Question

[phạm doãn đông quân]

so sánh rồi xếp theo thứ tự từ lớn đến bé:

18/19, 9/10, 6/7, 3/4, 36/37

Answer 1

[Nguyễn Đức Trí]

\(\dfrac{3}{4}< \dfrac{3+3}{4+3}=\dfrac{6}{7}\)

\(\dfrac{6}{7}< \dfrac{6+3}{7+3}< \dfrac{9}{10}\)

\(\dfrac{9}{10}< \dfrac{9+9}{10+9}=\dfrac{18}{19}\)

\(\dfrac{18}{19}< \dfrac{18+18}{19+18}=\dfrac{36}{37}\)

Vậy \(\dfrac{36}{37}>\dfrac{18}{19}>\dfrac{9}{10}>\dfrac{6}{7}>\dfrac{3}{4}\)

Answer 2

[Kiều Vũ Linh]

\(\dfrac{18}{19}=1-\dfrac{1}{19}\)

\(\dfrac{9}{10}=1-\dfrac{1}{10}\)

\(\dfrac{6}{7}=1-\dfrac{1}{7}\)

\(\dfrac{3}{4}=1-\dfrac{1}{4}\)

\(\dfrac{36}{37}=1-\dfrac{1}{37}\)

Do \(37>19>10>7>4\)

\(\Rightarrow\dfrac{1}{37}< \dfrac{1}{19}< \dfrac{1}{10}< \dfrac{1}{7}< \dfrac{1}{4}\)

\(\Rightarrow1-\dfrac{1}{37}>1-\dfrac{1}{19}>1-\dfrac{1}{10}>1-\dfrac{1}{7}>1-\dfrac{1}{4}\)

\(\Rightarrow\dfrac{36}{37}>\dfrac{18}{19}>\dfrac{9}{10}>\dfrac{6}{7}>\dfrac{3}{4}\)