Question

Sắp xếp các phân số theo thứ tự giảm dần:

\(\dfrac{-5}{8};\dfrac{7}{10};\dfrac{-16}{19};\dfrac{20}{23};\dfrac{214}{315};\dfrac{205}{107}\)

Answer 1

\(\dfrac{205}{107}>\dfrac{20}{23}>\dfrac{7}{10}>\dfrac{214}{315}>-\dfrac{5}{8}>-\dfrac{16}{19}\)

Answer 2

(+) Xét: \(\dfrac{-5}{8};\dfrac{-16}{19}\)
Ta có: \(\dfrac{-5}{8}=\dfrac{-5.19}{8.19}=\dfrac{-95}{152};\dfrac{-16}{19}=\dfrac{-16.8}{19.8}=\dfrac{-128}{152}\)
Vì \(95< 128\) nên \(\dfrac{-95}{125}>\dfrac{-128}{152}\)
hay \(\dfrac{-5}{8}>\dfrac{-16}{19}\) ₍₁₎
(+) Xét: \(\dfrac{7}{10};\dfrac{20}{23};\dfrac{214}{315};\dfrac{205}{107}\)
Vì \(\dfrac{7}{10}< 1;\dfrac{20}{23}< 1;\dfrac{214}{315}< 1;\dfrac{205}{107}>1\)
nên \(\dfrac{205}{107}\) là số lớn nhất. ₍₂₎
(+) Ta có: \(\dfrac{7}{10}=\dfrac{7.1449}{10.1449}=\dfrac{10143}{14490};\dfrac{20}{23}=\dfrac{20.630}{23.630}=\dfrac{12600}{14490}\)
                \(\dfrac{214}{315}=\dfrac{214.46}{315.46}=\dfrac{9844}{14490}\)
Vì \(12600>10143>9844\) nên \(\dfrac{12600}{14490}>\dfrac{10143}{14490}>\dfrac{9844}{14490}\)
hay \(\dfrac{20}{23}>\dfrac{7}{10}>\dfrac{214}{315}\) ₍₃₎
Từ _(1);(2);(3) ta có:
\(\dfrac{205}{107}>\dfrac{20}{23}>\dfrac{7}{10}>\dfrac{214}{315}>\dfrac{-5}{8}>\dfrac{-16}{19}\)
Vậy ta sắp xếp các phân số theo thứ tự giảm dần là:
\(\dfrac{205}{107};\dfrac{20}{23};\dfrac{7}{10};\dfrac{214}{315};\dfrac{-5}{8};\dfrac{-16}{19}\)

Answer 3

205/107 > 20/23 > 7/10 > 214/215 > -5/8 > -16/19