Question

$a) ( - \frac{1}{2}) + ( + \frac{5}{4} ) + ( - \frac{1}{10}) + ( \frac{3}{ - 5} ) =$
$b) \frac{ - 1}{3} + ( - \frac{5}{27} ) +( \frac{2}{ - 9} ) + ( \frac{ - 7}{ - 81} )=$
$c) \frac{7}{12} + ( - \frac{3}{16} ) + ( + \frac{1}{9} ) + ( - \frac{3}{4} ) =$
$d)( - \frac{5}{11} ) + ( - \frac{8}{33}) + ( + \frac{7}{12} ) + ( - \frac{3}{4} ) =$
$e)( - \frac{7}{6} ) + ( + \frac{13}{18} ) + ( - \frac{2}{9} ) + ( + \frac{1}{36} ) =$

Answer 1

a)

( - 1 / 2 ) + ( 5 / 4 ) + ( - 1 / 10 ) + ( 3 / - 5 ) = 1 / 20

= - 1 / 2 + 5 / 4 - 1 / 10 - 3 / 5 = → cmmmc ( 2; 4; 10; 5 ) = 4 x 5 = 20

= - 10 / 20 + 25 / 20 - 2 / 20 - 12 / 20 =

= ( - 10 + 25 - 2 - 12 ) / 20 =

= ( 15 - 14 ) / 20 =

= 1 / 20

_________

b)

- 1 / 3 - 5 / 27 - 2 / 9 + 7 / 81 = → aflu cmmmc al numitorilor

3 = 1 x 3

27 = 3³

9 = 3²

81 = 3⁴

________________

cmmmc al numitorilor ( 3; 27; 9 si 81 ) = 3⁴ = 81

→ aduc fractiile la acelasi numitor= 81

- 27 / 81 - 15 / 81 - 18 / 81 + 7 / 81 =

= ( - 27 - 15 - 18 + 7 ) / 81 =

= ( - 60 + 7 ) / 81 =

= - 53 / 81

___________________

c)

7 / 12 - 3 / 16 + 1 / 9 - 3 / 4 =

cmmmc al numitorilor ( 12; 16; 9; 4 ) = 144

= ( 7 × 12 ) / 144 - ( 3 × 9 ) / 144 + 16 / 144 - ( 3 × 36 ) / 144 =

= ( 84 - 27 + 16 - 108 ) / 144 =

= ( 57 + 16 - 108 ) / 144 =

= ( 73 - 108 ) / 144 =

= - 35 / 144

____________

d)

- 5 / 11 - 8 / 33 + 7 / 12 - 3 / 4 =

→ cmmmc al numitorilor ( 11; 33; 12; 4 ) = 4 x 3 x 11 = 132

= - 60 / 132 - 32 / 132 + 77 / 132 - 99 / 132 =

= ( - 60 - 32 + 77 - 99 ) / 132 =

= ( - 92 - 22 ) / 132 =

= - 114 / 132 = - 57 / 66 = - 19 / 22

_____________________

e)

- 7 / 6 + 13 / 18 - 2 / 9 + 1 / 36 =

→ cmmmc al numitorilor ( 6; 18; 9; 36 ) = 4 x 9 = 36

→ aduc fractiile la acelasi numitor comun 36

= ( - 7 × 6 ) / 36 + ( 13 × 2) / 36 - ( 2 × 4 ) / 36 + 1 / 36 =

= ( - 42 + 26 - 8 + 1 ) / 36 =

= ( - 16 - 7 ) / 36 =

= - 23 / 36