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\(-\dfrac{3}{13}-\dfrac{7}{17}+\left(-\dfrac{5}{19}\right)+\left(-\dfrac{10}{13}\right)+\dfrac{24}{17}-\dfrac{4}{19}\)
\(=\left(-\dfrac{3}{13}-\dfrac{10}{13}\right)-\left(\dfrac{7}{17}-\dfrac{24}{17}\right)+\left(-\dfrac{5}{19}-\dfrac{4}{19}\right)\)
\(=-\dfrac{13}{13}-\left(-\dfrac{17}{17}\right)+-\dfrac{9}{19}\)
\(=-1+1+-\dfrac{9}{19}=-\dfrac{9}{19}\)
\(\dfrac{-3}{13}-\dfrac{7}{17}+\left(\dfrac{-5}{19}\right)+\left(\dfrac{-10}{13}\right)+\dfrac{24}{17}-\dfrac{4}{19}\)
=\(\left(\dfrac{-3}{13}+\dfrac{-10}{13}\right)+\left(\dfrac{-7}{17}+\dfrac{24}{17}\right)+\left(\dfrac{-5}{19}-\dfrac{4}{19}\right)\)
=-1+1+\(\dfrac{-9}{19}\)
=0+\(\dfrac{-9}{19}\) =\(\dfrac{-9}{19}\)
\(A=\frac{19}{24}-\frac{1}{2}-\frac{1}{3}-\frac{7}{24}\)
\(A=\frac{19}{24}+\frac{-1}{2}+\frac{-1}{3}+\frac{-7}{24}\)
\(A=\left(\frac{19}{24}+\frac{-7}{24}\right)+\frac{-1}{2}+\frac{-1}{3}\)
\(A=\frac{1}{2}+\frac{-1}{2}+\frac{-1}{3}\)
\(A=0+\frac{-1}{3}=\frac{-1}{3}\)
\(B=\frac{7}{24}+\frac{5}{6}+\frac{1}{4}-\frac{3}{7}-\frac{5}{15}\)
\(B=\frac{7}{24}+\frac{5}{6}+\frac{1}{4}+\frac{-3}{7}+\frac{-1}{3}\)
\(B=\left(\frac{49}{168}+\frac{140}{168}+\frac{42}{168}\right)+\left(\frac{-72}{168}+\frac{-56}{168}\right)\)
\(B=\frac{231}{168}+\frac{-128}{168}=\frac{103}{168}\)
Có: \(A=\frac{-1}{3}=\frac{\left(-1\right)\cdot56}{3\cdot56}=\frac{-56}{168}\)
Mặt khác: \(-56< 103\)
\(\Rightarrow\)\(\frac{-56}{168}< \frac{103}{168}\)
\(hay\) \(A< B\)
\(A=\frac{19}{24}-\frac{1}{2}-\frac{1}{3}-\frac{7}{24}\)
\(A=\frac{19}{24}-\frac{12}{24}-\frac{8}{24}-\frac{7}{24}\)
\(A=\frac{19-12-8-7}{24}\)
\(A=\frac{-8}{24}\)\(=\frac{-1}{3}\)
\(B=\frac{7}{24}+\frac{5}{6}+\frac{1}{4}-\frac{3}{7}-\frac{5}{15}\)
\(B=\frac{7}{24}+\frac{30}{24}+\frac{6}{24}-\frac{3}{7}-\frac{1}{3}\)
\(B=\frac{7}{24}+\frac{30}{24}+\frac{6}{24}-\frac{3}{7}-\frac{8}{24}\)
\(B=\frac{7+30+6-8}{24}-\frac{3}{7}\)
\(B=\frac{21}{24}-\frac{3}{7}\)
\(B=\frac{7}{8}-\frac{3}{7}\)
\(\Rightarrow B=\frac{25}{56}\)
A,-3/-7+5/19+-4/7
=(-3/-7+-4/7)+5/19
=-1/7+5/19=16/133
B,-13/24+-5/24+7/21
=-3/4+7/21=-5/12
C,-5/13+(-8/13+1)
=(-5/13+-8/13)+1
=-1+1=0
D,2/3+(3/8+-2/3)
=(2/3+-2/3)+3/8
=0+3/8=3/8
E,(-3/4+5/8)+-1/8
=-1/8+1/8=0
`-3/5 - (-19/24)+ -7/24`
`=-3/5+19/24+ -7/24`
`=-3/5+ (19/24 + - 7/24)`
`=-3/5+ 1/2`
`=-1/10`
\(-\dfrac{3}{5}+\dfrac{19}{24}-\dfrac{7}{24}=\) \(-\dfrac{3}{5}+\dfrac{12}{24}=\) \(-\dfrac{3}{5}+\dfrac{1}{2}\) \(=\dfrac{-6+5}{10}=-\dfrac{1}{10}\)