Question

va rog ex 1 ( b c ) 5 (d) si 6 (a)

Answer 1

Ai răspuns pe foaie.

Answer 2

Răspuns

Explicație pas cu pas:

2 a)  (1 / 0,6 ) : 0,2 = x / 0,6

0,6 = 6 / 10 = 3 / 5

0,2 = 2 / 10 = 1 / 5

1 : 3 / 5 : 1 / 5 = 1 × 5 / 3 × 5 = 25 / 3

x / 0,6 = x : 3 / 5 = x × 5 / 3 = 5 x / 3

_____________________________

25 / 3 = 5 x / 3  ⇒   3 × 5 x = 3 ×25 ⇒  15 x = 75 ⇒  x = 75 / 15 ⇒  x = 5

_______________________________________________________

c)

( 1 / 2 + 1 / 2 : 2 ) / x = 6 / 7

→ calculez numaratorul

1 / 2 + 1 / 2 × 1 / 2 = 1 / 2 + 1 / 4 = ( 2 + 1 ) / 4 = 3 / 4

3 / 4  : x = 3 / 4 × 1 / x = 3 / 4 x

_________________________

3 / 4 x = 6 / 7 ⇒   24 x = 21 ⇒   x = 21 / 24 ⇒  x = 7 / 8

________________________________________________

3)  c)   ( x + 2 ) / 5 = ( 3 + 2² ) / 7

7( x + 2 ) = 5 × ( 3 + 4 )

7 x + 14 = 5 × 7

7 x = 35 - 14

7 x = 21 ⇒  x = 21 : 7 ⇒  x = 3

____________________________

5 ( d )

( 1 / 7 - 1 / 14 + 3 / 28 ) / ( 5 x / 8 ) = ( 1 intreg si 2 / 3 ) / ( 4 / 3 - 1 / 6)

→ le voi calcula pe rand:

1 / 7 - 1 / 14 + 3 / 28 =  → c.m.m.m.c al numitorilor ( 7; 14 si 28 ) = 28

= 4 / 28 - 2/ 28 + 3 / 28 =

= 5 / 28 → numaratorul

__________________

→ introduc intregii in fractie

1 intreg si 2 / 3 = ( 1 × 3 + 2 ) / 3 = 5 / 3

1 intreg si 1 / 3 = ( 1 × 3 + 1 ) / 3 = 4 / 3

_______________________________

1 intreg si 1 / 3 - 1 / 6 = 4 / 3 - 1 / 6 = 8 / 6 - 1 / 6 = 7 / 6

________________________________________

( 5 / 28 ) / ( 5 x / 8 ) = ( 5 / 3 ) / ( 7 / 6 ) =

5 / 28 ×  8 / 5 x = 5 / 3  × 6 / 7

40 / 140 x = 30 / 21

2 / 7 x = 10 / 7

⇒  10 × 7 x = 2 × 7

70 x = 14 ⇒  x = 14 / 70 ⇒   x = 1 / 5

_______________________________

6. a )   ( x + 1 ) / 3 = 4,2 / 7

⇒ 7 ( x + 1 ) = 3 × 4,2

7 x + 7 = 12,6

7 x = 12,6 - 7

7 x = 5,6

x = 5,6 / 7 ⇒   x = 0,8 ⇒   x = 8 / 10 = 4 / 5 ∈ Q