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

17/22

Cho \[M = \left( {\frac{1}{3} + \frac{{12}}{{67}} + \frac{{13}}{{41}}} \right) - \left( {\frac{{79}}{{67}} - \frac{{28}}{{41}}} \right)\] và \[N = \frac{{38}}{{45}} - \left( {\frac{8}{{45}} - \frac{{17}}{{51}} - \frac{3}{{11}}} \right)\]. Chọn câu đúng

M = N

N < 1 < M

1 < M < N

M < 1 < N

Giải thích

Trả lời:

\[M = \left( {\frac{1}{3} + \frac{{12}}{{67}} + \frac{{13}}{{41}}} \right) - \left( {\frac{{79}}{{67}} - \frac{{28}}{{41}}} \right)\]

\[M = \frac{1}{3} + \frac{{12}}{{67}} + \frac{{13}}{{41}} - \frac{{79}}{{67}} + \frac{{28}}{{41}}\]

\[M = \frac{1}{3} + \left( {\frac{{12}}{{67}} - \frac{{79}}{{67}}} \right) + \left( {\frac{{13}}{{41}} + \frac{{28}}{{41}}} \right)\]

\[M = \frac{1}{3} + \left( { - 1} \right) + 1\]

\[M = \frac{1}{3}\]

\[N = \frac{{38}}{{45}} - \left( {\frac{8}{{45}} - \frac{{17}}{{51}} - \frac{3}{{11}}} \right)\]

\[N = \frac{{38}}{{45}} - \frac{8}{{45}} + \frac{{17}}{{51}} + \frac{3}{{11}}\]

\[N = \left( {\frac{{38}}{{45}} - \frac{8}{{45}}} \right) + \frac{{17}}{{51}} + \frac{3}{{11}}\]

\[N = \frac{2}{3} + \frac{1}{3} + \frac{3}{{11}}\]

\[N = 1 + \frac{3}{{11}}\]

\[N = \frac{{14}}{{11}}\]

Vì \[\frac{1}{3} < 1 < \frac{{14}}{{11}}\] nên M < 1 < N

Đáp án cần chọn là: D