Question

Buenas tardes, alguien que por favor me ayude con las siguientes operaciones con fracciones paso a paso. Gracias a.)7/6 + 3/8 + 4/7. b.)(1/6 × 1/5) + 3/4 c.) 4 - 2/6 + 3/2. d.) (4/3 × 5/5) + (2/6 × 4/3) e.) (3/4 + 7/5 - 14/6) × 2/9

Answer 1

Respuesta:

$a)\frac{355}{168}$

$b)\frac{47}{60}$

$c)\frac{31}{6}$

$d)\frac{16}{9}$

$e)-\frac{11}{270}$

Explicación paso a paso:

$\frac{7}{6}+\frac{3}{8}+\frac{4}{7}\\\\\mathrm{Minimo\:comun\:multiplo\:de\:}6,\:8,\:7:\quad 168\\\\=\frac{196+63+96}{168}\\\\=\frac{355}{168}$

$\left(\frac{1}{6}\times \frac{1}{5}\right)+\frac{3}{4}\\\\=\frac{1}{6}\times \frac{1}{5}+\frac{3}{4}\\\\=\frac{1}{30}+\frac{3}{4}\\\\\mathrm{Minimo\:comun\:multiplo\:de\:}30,\:4:\quad 60\\\\=\frac{2+45}{60}\\\\=\frac{47}{60}$

$4-\frac{2}{6}+\frac{3}{2}\\\\=4-\frac{1}{3}+\frac{3}{2}\\\\\mathrm{Convertir\:a\:fraccion}:\quad \:4=\frac{4}{1}\\\\=\frac{4}{1}-\frac{1}{3}+\frac{3}{2}\\\\\mathrm{Minimo\:comun\:multiplo\:de\:}1,\:3,\:2:\quad 6\\\\=\frac{24-2+9}{6}\\\\=\frac{31}{6}$

$\left(\frac{4}{3}\times \frac{5}{5}\right)+\left(\frac{2}{6}\times \frac{4}{3}\right)\\\\=\frac{4}{3}\times \frac{5}{5}+\frac{2}{6}\times \frac{4}{3}\\\\=\frac{4}{3}+\frac{4}{9}\\\\\mathrm{Minimo\:comun\:multiplo\:de\:}3,\:9:\quad 9\\\\=\frac{12+4}{9}\\\\=\frac{16}{9}$

$\left(\frac{3}{4}+\frac{7}{5}-\frac{14}{6}\right)\frac{2}{9}\\\\=\frac{2}{9}\left(\frac{3}{4}+\frac{7}{5}-\frac{7}{3}\right)\\\\\mathrm{Simplificar}\:\frac{3}{4}+\frac{7}{5}-\frac{7}{3}\:\mathrm{en\:una\:fraccion}:\quad -\frac{11}{60}\\\\=\frac{2}{9}\left(-\frac{11}{60}\right)\\\\=-\frac{11}{60}\times \frac{2}{9}\\\\=\frac{11}{30}\times \frac{1}{9}\\\\=-\frac{11\times \:1}{30\times \:9}\\\\=-\frac{11}{30\times \:9}\\\\=-\frac{11}{270}$