Question

1.
a) Daca 2a+10b=22 , aflati 3a+15b.
b) Calculati media aritmetica a primelor 100 de numere natural.
c) Fie numarul B=10^15-15 . Calculati suma cifrelor numarului.

2.
a) Simplificati fractia 5+10+15+...+150/6+12+18+...+180
b) Calculati suma numerelor :
x= 1/2+2/3+3/4+4/5+...+10/11
y=1/2+1/3+1/4+1/5+...+1/11

3. Impartind numarul natural a la numarul natural b , obtinem catul 3 si restul 7 . Daca a-b <25 , aflati cele doua numere .

Answer 1

a) Daca 2a+10b=22 , aflati 3a+15b.
2a+10b=22   impartim la 2
a+5b=11      inmultim cu 3
3a+15b=33

b) Calculati media aritmetica a primelor 100 de numere natural.
(1+2+3+.....+100)/100 = [100(100+1)/2]/100=50x101/100=50,5

c) Fie numarul B=10^15-15 . Calculati suma cifrelor numarului.
10¹⁵ -15=1000000000000000-15=999999999999984
9x13+8+4=129

2.
a) Simplificati fractia 5+10+15+...+150/6+12+18+...+180
5+10+15+...+150/6+12+18+...+180 =
=5(1+2+.....30)/6(1+2+3...30)=5/6

b) Calculati suma numerelor :
x= 1/2+2/3+3/4+4/5+...+10/11=221209/27720
y=1/2+1/3+1/4+1/5+...+1/11=55991/27720
numitor comun = 2³×3²×5×7×11=27720

3. Impartind numarul natural a la numarul natural b , obtinem catul 3 si restul 7 . Daca a-b <25 , aflati cele doua numere .
a:b=3 si rest 7
a=3b+7   
a-b<25   a<25+b
3b+7<25+b
2b<25-7
2b<18
b<9
b=8
a=3x8+7=31
31: 8 =3 si rest 7
31-8=23    23<25