Question

4/5 (2 3/2-3/4)+1/9÷5/18-2/3 (9/5-12/5)

Answer 1

La resolución del ejercicio planteado da como resultando: $4/5\left(2\frac{3}{2}-3/4\right)+1/9\div \:5/18-2/3\left(9/5-12/5\right)=3$

Procedimiento por pasos

$4/5\left(2\frac{3}{2}-3/4\right)+1/9\div \:5/18-2/3\left(9/5-12/5\right)$

Convertir numero mixto en fracción impropia: $a\frac{b}{c}=\frac{a\cdot c+b}{c}$

$2\frac{3}{2}=\frac{2\cdot 2+3}{2}=\frac{7}{2}$

$4/5\left(\frac{7}{2}-3/4\right)+1/9\div \:5/18-2/3\left(9/5-12/5\right)$

$=\frac{4}{5}\left(\frac{7}{2}-\frac{3}{4}\right)+\frac{\frac{1}{9}}{\frac{5}{18}}-\frac{2}{3}\left(-\frac{3}{5}\right)$

Aplicar regla: $-\left(-a\right)=a$

$=\frac{4}{5}\left(\frac{7}{2}-\frac{3}{4}\right)+\frac{\frac{1}{9}}{\frac{5}{18}}+\frac{2}{3}\cdot \frac{3}{5}$

$\frac{4}{5}\left(\frac{7}{2}-\frac{3}{4}\right)=\frac{11}{5}$

$\frac{\frac{1}{9}}{\frac{5}{18}}=\frac{2}{5}$

$\frac{2}{3}\cdot \frac{3}{5}=\frac{2}{5}$

Sustituyendo

$=\frac{11}{5}+\frac{2}{5}+\frac{2}{5}$

Aplicando la regla: $\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}$

$=\frac{11+2+2}{5}$

$=\frac{15}{5}=3$