Bài 6:
a: \(-\dfrac{11}{6}< -1;\dfrac{8}{-9}>-1\)
Do đó: \(-\dfrac{11}{6}< -\dfrac{8}{9}\)
b: \(\dfrac{-25}{20}< 0;0< \dfrac{20}{25}\)
Do đó: \(-\dfrac{25}{20}< \dfrac{20}{25}\)
c: \(\dfrac{-19}{49}=\dfrac{-19\cdot47}{49\cdot47}=\dfrac{-893}{49\cdot47}\)
\(\dfrac{-23}{47}=\dfrac{-23\cdot49}{47\cdot49}=\dfrac{-1127}{47\cdot49}\)
mà -893>-1127
nên \(-\dfrac{19}{49}>-\dfrac{23}{47}\)
d: \(\dfrac{998}{555}=\dfrac{555+443}{555}=1+\dfrac{443}{555}\)
\(\dfrac{999}{556}=\dfrac{556+443}{556}=1+\dfrac{443}{556}\)
mà \(\dfrac{443}{555}>\dfrac{443}{556}\)
nên \(\dfrac{998}{555}>\dfrac{999}{556}\)
e: \(\dfrac{-315}{380}=\dfrac{-380+65}{380}=-1+\dfrac{65}{380}\)
\(\dfrac{-316}{381}=\dfrac{-381+65}{381}=-1+\dfrac{65}{381}\)
mà \(\dfrac{65}{380}>\dfrac{65}{381}\)
nên \(-\dfrac{315}{380}>-\dfrac{316}{381}\)
f: \(\dfrac{2025}{2024}=\dfrac{2024+1}{2024}=1+\dfrac{1}{2024}\)
\(\dfrac{2024}{2023}=\dfrac{2023+1}{2023}=1+\dfrac{1}{2023}\)
mà \(\dfrac{1}{2024}< \dfrac{1}{2023}\)(Vì 2024>2023)
nên \(\dfrac{2025}{2024}< \dfrac{2024}{2023}\)
Bài 7:
a: \(0,5+\dfrac{3}{16}-\dfrac{-3}{4}\)
\(=\dfrac{1}{2}+\dfrac{3}{16}+\dfrac{3}{4}\)
\(=\dfrac{8}{16}+\dfrac{3}{16}+\dfrac{12}{16}\)
\(=\dfrac{8+3+12}{16}=\dfrac{11+12}{16}=\dfrac{23}{16}\)
b: \(\dfrac{2}{3}-\left(2-\dfrac{1}{3}\right)+\dfrac{3}{2}+0,75\)
\(=\dfrac{2}{3}-2+\dfrac{1}{3}+\dfrac{3}{2}+0,75\)
\(=1-2+\dfrac{3}{2}+\dfrac{3}{4}\)
\(=\dfrac{3}{2}-1+\dfrac{3}{4}=\dfrac{1}{2}+\dfrac{3}{4}=\dfrac{5}{4}\)
c: \(\dfrac{5}{4}-\dfrac{5}{6}:\left(\dfrac{3}{8}-\dfrac{1}{6}\right)+\dfrac{11}{12}\)
\(=\dfrac{5}{4}-\dfrac{5}{6}:\left(\dfrac{9}{24}-\dfrac{4}{24}\right)+\dfrac{11}{12}\)
\(=\dfrac{5}{4}-\dfrac{5}{6}:\dfrac{5}{24}+\dfrac{11}{12}\)
\(=\dfrac{15}{12}+\dfrac{11}{12}-\dfrac{24}{6}\)
\(=\dfrac{26}{12}-\dfrac{24}{6}=\dfrac{13}{6}-\dfrac{24}{6}=-\dfrac{11}{6}\)
e: \(\dfrac{1}{3}-\dfrac{-5}{6}+\dfrac{3}{4}\)
\(=\dfrac{4}{12}+\dfrac{10}{12}+\dfrac{9}{12}\)
\(=\dfrac{4+10+9}{12}=\dfrac{23}{12}\)
f: \(1\dfrac{3}{10}:\dfrac{5}{7}+3\dfrac{7}{10}:\dfrac{5}{7}\)
\(=\left(1+\dfrac{3}{10}+3+\dfrac{7}{10}\right):\dfrac{5}{7}\)
\(=\left(4+1\right)\cdot\dfrac{7}{5}=5\cdot\dfrac{7}{5}=7\)
g: \(16\dfrac{3}{5}\cdot\dfrac{-1}{3}-13\dfrac{3}{5}\cdot\dfrac{-1}{3}\)
\(=-\dfrac{1}{3}\left(16+\dfrac{3}{5}-13-\dfrac{3}{5}\right)\)
\(=-\dfrac{1}{3}\cdot3=-1\)
i: \(\left(-\dfrac{13}{7}-\dfrac{4}{9}\right)-\left(-\dfrac{10}{7}-\dfrac{4}{9}\right)\)
\(=-\dfrac{13}{7}-\dfrac{4}{9}+\dfrac{10}{7}+\dfrac{4}{9}\)
\(=-\dfrac{13}{7}+\dfrac{10}{7}=-\dfrac{3}{7}\)
k: \(\dfrac{11}{24}-\dfrac{5}{41}+\dfrac{13}{24}+0,5-\dfrac{36}{41}\)
\(=\left(\dfrac{11}{24}+\dfrac{13}{24}\right)-\left(\dfrac{5}{41}+\dfrac{36}{41}\right)+0,5\)
\(=1-1+0,5=0,5\)
l: \(7+\left(\dfrac{7}{12}-\dfrac{1}{2}+3\right)-\left(\dfrac{1}{12}+5\right)\)
\(=7+\dfrac{7}{12}-\dfrac{1}{2}+3-\dfrac{1}{12}-5\)
\(=7+3-5=10\)
m: \(-\dfrac{4}{12}-\left(-\dfrac{13}{39}-0,25\right)+0,75\)
\(=-\dfrac{1}{3}+\dfrac{1}{3}+0,25+0,75\)
=0,25+0,75=1
Bài 4:
a, \(\dfrac{-6}{7}.\dfrac{-1}{6}\)
b, \(\dfrac{-6}{7}:\left(-6\right)\)
