Không quy đồng mẫu số, hãy so sánh các phân số sau:
\(a)\;\frac{{1995}}{{1996}}\;\,...\,\;\frac{{1996}}{{1997}}\) \(c)\;\;\frac{{2121}}{{3737}}\;\,...\,\;\frac{{212121}}{{373737}}\) \(e)\;\;\frac{{18}}{{17}}\;\,...\,\;\frac{{13}}{{27}}\)
\(b)\;\frac{{16}}{{27}}\;\,...\,\;\frac{{15}}{{29}}\) \(d)\;\frac{{2010}}{{2011}}\;\,...\,\;\frac{{17}}{{16}}\) \(f)\;\frac{{327}}{{326}}\;\,...\,\;\frac{{326}}{{325}}\)
Câu 282785: Không quy đồng mẫu số, hãy so sánh các phân số sau:
\(a)\;\frac{{1995}}{{1996}}\;\,...\,\;\frac{{1996}}{{1997}}\) \(c)\;\;\frac{{2121}}{{3737}}\;\,...\,\;\frac{{212121}}{{373737}}\) \(e)\;\;\frac{{18}}{{17}}\;\,...\,\;\frac{{13}}{{27}}\)
\(b)\;\frac{{16}}{{27}}\;\,...\,\;\frac{{15}}{{29}}\) \(d)\;\frac{{2010}}{{2011}}\;\,...\,\;\frac{{17}}{{16}}\) \(f)\;\frac{{327}}{{326}}\;\,...\,\;\frac{{326}}{{325}}\)
A. a) < c) = e) >
b) > d) < f) <
B. a) < c) = e) >
b) > d) < f) >
C. a) > c) = e) >
b) > d) < f) <
D. a) < c) = e) >
b) < d) > f) <
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Đáp án : A(0) bình luận (0) lời giải
Giải chi tiết:
\(a)\;\frac{{1995}}{{1996}}\;\,...\,\;\frac{{1996}}{{1997}}\)
Ta có: \(1 - \frac{{1995}}{{1996}} = \frac{1}{{1996}};\;\;1 - \frac{{1996}}{{1997}} = \frac{1}{{1997}}.\)
Vì \(\frac{1}{{1996}} > \frac{1}{{1997}}\) nên \(\frac{{1995}}{{1996}} < \frac{{1996}}{{1997}}.\)
\(c)\;\;\frac{{2121}}{{3737}}\;\,...\,\;\frac{{212121}}{{373737}}\)
Ta có: \(\frac{{2121}}{{3737}} = \frac{{2121:101}}{{3737:101}} = \frac{{21}}{{37}}\)
\(\;\frac{{212121}}{{373737}} = \frac{{212121:10101}}{{373737:10101}} = \frac{{21}}{{37}}\)
Vậy \(\frac{{2121}}{{3737}} = \frac{{212121}}{{373737}}\;\left( { = \frac{{21}}{{37}}} \right).\)
\(e)\,\,\frac{{18}}{{17}}\,\,...\,\,\frac{{13}}{{27}}\)
Vì \(\frac{{18}}{{17}} > 1,\;\;\frac{{13}}{{27}} < 1\) nên \(\frac{{18}}{{17}} > \frac{{13}}{{27}}.\)
\(b)\;\frac{{16}}{{27}}\;\,...\,\;\frac{{15}}{{29}}\)
Vì \(\frac{{16}}{{27}} > \frac{{16}}{{29}},\;\;\frac{{15}}{{29}} < \frac{{16}}{{29}}\) nên \(\frac{{16}}{{27}} > \frac{{15}}{{29}}.\)
\(d)\;\frac{{2010}}{{2011}}\;\,...\,\;\frac{{17}}{{16}}\)
Vì \(\frac{{2010}}{{2011}} < 1,\;\;\frac{{17}}{{16}} > 1\)
Nên \(\frac{{2010}}{{2011}} < \frac{{17}}{{16}}.\)
\(f)\;\frac{{327}}{{326}}\;\,...\,\;\frac{{326}}{{325}}\)
Ta có:
\(\frac{{327}}{{326}} - 1 = \frac{1}{{326}},\;\;\frac{{326}}{{325}} - 1 = \frac{1}{{325}}.\)
Vì: \(\frac{1}{{326}} < \frac{1}{{325}}\) nên \(\frac{{327}}{{326}} < \frac{{326}}{{325}}.\)
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