2)(+36-48-37+87): (-41+24-58+46) Luam fiecare paranteza in parte pentru a usura calculul
(+36-48-37+87)=-12-37+87=-49+87=38
(-41+24-58+56)=-17-58+56=-75+56=-19
38: (-19)=-2
sau
Adunarea si scaderea fiind comutative vom alege noi ordinea operatiilor din interiorul parantezelor
(+36-48-37+87 ) : (-41+24-58+46) =
Reordonam:
(+36-37+87-48) : (46-41+24-58)=
(-1+49) : (5-24) =38: (-19)= -2
3) [+36+43 · (-48+19+27)] : (-6)=
[+36+43 · (-48+46) ] : (-6)=
[+36+43 · (-2) ] : (-6)=
[+36 - 86] : (-6)=
(-50) : (-6)= [tex]\frac{50}{6}[/tex](simplificam prin 2)[tex]=\frac{25}{3}=8,(33)[/tex]
4) {+[tex]3^{4} [/tex] -[ [tex]8^{3} [/tex]-(+[tex] 1^{7} [/tex]-[tex]5^{4} [/tex]+22²) :(+70)] : (+257)}:(+79)=
[tex]3^{4} [/tex]=3 · 3 · 3 · 3=81
[tex]8^{3} [/tex]=8 ·8·8=64 · 8 =512
22²=22 ·22=484
[tex]5^{4} [/tex]=5·5·5·5=25·25=625
{81-[512-(1-625+484):70]:257}:(+79)=
{81-[512-(-625+485):70]:257}:(+79)=
{81-[512-(-140):70]:257}:(+79)=
{81-[512-(-2)]:257}:(+79)=
{81-[512-+2]:257}:(+79)=
{81-[514]:257}:(+79)=
(81-2):(+79)=
79:(+79)=1
5){[tex](-3)^{3}[/tex]·[tex]3^{6}[/tex]:[tex]3^{7}[/tex]-[tex](-2^{4})^{3}:2^{9}-(-5)^{3}:(+25)[/tex]=
2 numere care au aceasi baza si puteri diferite:
La inmultire se aduna puterile
La impartire se scad puterile
[tex](-2^{4})^{3}[/tex]= se inmultesc puterile intre ele [tex]-2^{12}[/tex]
{-[tex]3^{9}[/tex]:[tex]3^{7}[/tex]-([tex]-2^{4})^{3}):2^{9}-(-5)^{3}:(+25)[/tex]=
{-[tex]-3^{9}[/tex]:[tex]3^{7}[/tex]-([tex]-2^{12}[/tex]):[tex]2^{9}-(-5)^{3}:5^{2} [/tex]=
{-[tex]3^{2}[/tex] - ([tex]-2^{3}[/tex])-[tex](-5)^{1}[/tex]=
{-[tex]3^{2}[/tex] - ([tex]-2^{3}[/tex])-[tex](-5)^{1}[/tex]=
-9+8+5=4
6)a) suma de 5 numere intregi consecutive
(a-2)+ (a-1) + a+ (a+1 )+ (a+2) = 5
a-2+a-1+a+a+1+a+2=5
5a=5 => a=1
(a-2)=1-2=-1
(a-1)=1-1=0
a=1
(a+1)=1+1=2
(a+2)=1+2 =3
Numerele sunt : -1+0+1+2+3= 5 (A)
Forma celor cinci numere consecutive putea fi si : a+(a+1)+ (a+2)+ (a+3) + (a+4)=5 Numerele fiind tot -1, 0 ,1,2,3
b)suma de 5 numere intregi consecutive
Analog ca la a / folosim acelasi rationament
(a-4)+(a-3)+(a-2)+ (a-1) + a+ (a+1 )+ (a+2)+(a+3)+ (a+4) + (a+5) = 5
a-4+a-3+a-2+ a-1 + a+ a+1 + a+2+a+3+ a+4 + a+5=
10 a +5=5
10a=0
a=0
(a-4)= 0-4=-4
(a-3)=0-3=-3
(a-2)=0-2=-2
(a-1)=-1
(a+1)=0+1=1
(a+2)=0+2=2
(a+3)=0+3=3
(a+4)=0+4=4
(a+5)=0+5=5
-4 + (-3)+ (-2)+(-1)+0+1+2+3+4+5=5
Sper ca iti este totul clar si sper ca toate explicatiile mele ti-au fost de ajutor.
