Question

Como se resuelve 5\4×2\3÷1\5+2\5÷1\10×3\4+1\2×4\3÷1\6=

Answer 1

El resultado de efectuar 5\4×2\3÷1\5+2\5÷1\10×3\4+1\2×4\3÷1\6 es  67/6

Explicación

$\frac{5}{4}\times \frac{2}{3}\div \frac{1}{5}+\frac{2}{5}\div \frac{1}{10}\times\frac{3}{4}+\frac{1}{2}\times\frac{4}{3}\div \frac{1}{6}$

Aplicamos propiedades de fracciones:

$\frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}$

= $\frac{5}{4}\times \frac{2}{3}\times \frac{5}{1}+\frac{2}{5}\div \frac{1}{10}\times \frac{3}{4}+\frac{1}{2}\times \frac{4}{3}\div \frac{1}{6}$

= $=\frac{5}{4}\times \frac{2}{3}\times \frac{5}{1}+\frac{2}{5}\times \frac{10}{1}\times \frac{3}{4}+\frac{1}{2}\times \frac{4}{3}\div \frac{1}{6}$

= $(\frac{5}{4}\times \frac{2}{3}\times \frac{5}{1})+(\frac{2}{5}\times \frac{10}{1}\times \frac{3}{4})+(\frac{1}{2}\times \frac{4}{3}\times \frac{6}{1}$)

Resolvemos los productos dentro de los paréntesis:

• $\frac{5}{4}\times \frac{2}{3}\times \frac{5}{1} = \frac{25}{6}$
• $\frac{2}{5}\times \frac{10}{1}\times \frac{3}{4}=3$
• $\frac{1}{2}\times \frac{4}{3}\times \frac{6}{1}=4$

Por lo tanto, la expresión queda reducida a:

$=\frac{25}{6}+3+4$

Luego,

$=\frac{25}{6}+7=\frac{67}{6}$