Question

1. Cu ajutorul numerelor naturale de la 1 la 9 si fara a schimba ordinea, folosindu-te de operatiile invatate poti opbtine numarul 100?

2. Cu cinci cifre de cinci si cu cele patru operatii cunoscute, poti obtine pe rand numerele: 70, 7, 150, 50?

3. Facand produsul tuturor numerelor naturale de la 0 la 20 se obtine un numar natural. In cate zorouri se termina acest numar?

Answer 1

(1x2x3x4x5)x(6-7)x(8-9)=100x(-1)x(-1)=100


(5 +5 + 5) x 5 - 5=70 
(5:5) + 5 + (5: 5)=1+5+1=7 
(5+5) x 5 x (5: 5)=10x5x1=50 
(5+5) x( 5 + 5+ 5)=10x15=150

3.
1x2x3x4x5x6x7x8x9x10x11x12x13x14x15x16x17x18x19x20 
4 zerouri
avem 2 cifre de 5 care inmultite cu un nr par  vor da 2 zerouri
de la 10 avem 1 zero
de la 20 avem 1 zero

Answer 2

1)
(9x8)+7+6+5+4+3+2+1=72+7+6+5+4+3+2+1=79+6+5+4+3+2+1=85+5+4+3+2+1=90+4+3+2+1=94+3+2+1=97+2+1=99+1=100
2)
(5+5+5)x5-5=(10+5)x5-5=15x5-5=75-5=70
(5:5)+5+(5:5)=1+5+1=6+1=7
(5:5+5)x5x5=(1+5)x5x5=6x5x5=30x5=150
(5+5)x5x(5:5)=10x5x1=50x1=50
3)
1x2x3x4x5x.....x20=20!(!=factoria)
trebuie aflat in cati de zeros se termina si folosim exponentii lui 5.
[20/5]+[20/25]+[20/125]=4+0+0=4 zerouri
[  ]=partea intreaga