Câu hỏi của Đào Thị Phúc - Toán lớp 6 | Học trực tuyến

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\(1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{19}-\dfrac{1}{20}\)

\(=1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{19}-\dfrac{1}{20}+\left(\dfrac{1}{2}-\dfrac{1}{2}\right)+\left(\dfrac{1}{4}-\dfrac{1}{4}\right)+...+\left(\dfrac{1}{20}-\dfrac{1}{20}\right)\)

\(=1+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{20}-2\left(\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{20}\right)\)

\(=1+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{20}-\left(1+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{10}\right)\)

\(=\dfrac{1}{11}+\dfrac{1}{12}+...+\dfrac{1}{20}\) (đpcm)

1) \(\dfrac{1}{2}+\dfrac{13}{19}-\dfrac{4}{9}+\dfrac{6}{19}+\dfrac{5}{18}\)

\(=\dfrac{1}{2}+\left(\dfrac{13}{19}+\dfrac{6}{19}\right)-\dfrac{4}{9}+\dfrac{5}{18}\)

\(=\dfrac{3}{2}-\dfrac{4}{9}+\dfrac{5}{18}\)

\(=\dfrac{19}{18}+\dfrac{5}{18}\)

\(=\dfrac{24}{18}\)

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

2) \(\dfrac{-20}{23}+\dfrac{2}{3}-\dfrac{3}{23}+\dfrac{2}{5}+\dfrac{7}{15}\)

\(=\left(-\dfrac{20}{23}-\dfrac{3}{23}\right)+\dfrac{2}{3}+\dfrac{2}{5}+\dfrac{7}{15}\)

\(=-1+\dfrac{2}{3}+\dfrac{2}{5}+\dfrac{7}{15}\)

\(=-\dfrac{1}{3}+\dfrac{2}{5}+\dfrac{7}{15}\)

\(=\dfrac{1}{15}+\dfrac{7}{15}\)

\(=\dfrac{8}{15}\)

3) \(\dfrac{4}{3}+\dfrac{-11}{31}+\dfrac{3}{10}-\dfrac{20}{31}-\dfrac{2}{5}\)

\(=\left(\dfrac{-11}{31}-\dfrac{20}{31}\right)+\dfrac{4}{3}+\dfrac{3}{10}-\dfrac{2}{5}\)

\(=-1+\dfrac{4}{3}+\dfrac{3}{10}-\dfrac{2}{5}\)

\(=\dfrac{1}{3}+\dfrac{3}{10}-\dfrac{2}{5}\)

\(=\dfrac{1}{3}-\dfrac{1}{10}\)

\(=\dfrac{7}{30}\)

4) \(\dfrac{5}{7}.\dfrac{5}{11}+\dfrac{5}{7}.\dfrac{2}{11}-\dfrac{5}{7}.\dfrac{14}{11}\)

\(=\dfrac{5}{7}.\left(\dfrac{5}{11}+\dfrac{2}{11}-\dfrac{14}{11}\right)\)

\(=\dfrac{5}{7}.-\dfrac{7}{11}\)

\(=-\dfrac{35}{77}\)

\(=-\dfrac{5}{11}\)

a, \(=\dfrac{2}{9}-\dfrac{10}{10}=\dfrac{2}{9}-1=-\dfrac{7}{9}\)

b, \(=-\dfrac{12}{6}+\dfrac{2}{5}=-2+\dfrac{2}{5}=-\dfrac{8}{5}\)

c, \(=\dfrac{27}{13}-1=\dfrac{14}{13}\)

d, \(=\dfrac{12}{11}+\dfrac{7}{19}+\dfrac{12}{19}=\dfrac{12}{11}+1=\dfrac{23}{11}\)

a) \(\dfrac{2}{9}+\dfrac{-3}{10}+\dfrac{-7}{10}\)

\(=\dfrac{2}{9}+\dfrac{-10}{10}=\dfrac{2}{9}-1=-\dfrac{7}{9}\)

b) \(\dfrac{-11}{6}+\dfrac{2}{5}+\dfrac{-1}{6}\)

\(=-2+\dfrac{2}{5}=-\dfrac{8}{5}\)

a,\(=\dfrac{2}{9}+\left(\dfrac{-3}{10}+\dfrac{-7}{10}\right)=\dfrac{2}{9}+\left(-1\right)=\dfrac{-7}{9}\)

b,\(=\left(\dfrac{-11}{6}+\dfrac{-1}{6}\right)+\dfrac{2}{5}=-2+\dfrac{2}{5}=\dfrac{-8}{5}\)

c,\(=\dfrac{27}{13}-\left(\dfrac{106}{111}+\dfrac{-5}{111}\right)=\dfrac{27}{13}-1=\dfrac{14}{13}\)

\(C=\dfrac{4}{9}\times\dfrac{13}{17}+\dfrac{4}{17}\times\dfrac{4}{9}+\dfrac{2}{9}\\ =\dfrac{4}{9}\times\left(\dfrac{13}{17}+\dfrac{4}{17}\right)+\dfrac{2}{9}\\ =\dfrac{4}{9}\times1+\dfrac{2}{9}\\ =\dfrac{4}{9}+\dfrac{2}{9}\\ =\dfrac{6}{9}=\dfrac{2}{3}\)

\(D=\dfrac{8}{19}\times\dfrac{5}{11}+\dfrac{7}{11}\times\dfrac{8}{19}+\dfrac{12}{11}\times\dfrac{11}{19}\\ =\dfrac{8}{19}\times\left(\dfrac{5}{11}+\dfrac{7}{11}\right)+\dfrac{12}{11}\times\dfrac{11}{19}\\ =\dfrac{8}{19}\times\dfrac{12}{11}+\dfrac{12}{11}\times\dfrac{11}{19}\\ =\dfrac{12}{11}\times\left(\dfrac{8}{19}+\dfrac{11}{19}\right)\\ =\dfrac{12}{11}\times19\\ =\dfrac{12}{11}\)

\(C=\dfrac{4}{9}\cdot\dfrac{13}{17}+\dfrac{4}{17}\cdot\dfrac{4}{9}+\dfrac{2}{9}\)

\(C=\dfrac{4}{9}\cdot\left(\dfrac{13}{17}+\dfrac{4}{17}\right)+\dfrac{2}{9}\)

\(C=\dfrac{4}{9}\cdot\dfrac{13+4}{17}+\dfrac{2}{9}\)

\(C=\dfrac{4}{9}\cdot\dfrac{17}{17}+\dfrac{9}{2}\)

\(C=\dfrac{4}{9}\cdot1+\dfrac{2}{9}\)

\(C=\dfrac{4}{9}+\dfrac{2}{9}\)

\(C=\dfrac{4+2}{9}\)

\(C=\dfrac{6}{9}\)

\(C=\dfrac{2}{3}\)

\(D=\dfrac{8}{19}\cdot\dfrac{5}{11}+\dfrac{7}{11}\cdot\dfrac{8}{19}+\dfrac{12}{11}\cdot\dfrac{11}{19}\)

\(D=\dfrac{8}{19}\cdot\left(\dfrac{5}{11}+\dfrac{7}{11}\right)+\dfrac{12}{11}\cdot\dfrac{11}{19}\)

\(D=\dfrac{8}{19}\cdot\dfrac{12}{11}+\dfrac{12}{11}\cdot\dfrac{11}{19}\)

\(D=\dfrac{12}{11}\cdot\left(\dfrac{8}{19}+\dfrac{11}{19}\right)\)

\(D=\dfrac{12}{11}\cdot\dfrac{19}{19}\)

\(D=\dfrac{12}{11}\cdot1\)

\(D=\dfrac{12}{11}\)

1: \(\dfrac{1}{2}+\dfrac{9}{10}+\dfrac{5}{6}-\dfrac{11}{14}-\dfrac{1}{3}+\dfrac{-4}{35}\)

\(=\left(\dfrac{1}{2}+\dfrac{5}{6}-\dfrac{1}{3}\right)+\dfrac{9}{10}-\left(\dfrac{11}{14}+\dfrac{4}{35}\right)\)

\(=\dfrac{3+5-2}{6}+\dfrac{9}{10}-\dfrac{55+8}{70}\)

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

=1

\(A=1-\dfrac{1}{2}+1-\dfrac{1}{6}+1-\dfrac{1}{12}+1-\dfrac{1}{20}\)

\(=4-\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}\right)\)

\(=4-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}\right)\)

=4-4/5=16/5

`A=1/2+5/6+11/12+19/20`

`A=(1/2+19/20)+(5/6+11/12)`

`A=(10/20+19/20)+(10/12+11/12)`

`A=29/20+21/12`

`A=87/60+105/60=192/60=16/5`