
→ aduc fractiile la acelasi numitor comun in fiecare paranteza
_______________________________________________
→ aflu si cmmmc al numitorilor 9 si 12
9 = 3²
12 = 2² x 3
__________
cmmmc al numitorilor 9 si 12 = 2² x 3² = 36
___________________________________________
b) → introduc intregul in fractie:
1 intreg si 7 / 8 = ( 1 x 8 + 7 ) / 8 = 15 / 8
( - 4 / 9 + 3 / 8 ) : ( - 15 / 8 ) + ( - 5 / 6 + 3 / 4 ) : ( - 2 / 3 ) =
= ( - 32 / 72 + 27 / 72 ) × ( - 8 / 15 ) + ( - 10 / 12 + 9 / 12 ) × ( - 3 / 2 ) =
= ( - 5 / 72 ) × ( - 8 / 15 ) + ( - 1 / 12 ) × ( - 3 / 2 ) =
= 1 / 27 + 1 / 8 =
= 8 / 216 + 27 / 216 =
= 35 / 216
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