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ACTIVIDAD 9

Realiza las siguientes sumas y/o restas entre racionales.

a. [tex]\frac{1}{6} + \frac{4}{5} =[/tex]

b. [tex]\frac{7}{10} - \frac{1}{8} =[/tex]

c. [tex]\frac{6}{14} + \frac{8}{-21} =[/tex]

d. [tex]-\frac{5}{4} + \frac{7}{3} =[/tex]

e. [tex]\frac{6}{5} + \frac{-3}{8} - \frac{8}{-5} =[/tex]

f. [tex]\frac{6}{7} - \frac{-3}{14} - \frac{18}{5} =[/tex]

g. [tex]-\frac{12}{35} - \frac{6}{14} =[/tex]

h. [tex]\frac{1}{2} - \frac{1}{3} + \frac{2}{5} =[/tex]

i. [tex]-\frac{9}{16} + \frac{3}{8} - \frac{1}{4} =[/tex]

j. [tex]\frac{6}{15} - \frac{-2}{3} + \frac{8}{6} =[/tex]

k. [tex]\frac{5}{6} - \frac{9}{4} + 2 =[/tex]

l. [tex]-5 - \frac{1}{4} + \frac{7}{3} =[/tex]

Sagot :

GinnyAnsweridn
¡Claro! Vamos a resolver cada una de las operaciones con fracciones de forma detallada paso a paso.

### a. [tex]\(\frac{1}{6} + \frac{4}{5}\)[/tex]
Para sumar fracciones, primero encontramos un denominador común:
[tex]\[ \frac{1}{6} + \frac{4}{5} = \frac{5 \times 1}{30} + \frac{6 \times 4}{30} = \frac{5}{30} + \frac{24}{30} = \frac{5 + 24}{30} = \frac{29}{30} \][/tex]
[tex]\[ \boxed{\frac{29}{30}} \][/tex]

### b. [tex]\(\frac{7}{10} - \frac{1}{8}\)[/tex]
Primero encontramos un denominador común:
[tex]\[ \frac{7}{10} - \frac{1}{8} = \frac{7 \times 8}{80} - \frac{1 \times 10}{80} = \frac{56}{80} - \frac{10}{80} = \frac{56 - 10}{80} = \frac{46}{80} = \frac{23}{40} \][/tex]
[tex]\[ \boxed{\frac{23}{40}} \][/tex]

### c. [tex]\(\frac{6}{14} + \frac{8}{-21}\)[/tex]
Primero simplificamos las fracciones:
[tex]\[ \frac{6}{14} = \frac{3}{7}, \quad \frac{8}{-21} = -\frac{8}{21} \][/tex]
Luego encontramos un denominador común:
[tex]\[ \frac{3}{7} + \left(-\frac{8}{21}\right) = \frac{3 \times 3}{21} - \frac{8}{21} = \frac{9}{21} - \frac{8}{21} = \frac{9 - 8}{21} = \frac{1}{21} \][/tex]
[tex]\[ \boxed{\frac{1}{21}} \][/tex]

### d. [tex]\(-\frac{5}{4} + \frac{7}{3}\)[/tex]
Encontramos un denominador común:
[tex]\[ -\frac{5}{4} + \frac{7}{3} = \frac{-15}{12} + \frac{28}{12} = \frac{-15 + 28}{12} = \frac{13}{12} \][/tex]
[tex]\[ \boxed{\frac{13}{12}} \][/tex]

### e. [tex]\(\frac{6}{5} + \frac{-3}{8} - \frac{8}{-5}\)[/tex]
La tercera fracción se vuelve positiva:
[tex]\[ \frac{8}{-5} = -\frac{8}{5} \][/tex]
Entonces, sumamos:
[tex]\[ \frac{6}{5} - \frac{3}{8} + \frac{8}{5} = \frac{6 \times 8 + 8 \times (-3) + 8 \times 8}{40} = \frac{48 - 3 \times 5 + 64}{5} = \frac{48 - 15 + 64}{40} = \frac{163}{40} = \boxed{\frac{97}{40}} \][/tex]

### f. [tex]\(\frac{6}{7} - \frac{-3}{14} - \frac{18}{5}\)[/tex]
Simplificamos pasos:
[tex]\[ \frac{6}{7} + \frac{3}{14} = \frac{12}{14} + \frac{3}{14} = \frac{15}{14} - \frac{18}{5} \][/tex]
Adquiriendo denominador común:
[tex]\[ \frac{-177}{70} \][/tex]

### g. [tex]\(-\frac{12}{35} - \frac{6}{14}\)[/tex]
Primero simplificamos:
[tex]\[ -\frac{12}{35} - \frac{3}{7} \][/tex]
[tex]\[ \boxed{\frac{-27}{35}} \][/tex]

### h. [tex]\(\frac{1}{2} - \frac{1}{3} + \frac{2}{5}\)[/tex]
[tex]\[ \frac{15}{30} + \frac{-10}{30} + \frac{12}{30} = \frac}{30} = \boxed{\frac{17}{30}} \][/tex]
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