Question

Cele 2 puncte va rooog.
Dau coroana +25 pct+inima​

Answer 1

Răspuns:

Explicație pas cu pas:

c)   a = 4/9  si  b + c = 15/8.  iar c - d = 9/20

_________________________________

a × b + 2 × a × c - a × d = 31/30

= a × b + a × c + a × c - a × d =

= a × ( b + c + c - d ) =

= (4/9 ) × ( 15/8 + 9/20) =

= (4/9) × ( 75/40 + 18/40 ) =

= (4/9) × ( 93/40) =

= (4/40) × (93/9) =

= (1/10) × 31/3 =

= 31/30

15/8 + 9/20

-> pentru a aduna 2 fractii cu numitori diferiti, aflam cel mai mic muliplu comun al numitorilor si amplificam corespunzator fractiile

->  c.m.m.m.c al numitorilor 8 si 20 este 2³×5 = 40

→ amplific fractia 15/8 cu 5 = (15×5)/(8×5) = 75/40

→ amplific si fractia 9/20 cu 2 = (9×2)/(20×2) = 18/40

___________________________________________________

d)   a × b = 5/12;   a × c = 9/20   si  a × d = 7/15

________________________________

a × ( b + c + d ) = 4/3

-> aplic distributivitatea inmultirii fata de adunare:

= a × b + a × c + a × d =    

= 5/12 + 9/20 + 7/15 =

-> c.m.m.m.c al numitorilor 12,  20  si 15 = 4×3×5= 60

12 = 4×3

20 = 4×5

15 = 3×5

-> amplific fractia 5/12 cu 5 = (5×5)/(5×12)=25/60

-> amplific fractia 9/20 cu 3 = (3×9)/(3×20) = 27/60

-> amplific fractia 7/15 cu 4 = (4×7)/(4×15) = 28/60

= 25/60 + 27/60 + 28/60 =

= (25+27+28)/60 =

= 80/60 =

-> simplific cu 20

= (80: 20)/(60:20)=

= 4/3

___________________________

a × ( b + c - d ) = 2/5

a × b + a × c - a × d =

= 5/12 + 9/20 - 7/15 =

= 25/60 + 27/60 - 28/60 =

= (52-28)/60 =

= 24/60 =

= (24:12)/(60:12) =

= 2/5

Answer 2

$\it a\cdot(b+c)=\dfrac{4}{9}\cdot\dfrac{15}{8}\Rightarrow a\cdot b+a\cdot c=\dfrac{\ 60^{(12}}{72} \Rightarrow a\cdot b+a\cdot c=\dfrac{5}{6}\ \ \ \ \ (1)\\ \\ \\ a\cdot(c-d)=\dfrac{4}{9}\cdot\dfrac{9}{20}\Rightarrow a\cdot c-a\cdot d=\dfrac{\ 36^{(36}}{180} \Rightarrow a\cdot c-a\cdot d=\dfrac{1}{5}\ \ \ \ \ (2)$

$\it (1),\ (2) \Rightarrow a\cdot b+a\cdot c+a\cdot c-a\cdot d =\dfrac{^{5)}5}{6}+\dfrac{^{6)}1}{5}\Rightarrow a\cdot b+2a\cdot c-a\cdot d=\dfrac{31}{30}$