Question

[Nachi]

bài 1 không quy đồng, hãy so sánh các phân số

Answer 1

[Nguyễn Đức Trí]

Bài 1 :

a) \(\dfrac{12}{15}< \dfrac{12}{14}< \dfrac{13}{14}\Rightarrow\dfrac{12}{15}< \dfrac{13}{14}\)

b) \(\dfrac{11}{12}< \dfrac{11+1984}{12+1984}=\dfrac{1995}{1996}\)

\(\Rightarrow\dfrac{11}{12}< \dfrac{1995}{1996}\)

c) \(\dfrac{499}{498}>\dfrac{499+1}{498+1}=\dfrac{500}{499}\)

\(\Rightarrow\dfrac{499}{498}>\dfrac{500}{499}\)

d) \(\dfrac{51}{80}< \dfrac{51}{79}< \dfrac{53}{79}\)

\(\Rightarrow\dfrac{51}{80}< \dfrac{53}{79}\)

Answer 2

[HT.Phong (9A5)]

Bài 2:

a) \(\dfrac{1}{9\times10}+\dfrac{1}{10\times11}+\dfrac{1}{11\times12}+...+\dfrac{1}{29\times30}\)

\(=\dfrac{1}{9}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{11}+...+\dfrac{1}{29}-\dfrac{1}{30}\)

\(=\dfrac{1}{9}-\dfrac{1}{30}\)

\(=\dfrac{10}{90}-\dfrac{3}{90}\)

\(=\dfrac{7}{90}\)

b) \(\dfrac{2}{7\times9}+\dfrac{2}{9\times11}+\dfrac{2}{11\times13}+....+\dfrac{2}{37\times39}\)

\(=\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+...+\dfrac{1}{37}-\dfrac{1}{39}\)

\(=\dfrac{1}{7}-\dfrac{1}{39}\)

\(=\dfrac{32}{273}\)

c) \(\dfrac{1}{1\times4}+\dfrac{1}{4\times7}+...+\dfrac{1}{31\times34}\)

\(=\dfrac{1}{3}\cdot\left[3\cdot\left(\dfrac{1}{1\times4}+\dfrac{1}{4\times7}+...+\dfrac{1}{31\times34}\right)\right]\)

\(=\dfrac{1}{3}\cdot\left(\dfrac{3}{1\times4}+\dfrac{3}{4\times7}+...+\dfrac{3}{31\times34}\right)\)

\(=\dfrac{1}{3}\cdot\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{31}-\dfrac{1}{34}\right)\)

\(=\dfrac{1}{3}\cdot\left(1-\dfrac{1}{34}\right)\)

\(=\dfrac{1}{3}\cdot\dfrac{33}{34}\)

\(=\dfrac{11}{34}\)