Question

resolva as seguntes expreções, simplificando se possivel
a) (3/4 + 1/3 x 2/5):(4/3 x 5/2 - 3/4)
b) (1 x 2/3 x 12/5 + 3/8) : (3/8 + 1/3 : 4/3)

Answer 1

a) (3/4 + 1/3 x 2/5):(4/3 x 5/2 - 3/4) = (3/4 + 2/15) : (20/6 - 3/4) = (45/60 + 8/60) : (80/24 - 18/24) = 53/60 : 62/24 = 53/60 x 24/62 = 1272/3720

b) (1 x 2/3 x 12/5 + 3/8) : (3/8 + 1/3 : 4/3) = (24/15 + 3/8) : (3/8 + 1/3 x 3/4) = (192/120 + 45/120) : (3/8 + 3/12) = 237/120 : (9/24 + 6/24) = 237/120 : 15/24 = 237/120 x 24/15 = 5688/1800

Answer 2

Procedimento
1° retirar parentese (efetuadas todas as operações dentro)
2° efetuar
     1 multiplicações
     2 somas e sustrações
3° usar mmc quando necessário

a)
           $( \frac{3}{4} + \frac{1}{3}x \frac{2}{5} ):( \frac{4}{3} x \frac{5}{2} - \frac{3}{4}) \\ \\ =( \frac{3}{4} + \frac{2}{15} ):( \frac{20}{6} - \frac{3}{4} ) \\ \\ =( \frac{3x15+2x4}{60} ):( \frac{20x2-3x3}{12}) \\ \\ =( \frac{53}{60}):( \frac{31}{12}) \\ \\ = \frac{53x12}{60x31} \\ \\ = \frac{53}{155}$

b)
           $(1x\frac{2}{3} x \frac{12}{5} + \frac{3}{8} ):( \frac{3}{8}+ \frac{1}{3} : \frac{4}{3} ) \\ \\ =( \frac{24}{15}+ \frac{3}{8}):( \frac{3}{8} + \frac{1x3}{3x4} ) \\ \\ =( \frac{24x8+3x15}{120} ):( \frac{3}{8} + \frac{1}{4} ) \\ \\ = \frac{237}{120} : \frac{5}{8} \\ \\ = \frac{237x8}{120x5} \\ \\ = \frac{237}{75}$