\(\dfrac{5}{7}\).\(\dfrac{-3}{11}\)-\(\dfrac{5}{7}\).\(\dfrac{8}{11}\)+1\(\dfrac{5}{7}\)

= \(\dfrac{5}{7}\).(\(\dfrac{-3}{11}\) - \(\dfrac{8}{11}\)) + 1\(\dfrac{5}{7}\)

= \(\dfrac{5}{7}\). -1             + 1\(\dfrac{5}{7}\)

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

= -1

\(\dfrac{5}{7}.-\dfrac{3}{11}-\dfrac{5}{7}.\dfrac{8}{11}+1\dfrac{5}{7}\)

\(=\dfrac{5}{7}.\left(\dfrac{3}{11}-\dfrac{8}{11}\right)+1\dfrac{5}{7}\)

\(=\dfrac{5}{7}.\left(-1\right)+1\dfrac{5}{7}\)

\(=1\)

a: 1152-(374+1152)+(-65+374)

=1152-374-1152-65+374

=(1152-1152)+(-374+374)-65

=0+0-65

=-65

b: \(\left\lbrack53+\left(-76\right)\right\rbrack-\left\lbrack-76-\left(-53\right)\right\rbrack\)

\(=\left\lbrack53-76\right\rbrack-\left\lbrack-76+53\right\rbrack\)

=0

c: \(-48+48\cdot\left(-78\right)+21\cdot\left(-48\right)\)

\(=\left(-48\right)\left(1+78+21\right)\)

\(=-48\cdot100=-4800\)

d:Sửa đề: \(\left(-12\right)\cdot47+\left(-12\right)\cdot52+\left(-12\right)\)

\(=\left(-12\right)\left(47+52+1\right)\)

\(=-12\cdot100=-1200\)

e: \(\left(-1\right)+\left(-3\right)+\cdots+\left(-199\right)+\left(-201\right)\)

=-(1+3+...+199+201)

Số số hạng của dãy số 1;3;...;199;201 là:

\(\frac{201-1}{2}+1=\frac{200}{2}+1=100+1=101\) (số)

Tổng của dãy số 1;3;...;199;201 là:

\(\left(201+1\right)\cdot\frac{101}{2}=202\cdot\frac{101}{2}=101\cdot101=10201\)

=>(-1)+(-3)+...+(-199)+(-201)=-10201

f:

Số số hạng hạng trong dãy số 17;20;23;..;53;56 là:

(56-17):3+1=39:3+1=13+1=14(số)

17+(-20)+23+(-26)+...+53+(-56)

=(17-20)+(23-26)+...+(53-56)

=(-3)+(-3)+...+(-3)

\(=-3\cdot\frac{14}{2}=-21\)

\(a,=-17+91-91+17+2011=\left(-17+17\right)+\left(91-91\right)+2011\)

\(=0+0+2011=2011\)

ai tick ông v

=54.(-76)+12.(-76)-(-76).34

=(-76).(54+12-34)

=-76.32

=-2432

-54.76+12.(-76)-76.(-34)

=(-54).76+(-12).76-76.(-34)

=76 [(-54)+(-12)-(-34)]

=76 (-32)

= -2432

22. \(\dfrac{\dfrac{3}{4}+\dfrac{3}{7}-\dfrac{3}{8}}{\dfrac{5}{4}+\dfrac{5}{7}-\dfrac{5}{8}}+1=\dfrac{3\left(\dfrac{1}{4}+\dfrac{1}{7}-\dfrac{1}{8}\right)}{5\left(\dfrac{1}{4}+\dfrac{1}{7}-\dfrac{1}{8}\right)}+1=\dfrac{3}{5}+1=\dfrac{8}{5}\)

23. \(\dfrac{2}{5}+\dfrac{3}{5}:\left(\dfrac{3}{5}+\dfrac{-2}{3}\right)+\dfrac{7}{2}=\dfrac{2}{5}+\dfrac{3}{5}:\left(\dfrac{9-10}{15}\right)+\dfrac{7}{2}=\dfrac{2}{5}+\dfrac{3}{5}.\dfrac{-15}{1}+\dfrac{7}{2}=\dfrac{2}{5}-\dfrac{45}{5}+\dfrac{7}{2}\)

\(=\dfrac{4}{10}-\dfrac{90}{10}+\dfrac{35}{10}=\dfrac{4-90+35}{10}=-\dfrac{51}{10}\)

24. \(\dfrac{4+\dfrac{4}{73}-\dfrac{4}{115}}{5+\dfrac{5}{73}-\dfrac{1}{23}}=\dfrac{4\left(1+\dfrac{1}{73}-\dfrac{1}{115}\right)}{5+\dfrac{5}{73}-\dfrac{5}{115}}=\dfrac{4\left(1+\dfrac{1}{73}-\dfrac{1}{115}\right)}{5\left(1+\dfrac{1}{73}-\dfrac{1}{115}\right)}=\dfrac{4}{5}\)

4. \(\dfrac{5}{7}-\dfrac{2}{11}+\dfrac{5}{7}-\dfrac{9}{11}=\dfrac{5}{7}\left(-\dfrac{2}{11}-\dfrac{9}{11}\right)=-\dfrac{5}{7}\)

9. \(\dfrac{5}{9}.\dfrac{7}{13}+\dfrac{5}{9}.\dfrac{9}{13}-\dfrac{5}{9}.\dfrac{3}{13}=\dfrac{5}{9}\left(\dfrac{7}{13}+\dfrac{9}{13}-\dfrac{3}{13}\right)=\dfrac{5}{9}\)

10. \(\dfrac{-5}{9}+\dfrac{8}{15}-\dfrac{2}{11}-\dfrac{4}{9}+\dfrac{7}{15}=\left(-\dfrac{5}{9}-\dfrac{4}{9}\right)+\left(\dfrac{8}{15}+\dfrac{7}{15}\right)-\dfrac{2}{11}=-\dfrac{2}{11}\)

a: =49+25

=74

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5/-8+7/8