Question

Calcule as frações e simplifique os resultados, se for possível:

a)3 /5 +1 /5 + 2/ 5=
b)2 /5 +8 /9 + 7/12=
c) 2/3 + 1/7=
d)1 /6 +1 /7=
e)6 /7 + 2/14 =​​

Answer 1

✻ Os resultado das frações são :

A) 6/5

B) 337/180

C) 17/21

D) 13/42

E) 1

--

Explicação passo-a-passo :

$\\ {\large \displaystyle \sf {a) \ \frac{3}{5} +\frac{1}{5} +\frac{2}{5} =\frac{3+1+2}{5} = }} \ \large \displaystyle \sf {\purple{ \boxed{{ \large \displaystyle \sf {\purple{ \ \ \frac{6}{5} \ \ }}}}}}$

${\large \displaystyle \sf {b) \ \frac{2}{5} +\frac{8}{9} +\frac{7}{12} }}$

• MMC ( Mínimo Múltiplo Comum) de 5,9 e 12 :

$\begin{array}{r|l} \large \displaystyle \sf 5,9,12 & \large \displaystyle \sf 2\\ \large \displaystyle \sf 5,9,6& \large \displaystyle \sf 2\\ \large \displaystyle \sf 5,9,3& \large \displaystyle \sf 3\\ \large \displaystyle \sf 5,3,1& \large \displaystyle 3\\ \large \displaystyle \sf 5,1,1& \large \displaystyle \sf 5\\ \large \displaystyle \sf 1,1,1 \large \displaystyle \sf \end{array}$

• MMC de 5,9 e 12 = 2 · 2 · 3 · 3 · 5 = 180

$\\ {\large \displaystyle \sf { \frac{2}{5} +\frac{8}{9} +\frac{7}{12}=\frac{72}{180} +\frac{160}{180} +\frac{105}{180} =\frac{72+160+105}{180} = }} \ \large \displaystyle \sf {\purple{ \boxed{{ \large \displaystyle \sf {\purple{ \ \frac{337}{108} \ }}}}}}$

${\large \displaystyle \sf {c) \ \frac{2}{3} +\frac{1}{7} = }}$

• MMC ( Mínimo Múltiplo Comum) de 3 e 7 :

$\begin{array}{r|l} \large \displaystyle \sf 3,7 & \large \displaystyle \sf 3\\ \large \displaystyle \sf 1,7& \large \displaystyle \sf 7\\ \large \displaystyle \sf 1,1 \large \displaystyle \sf \end{array}\\\\ \\ \large \displaystyle \sf \ MMC \ de \ (3 \ e \ 7 ) =3\times7=\red{21}$

${\large \displaystyle \sf { \frac{2}{3} +\frac{1}{7} = \frac{2\times7}{21} +\frac{3\times1}{21} =\frac{14}{21}+\frac{3}{21} =\frac{14+3}{21} = }} \ \large \displaystyle \sf {\purple{ \boxed{{ \large \displaystyle \sf {\purple{ \ \frac{17}{21} \ }}}}}}$

${\large \displaystyle \sf {d) \ \frac{1}{6} +\frac{1}{7} = }}$

• MMC ( Mínimo Múltiplo Comum) de 6 e 7 :

$\begin{array}{r|l} \large \displaystyle \sf 6,7 & \large \displaystyle \sf 2\\ \large \displaystyle \sf 3,7& \large \displaystyle \sf 3\\ \large \displaystyle \sf 1,7 & \large \displaystyle \sf 7 \\ \large \displaystyle \sf 1,1 \end{array}\\\\ \\ \large \displaystyle \sf \ MMC \ de \ (6 \ e \ 7 ) =2\times3\times7=\red{42}$

${\large \displaystyle \sf { \frac{1}{6} +\frac{1}{7} = \frac{1\times7}{42} +\frac{6\times1}{42} =\frac{7}{42}+\frac{6}{42} =\frac{7+6}{42} = }} \ \large \displaystyle \sf {\purple{ \boxed{{ \large \displaystyle \sf {\purple{ \ \frac{13}{42} \ }}}}}}$

${\large \displaystyle \sf {e) \ \frac{6}{7} +\frac{2}{14} = }}$

• Reduza a fração 2/14 com o MDC 2 e 14 :

$\\ \begin{array}{r|l} \large \displaystyle \sf 2,14 & \large \displaystyle \sf \red 2\\ \large \displaystyle \sf 1,7& \large \displaystyle \sf 7\\ \large \displaystyle \sf 1,1 \end{array}\\\\ \\ \large \displaystyle \sf \ MDC \ de \ (2 \ e \ 14 ) =\red{2}$

${\large \displaystyle \sf { \frac{6}{7} +\frac{2\div2}{14\div2} = \frac{6}{7} +\frac{1}{7} = \frac{7}{7} }}$

• Simplifique ( divisão ) a fração 7/7 por 7 .

${\large \displaystyle \sf { \frac{7}{7} = 7\div7= }} \ \large \displaystyle \sf {\purple{ \boxed{{ \large \displaystyle \sf {\purple{ \ 1 \ }}}}}}$

✏️ Resposta :

A) 6/5

B) 337/180

C) 17/21

D) 13/42

E) 1

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Espero ter ajudado! ❤️