Toán 6 Tính: $\dfrac{31}{32}-\left ( \dfrac{7}{32}+\dfrac{8}{32} \right )$

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Tính bằng phương pháp hợp lí nhất:

a. $\dfrac{31}{23}-\left(\dfrac{7}{32}+\dfrac{8}{23}\right)$
b. $\left(\dfrac13+\dfrac{12}{67}+\dfrac{13}{41}\right)-\left(\dfrac{79}{67}-\dfrac{28}{41}\right)$
c. $\dfrac{38}{45}-\left(\dfrac{8}{45}-\dfrac{17}{51}-\dfrac{3}{11}\right)$
d. $\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{49.50}$
e. $\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{37.39}$

 

[Blue Plus]

a. $\dfrac{31}{23}-\left(\dfrac{7}{32}+\dfrac{8}{23}\right)$
b. $\left(\dfrac13+\dfrac{12}{67}+\dfrac{13}{41}\right)-\left(\dfrac{79}{67}-\dfrac{28}{41}\right)$
c. $\dfrac{38}{45}-\left(\dfrac{8}{45}-\dfrac{17}{51}-\dfrac{3}{11}\right)$
d. $\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{49.50}$
e. $\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{37.39}$

a)

3123− (732+823)3123- (732+823)​

$\dfrac{31}{23}-\left(\dfrac{7}{32}+\dfrac{8}{23}\right)=\dfrac{31}{23}-\dfrac{7}{32}-\dfrac{8}{23}=\left(\dfrac{31}{23}-\dfrac{8}{23}\right)-\dfrac{7}{32}=1-\dfrac{7}{32}=\dfrac{25}{32}$

b)

(13+1267+1341)−(7967−2841)(13+1267+1341)-(7967-2841)​

$\left(\dfrac13+\dfrac{12}{67}+\dfrac{13}{41}\right)-\left(\dfrac{79}{67}-\dfrac{28}{41}\right)\\=\dfrac13+\dfrac{12}{67}+\dfrac{13}{41}-\dfrac{79}{67}+\dfrac{28}{41}\\=\dfrac13+\left(\dfrac{12}{67}-\dfrac{79}{67}\right)+\left(\dfrac{13}{41}+\dfrac{28}{41}\right)\\=\dfrac13+(-1)+1\\=\dfrac13$

c)

3845−(845−1751−311)3845-(845-1751-311)​

$\dfrac{38}{45}-\left(\dfrac{8}{45}-\dfrac{17}{51}-\dfrac{3}{11}\right)\\=\dfrac{38}{45}-\dfrac{8}{45}+\dfrac{17}{51}+\dfrac{3}{11}\\=\dfrac{30}{45}+\dfrac{17}{51}+\dfrac{3}{11}\\=\dfrac23+\dfrac13+\dfrac{3}{11}\\=\dfrac{14}{11}$

d)

11.2+12.3+...+149.5011.2+12.3+...+149.50​

$\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{49.50}\\=\dfrac11-\dfrac12+\dfrac12-\dfrac13+...+\dfrac1{49}-\dfrac1{50}\\=1-\dfrac1{50}\\=\dfrac{49}{50}$

e)

23.5+25.7+...+237.39​

$\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{37.39}\\=\dfrac13-\dfrac15+\dfrac15-\dfrac17+...+\dfrac1{37}-\dfrac1{39}\\=\dfrac13-\dfrac1{39}\\=dfrac{12}{39}$