Question

Resolva as seguintes expressões fracionárias:
a)[(3/4 + 2/5) – (1/2 – 1/5)] – 7/10=
b){(2/2)² + [1/3 – (1/2 – 1/3)²] – 5/12} – (1/3 – 1/4)=
c)[(1/3 – 2/7) + 2 1/7] – (4/3 – 5/21)=
d)(3/5 . 2/7) : (1/2 . 4/5)=

Answer 1

a) [(3/4 + 2/5) – (1/2 – 1/5)] – 7/10 =

[(3/4 + 2/5) – (1/2 – 1/5)] – 7/10 =   mmc(4,5) = 20    mmc(2,5) = 10

[(5.3/20 + 4.2/20) – (5.1/10 – 2.1/10)] – 7/10 =

[(15/20 + 8/20) – (5/10 – 2/10)] – 7/10 =        Eliminar os parênteses

[23/20 – 3/10] – 7/10 =         mmc (20,10) = 20

[1.23/20 – 2.3/10] – 7/10 =

[23/20 – 6/20] – 7/10 =            Eliminar os colchetes

17/20 - 7/10 =        mmc(20,10) = 20

1.17/20 - 2.7/20 =

17/20 - 14/20 =

3/20

b) {(2/2)² + [1/3 – (1/2 – 1/3)²] – 5/12} – (1/3 – 1/4) =      

{4/4 + [1/3 – (1/2 – 1/3)²] – 5/12} – (1/3 – 1/4) =   mmc(2,3) = 6    mmc(3,4) = 12

{4/4 + [1/3 – (3.1/6 – 2.1/6)²] – 5/12} – (4.1/12 – 3.1/12) =

{4/4 + [1/3 – (3/6 – 2/6)²] – 5/12} – (4/12 – 3/12) =

{4/4 + [1/3 – (1/6)²] – 5/12} – 1/12 =

{4/4 + [1/3 – 1/36] – 5/12} – 1/12 =            mmc(3,36)= 36

{4/4 + [12.1/36 – 1.1/36] – 5/12} – 1/12 =      

{4/4 + [12/36 – 1/36] – 5/12} – 1/12 =

{4/4 + 11/36 – 5/12} – 1/12 =       mmc(4,36,12) = 288

{72.4/288 + 8.11/36 - 24.1/288} – 1/12 =

{296/288 + 88/288 - 24/288} – 1/12 =

360/288 – 1/12 =   mmc(288,12) = 288

1.360/288 - 24.1/288 =

360/288 - 24/288 =

336/288 =        simplificamos por 48

7/6

c) [(1/3 – 2/7) + 21/7] – (4/3 – 5/21) =

[(1/3 – 2/7) + 21/7] – (4/3 – 5/21) =         mmc(3,7) = 21      mmc(3,21) = 21

[(7.1/21 – 3.2/21) + 21/7] – (7.4/21 – 1.5/21) =

[(7/21 – 6/21) + 21/7] – (28/21 – 5/21) =

[1/21 + 21/7] – 23/21 =        mmc(21,7) = 21

[1.1/21 + 3.21/21] – 23/21 =

[1/21 + 63/21] – 23/21 =

64/21 – 23/21 =

41/21

d) (3/5 . 2/7) : (1/2 . 4/5) =  

Multiplicamos numerador c/ numerador e denominador com denominador

6/35 : 4/10 =

Na divisão de frações, multiplicamos a primeira pela inversa da segunda

6/35 x 10/4 =

60/140 =       simplificando por 20

3/7