Răspuns:
36. a) aducem la acelasi numitor 4
[tex]\frac{2*1+3}{4}[/tex]= [tex]\frac{5}{4}[/tex]
b) [tex]\frac{5*2}{6} - \frac{4}{6}[/tex]= [tex]\frac{10-4}{6} =\frac{6}{6} =1[/tex]
c) 10=2*5 12=[tex]2^{2}[/tex] *3 20= [tex]2^{2}[/tex] *5 n.c= [tex]2^{2}[/tex] *3*5= 60
[tex]\frac{7*6 - 8*5+9*3}{60}[/tex]= [tex]\frac{42-40+27}{60}[/tex]= [tex]\frac{29}{60}[/tex]
d) [tex]\frac{20}{27}[/tex]+ [tex]\frac{2}{3} *\frac{12}{8}[/tex]= [tex]\frac{20}{27}[/tex] + [tex]\frac{1*4}{1*4}[/tex]= [tex]\frac{20}{27}[/tex] + 1= [tex]\frac{20+27}{27}[/tex]= [tex]\frac{47}{27}[/tex]
e) [tex]\frac{6}{3} - \frac{15}{8} - \frac{1}{2}[/tex]= 2- [tex]\frac{15}{8} -\frac{1}{2}[/tex]= [tex]\frac{16-15-1}{8} =0/8=0[/tex]
f) [tex]\frac{5}{4} - \frac{3}{4} *\frac{12}{8} + \frac{3}{4}[/tex] + 8 +9-1= [tex]\frac{5}{4} - \frac{9}{8} - \frac{3}{4} + 16[/tex] = [tex]\frac{10-9+6+16*8}{8}[/tex]= [tex]\frac{7+128}{8}[/tex]= [tex]\frac{135}{8}[/tex]
g)[tex]\frac{1}{4} + \frac{8}{8} - \frac{1}{4}[/tex]= 0+1=1
37. a) 24= [tex]2^{3}[/tex]*3
56= [tex]2^{3}[/tex]*7
cmmdc(24, 56)= [tex]2^{3}[/tex]=8
b) 5= [tex]5^{1}[/tex] 15=[tex]3^{1} *5^{1}[/tex] 30= [tex]2^{1} *3^{1} *5^{1}[/tex] 45= [tex]3^{2} *5[/tex]
cmmdc(5, 15,30,45)= 5
c) 450= 2*[tex]3^{2} *5^{2}[/tex] 1300= 13* [tex]2^{2} *5^{2}[/tex]
cmmdc(450, 1300)= 2*[tex]5^{2}[/tex]= 50 se ia factorii comuni la puterea cea mai mica
38. a) cmmmc= [tex]2^{3} *3*7[/tex]= 8*21=168
b) cmmmc= [tex]2^{1} *3^{2} *5[/tex]=90
c) 4500= [tex]2^{2} *3^{2} *5^{3}[/tex] 130= 13* 2*5
cmmmc= [tex]2^{2} *3^{2} *5^{3}[/tex] *13=58500
40 . a)2 + [ 76-2 *(20+20):5 - 12= 2+ (76-2 *40:5-12)= 2 + (76-2*8-12)=
2+ 76-16-12= 2+48= 50
b) (111 +22+66):1+10= (111+88):1+10 = 199:1+10= 199+10=209
41. a) M3= 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51
b) M5=5, 10, 15, 20, 25, 30, 35, 40, 45, 50
c) M6= 6, 12, 18, 24, 30, 36, 42, 48
