Cho M = 1 3 + 12 67 + 13 41 − 79 67 − 28 41 và N = 38 45 − 8 45 − 17 51 − 3 11 . Chọn câu đúng.
A. M = N
B. N < 1 < M
C. 1 < M < N
D. M < 1 < N
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\(a\frac{31}{23}-\left(\frac{7}{23}+\frac{8}{23}\right)\)
\(=\frac{31}{23}-\frac{7}{23}-\frac{8}{23}\)
\(=\frac{16}{23}\)
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a)\(\frac{31}{23}-\left(\frac{7}{23}+\frac{8}{23}\right)=\frac{31}{23}-\frac{8}{23}+\frac{7}{23}=1+\frac{7}{23}=1\frac{7}{23}\)
b)\(\left(\frac{1}{3}+\frac{12}{67}+\frac{13}{41}\right)-\left(\frac{79}{67}-\frac{28}{41}\right)=\left(\frac{13}{41}+\frac{28}{41}\right)+\left(\frac{79}{67}-\frac{12}{67}\right)-\frac{1}{3}=1+1-\frac{1}{3}\)
\(=2-\frac{1}{3}=\frac{5}{3}\)
`a,`
`31/23-(7/32+8/23)`
`=31/23-7/32-8/23`
`=(31/23-8/23)-7/32`
`=1-7/32=25/32`
`b,`
`38/45-(8/45-17/51-3/11)`
`=38/45-8/45+17/51+3/11`
`= (38/45-8/45)+17/51+3/11`
`=2/3+17/51+3/11`
`=1+3/11=14/11`
`c,`
`(1/3+12/67+13/41)-(79/67-28/41)`
`= 1/3+12/67+13/41-79/67+28/41`
`= 1/3+(12/67-79/67)+(13/41+28/41)`
`= 1/3+(-1)+1=1/3+(-1+1)=1/3+0=1/3`
`d,`
`1/5+(-1/6)+1/7+(-1/8)+1/9+1/8+(-1/7)+1/6+(-1/5)`
`= (1/5+ -1/5)+(-1/6+1/6)+(1/7+ -1/7)+(-1/8 +1/8)+1/9`
`= 0+0+0+0+1/9=1/9 .`
\(\left(\frac{1}{3}+\frac{12}{67}+\frac{13}{41}\right)-\left(\frac{79}{67}-\frac{28}{41}\right)\)
\(=\frac{1}{3}+\frac{12}{67}+\frac{13}{41}-\frac{79}{67}+\frac{28}{41}\)
\(=\left(\frac{12}{67}-\frac{79}{67}\right)+\left(\frac{13}{41}+\frac{28}{41}\right)+\frac{1}{3}\)
\(=\left(-1\right)+1+\frac{1}{3}\)
\(=\frac{1}{3}\)
\(\left(\dfrac{1}{3}+\dfrac{12}{67}+\dfrac{13}{41}\right)-\left(\dfrac{79}{67}-\dfrac{28}{41}\right)\\ =\left(\dfrac{103}{201}+\dfrac{13}{41}\right)-\dfrac{1363}{2747}\\ =\dfrac{6836}{8241}-\dfrac{1363}{2747}\\ =\dfrac{1}{3}\)
\(\left(\dfrac{1}{3}+\dfrac{12}{67}+\dfrac{13}{41}\right)-\left(\dfrac{79}{67}-\dfrac{28}{41}\right)\\ =\dfrac{1}{3}+\dfrac{12}{67}+\dfrac{13}{41}-\dfrac{79}{67}+\dfrac{28}{41}\\ =\dfrac{1}{3}+\left(\dfrac{12}{67}-\dfrac{79}{67}\right)+\left(\dfrac{13}{41}+\dfrac{28}{41}\right)\\ =\dfrac{1}{3}-\dfrac{67}{67}+\dfrac{41}{41}\\ =\dfrac{1}{3}-1+1\\ =\dfrac{1}{3}\)
\(\left(\frac{1}{3}+\frac{12}{67}+\frac{13}{41}\right)-\left(\frac{79}{67}-\frac{28}{41}\right)\)
=\(\frac{1}{3}+\frac{12}{67}+\frac{13}{41}-\frac{79}{67}+\frac{28}{41}\)
\(=\frac{1}{3}+\left(\frac{12}{67}-\frac{79}{67}\right)+\left(\frac{13}{41}+\frac{28}{41}\right)\)
\(=\frac{1}{3}-1+1\)
\(=\frac{1}{3}\)
(1/3+12/67+13/41)-(79/67-28/41). =1/3+12/613/41-79/67+28/41. =1/3+(12/67-79/67)+(13/41+28/41) =1/3+(-1)+1=1/3+0. =1/3
Đáp án cần chọn là: D
M = 1 3 + 12 67 + 13 41 − 79 67 − 28 41 M = 1 3 + 12 67 + 13 41 − 79 67 + 28 41 M = 1 3 + 12 67 − 79 67 + 13 41 + 28 41 M = 1 3 + − 1 + 1 M = 1 3
N = 38 45 − 8 45 − 17 51 − 3 11 N = 38 45 − 8 45 + 17 51 + 3 11 N = 38 45 − 8 45 + 17 51 + 3 11 N = 2 3 + 1 3 + 3 11 N = 1 + 3 11 N = 14 11
Vì 1 3 < 1 < 14 11 nên M < 1 < N