Răspuns :
1) 3,(3) = ( 33 - 3) / 9 = 30 / 9 = 10 / 3
2) 3 / 5 × 4 / 3 + 2 / 5 + 1 = 4 / 5 + 2 / 5 + 5 / 5 = 11 / 5 = 2,2
3) [1,4+1,(3)+2/3] : 1 / 5 =
1,( 3) = ( 13 - 1) / 9 = 12 / 9 = 4 / 3
1,4 = 14 / 10 = 7 / 5
( 7 / 5 + 4 / 3 + 2 / 3 ) × 5 / 1 =
= ( 21 / 15 + 20 / 15 + 10 / 15) × 5 =
= 51 / 15 × 5 = 51 / 3 = 17
4) a = suma de bani
a - 2 a / 5 - ( a - 2a / 5 ) : 2 = 90
a - 2a / 5 - 3 a / 10 = 90
10 a - 4 a - 3 a = 10 × 90
3 a = 900
a = 900 : 3
a = 300 lei → suma initiala de bani
b) ( 300 - 300 : 5 × 2) : 2 = ( 300 - 120) : 2 = 180 : 2 = 90 lei a cheltuit a doua zi
c) 2 a / 5 + 3 a / 10 = 4 a / 10 + 3 a / 10 = 7 a / 10 → fractia
5)
5/7 din 56 ⇒ 56 : 7 × 5 = 8 × 5 = 40
6)
12 / 18 = 2 / 3 → am simplificat prin 6
2) 3 / 5 × 4 / 3 + 2 / 5 + 1 = 4 / 5 + 2 / 5 + 5 / 5 = 11 / 5 = 2,2
3) [1,4+1,(3)+2/3] : 1 / 5 =
1,( 3) = ( 13 - 1) / 9 = 12 / 9 = 4 / 3
1,4 = 14 / 10 = 7 / 5
( 7 / 5 + 4 / 3 + 2 / 3 ) × 5 / 1 =
= ( 21 / 15 + 20 / 15 + 10 / 15) × 5 =
= 51 / 15 × 5 = 51 / 3 = 17
4) a = suma de bani
a - 2 a / 5 - ( a - 2a / 5 ) : 2 = 90
a - 2a / 5 - 3 a / 10 = 90
10 a - 4 a - 3 a = 10 × 90
3 a = 900
a = 900 : 3
a = 300 lei → suma initiala de bani
b) ( 300 - 300 : 5 × 2) : 2 = ( 300 - 120) : 2 = 180 : 2 = 90 lei a cheltuit a doua zi
c) 2 a / 5 + 3 a / 10 = 4 a / 10 + 3 a / 10 = 7 a / 10 → fractia
5)
5/7 din 56 ⇒ 56 : 7 × 5 = 8 × 5 = 40
6)
12 / 18 = 2 / 3 → am simplificat prin 6