16)
a) - 7 + ( - 5 + 5 ) = - 7 + 0 = - 7
b) - 4 + ( 4 - 8 ) = - 4 + ( - 4 ) = - 4 - 4 = - 8
c) - 4 509 + 2 315 + 4 509 = ( - 4 509 + 4 509 ) + 2 315 = 0 + 2 315 = 2 315
d ) 123 - ( 117 - 0 ) + ( - 123 ) + 118 = ( 123 - 123 ) - 117 + 118 = 0 + 1 = 1
e) 135 - 143 - ( 135 - 143 ) + 1 = - 1 - ( - 1) + 1 = - 1 + 1 + 1 =0 + 1 = 1
f) - 6 - [ 2 + ( - 8 ) + 0 ] = - 6 - ( 2 - 8 ) = - 6 - ( - 6 ) = - 6 + 6 = 0
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17) - 100 - 99 - 98 - 97 - ........ - 1 + 0 + 1 + 2 + 3 + ......... + 101 + 102 = 203
= ( - 100 + 100 ) + ( - 99 + 99 ) + .......... ( - 1 + 1 ) + 0 + 101 + 102 =
= 0 + 0 + ...... + 0 + 203 =
= 203
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19)
7 ⇔ [ 12 + ( - 5 ) = 12 - 7 = 5 ]
12 - 5 ⇔ [ 2 + 10 = 12; 10 + ( - 15 ) = 10 - 15 = - 5 ]
2 10 - 15 ⇔ [ - 5 + 7 = 2; 7 + 3 = 10; 3 + ( - 18 ) = 3 - 18 = - 15 ]
- 5 7 3 - 18 → numerele de la baza piramidei
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20) a) ( - 3) × ( + 4 ) = - 12
b) ( - 21 ) × ( - 5 ) = + 105
c) 2 × ( - 3 ) = - 6
d ) ( - 3 ) × 47 = - 141
e) - 7 × 315 × 0 = 0 → daca intr -un produs , un factor este 0, atunci produsul e 0
f) ( - 21 ) × 1 × ( - 1 ) = + 21 ; ( - ) × ( - ) = +
g) - 10 × ( - 3 / 7 ) = + 30 / 7
h ) - 20 × 173 × ( - 5 ) = + 17 300
i ) ( - 5 ) × ( - 115 ) × ( - 20 ) = - 11 500
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21 )
a) produsul sa fie - 1
1 1 - 1 → 1 × 1 × ( - 1 ) = - 1
- 1 1 1 → ( - 1 ) × 1 × 1 = - 1
1 - 1 1 → 1 × ( - 1 ) × 1 = - 1
↓ ↓ ↓
- 1 - 1 - 1
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b) produsul sa fie 1
1 - 1 - 1 → 1 × ( - 1 ) × ( - 1 ) = 1
1 1 1 → 1 × 1 × 1 = 1
1 - 1 - 1 → 1 × ( - 1 ) × ( - 1 ) = 1
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22 ) a ) - 5 × 3 + 10 = - 15 + 10 = - 5
b) - 5 × ( - 7 ) + ( - 5 ) × 3 = ( - 5 ) × ( - 7 + 3 ) = ( - 5 ) × ( - 4 ) = + 20
c) - 5 × ( - 7 + 3 ) = - 5 × ( - 4 ) = + 20
d ) - 8 × 6 + ( - 8 ) × ( - 7 ) = - 48 + 56 = 8
e ) 12 + ( - 12 ) × 35 + 12 × 34 = 12 × ( 1 - 35 + 34 ) = 12 × 0 = 12
f) 3 × ( 1 + 2 + 3 + ........ + 1 000 ) + ( 3 + 4 + 5 + ........... + 1 000 ) × ( - 3 ) = 9
= 3 × 1 000 × 1001 / 2 +( - 3 ) × ( 1 000 - 3 + 1 ) termeni × 1 003 / 2 =
= 3 × 500 × 1001 - 3 × 499 × 1 003 =
= 3 × ( 500 500 - 500 497 ) = → l-am dat factor comun pe 3
= 3 × 3 =
= 9
