Question

Por Favor me ajude a resolver expressão....

50/48 - [(6/5 - 1/3) dividido por 8/5 + 3/4 * ( 11/4 dividido por 22/5 ) ] =

Answer 1

$\dfrac{50}{48}-\left[\dfrac{(\frac{6}{5}-\frac{1}{3})}{(\frac{8}{5})}+\dfrac{3}{4}\left(\dfrac{(\frac{11}{4})}{(\frac{22}{5})}\right)\right]$

Simplificando (50 / 48) por 2, colocando (6 / 5) e (1 / 3) no mesmo denominador e fazendo a divisão de (11 / 4) por (22 / 5):

$\dfrac{50}{48}-\left[\dfrac{(\frac{18}{15}-\frac{5}{15})}{(\frac{8}{5})}+\dfrac{3}{4}\left(\dfrac{11}{4}\cdot\dfrac{5}{22}}\right)\right]\\\\\\\dfrac{50}{48}-\left[\dfrac{(\frac{18-5}{15})}{(\frac{8}{5})}+\dfrac{3}{4}\left(\dfrac{1}{4}\cdot\dfrac{5}{2}}\right)\right]\\\\\\\dfrac{50}{48}-\left[\dfrac{(\frac{13}{15}}{(\frac{8}{5})}+\dfrac{3}{4}\cdot\dfrac{5}{8}\right]\\\\\\\dfrac{50}{48}-\left[\dfrac{13}{15}\cdot\dfrac{5}{8}}+\dfrac{15}{32}\right]$

$\dfrac{50}{48}-\left[\dfrac{13}{3}\cdot\dfrac{1}{8}}+\dfrac{15}{32}\right]\\\\\\\dfrac{25}{24}-\left[\dfrac{13}{24}+\dfrac{15}{32}\right]$

Vamos achar o m.m.c entre 24 e 32, fazendo uma fatoração simultânea:

24, 32 | 2
12, 16 | 2
06, 08 | 2
03, 04 | 2
03, 02 | 2
03, 01 | 3
01, 01

Então, o m.m.c entre 75 e 32 é:

$2^{5}\cdot3=32\cdot3=96$

Logo:

$\dfrac{50}{48}-\left[\dfrac{13\cdot4}{24\cdot4}+\dfrac{15\cdot3}{32\cdot3}\right]\\\\\\\dfrac{50}{48}-\left[\dfrac{52}{96}+\dfrac{45}{96}\right]\\\\\\\dfrac{50}{48}-\left[\dfrac{52+45}{96}\right]\\\\\\\dfrac{50}{48}-\dfrac{97}{96}$

O m.m.c entre 48 e 96 é 96:

$\dfrac{50\cdot2}{48\cdot2}-\dfrac{97}{96}\\\\\\\dfrac{100}{96}-\dfrac{97}{96}\\\\\\\dfrac{3}{96}$

Simplificando por 3:

$\dfrac{3\div3}{96\div3}\\\\\\\dfrac{1}{32}$
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$\boxed{\boxed{\dfrac{50}{48}-\left[\dfrac{(\frac{6}{5}-\frac{1}{3})}{(\frac{8}{5})}+\dfrac{3}{4}\left(\dfrac{(\frac{11}{4})}{(\frac{22}{5})}\right)\right]=\dfrac{1}{32}}}$