Add or Subtract. Write In simplest form. (Examples 3,4,6,7) 3(5)/(6)+(-1(2)/(6)) -(2)/(3)+2(3)/(8) 8. -32+(1)/(4) 9. (1)/(3)+42 10. -1(1)/(4)+0.75+0.45 -2.45-(-3.9)

Vamos a resolver cada uno de los problemas paso a paso:<br /><br />1. \(3\frac{5}{6} + (-1\frac{2}{6})\)<br /><br />Primero, simplificamos las fracciones:<br />\[3\frac{5}{6} = 3 + \frac{5}{6} = \frac{18}{6} + \frac{5}{6} = \frac{23}{6}\]<br />\[-1\frac{2}{6} = -1 - \frac{2}{6} = -\frac{6}{6} - \frac{2}{6} = -\frac{8}{6} = -\frac{4}{3}\]<br /><br />Ahora sumamos:<br />\[\frac{23}{6} + \left(-\frac{4}{3}\right) = \frac{23}{6} - \frac{8}{6} = \frac{15}{6} = 2\frac{3}{6} = 2\frac{1}{2}\]<br /><br />2. \(-\frac{2}{3} + 2\frac{3}{8}\)<br /><br />Convertimos el número mixto a una fracción:<br />\[2\frac{3}{8} = \frac{16}{8} + \frac{3}{8} = \frac{19}{8}\]<br /><br />Ahora sumamos:<br />\[-\frac{2}{3} + \frac{19}{8}\]<br /><br />Encontramos un denominador común (24):<br />\[-\frac{2}{3} = -\frac{16}{24}\]<br />\[\frac{19}{8} = \frac{57}{24}\]<br /><br />Sumamos:<br />\[-\frac{16}{24} + \frac{57}{24} = \frac{41}{24} = 1\frac{17}{24}\]<br /><br />3. \(-32 + \frac{1}{4}\)<br /><br />Convertimos \(-32\) a una fracción con denominador 4:<br />\[-32 = -\frac{128}{4}\]<br /><br />Sumamos:<br />\[-\frac{128}{4} + \frac{1}{4} = -\frac{127}{4} = -31\frac{3}{4}\]<br /><br />4. \(\frac{1}{3} + 42\)<br /><br />Convertimos 42 a una fracción con denominador 3:<br />\[42 = \frac{126}{3}\]<br /><br />Sumamos:<br />\[\frac{1}{3} + \frac{126}{3} = \frac{127}{3} = 42\frac{1}{3}\]<br /><br />5. \(-1\frac{1}{4} + 0.75 + 0.45\)<br /><br />Convertimos \(-1\frac{1}{4}\) a una fracción:<br />\[-1\frac{1}{4} = -1 - \frac{1}{4} = -\frac{4}{4} - \frac{1}{4} = -\frac{5}{4}\]<br /><br />Convertimos 0.75 y 0.45 a fracciones:<br />\[0.75 = \frac{3}{4}\]<br />\[0.45 = \frac{45}{100} = \frac{9}{20}\]<br /><br />Encontramos un denominador común (20):<br />\[-\frac{5}{4} = -\frac{25}{20}\]<br />\[\frac{3}{4} = \frac{15}{20}\]<br /><br />Sumamos:<br />\[-\frac{25}{20} + \frac{15}{20} + \frac{9}{20} = -\frac{25}{20} + \frac{24}{20} = -\frac{1}{20}\]<br /><br />6. \(-2.45 - (-3.9)\)<br /><br />Convertimos a fracciones:<br />\[-2.45 = -\frac{245}{100} = -\frac{49}{20}\]<br />\[-3.9 = -\frac{39}{10} = -\frac{78}{20Restamos:<br />\[-\frac{49}{20} - \left(-\frac{78}{20}\right) = -\frac{49}{20} + \frac{78}{20} = \frac{29}{20} = 1\frac{9}{20}\]<br /><br />Por lo tanto, las respuestas son:<br /><br />1. \(2\frac{1}{2}\)<br />2. \(1\frac{17}{24}\)<br />3. \(-31\frac{3}{4}\)<br />4. \(42\frac{1}{3}\)<br />5. \(-\frac{1}{20}\)<br />6. \(1\frac{9}{20}\)