Bài 1:

a) Ta có: \(\frac{8}{40}+\frac{-4}{20}-\frac{3}{5}\)

\(=\frac{1}{5}+\frac{-1}{5}-\frac{3}{5}\)

\(=\frac{-3}{5}\)

b) Ta có: \(\frac{-7}{12}+\frac{-2}{12}-\frac{-3}{36}\)

\(=\frac{-7}{12}+\frac{-2}{12}-\frac{-1}{12}\)

\(=\frac{-9+1}{12}=\frac{-8}{12}=\frac{-2}{3}\)

c) Ta có: \(\left(\frac{1}{6}+\frac{-4}{13}\right)-\left(-\frac{17}{6}-\frac{30}{13}\right)\)

\(=\frac{1}{6}+\frac{-4}{13}+\frac{17}{6}+\frac{30}{13}\)

\(=3+2=5\)

d) Ta có: \(-\frac{-5}{4}+\frac{7}{4}-\frac{-11}{7}+\frac{2}{7}\)

\(=\frac{5}{4}+\frac{7}{4}+\frac{11}{7}+\frac{2}{7}\)

\(=3+\frac{13}{7}=\frac{21}{7}+\frac{13}{7}=\frac{34}{7}\)

e) Ta có: \(-\frac{1}{8}+\frac{-7}{9}+\frac{-7}{8}+\frac{6}{7}+\frac{2}{14}\)

\(=-1+1+\frac{-7}{9}\)

\(=-\frac{7}{9}\)

f) Ta có: \(\frac{-2}{9}-\frac{11}{-9}+\frac{5}{7}-\frac{-6}{-7}\)

\(=\frac{-2-\left(-11\right)}{9}+\frac{5-6}{7}\)

\(=1+\frac{-1}{7}=\frac{7}{7}+\frac{-1}{7}=\frac{6}{7}\)

Đặt S=1/12+1/13+1/14+1/15+...+1/23

ta có 1/12+1/13+1/14+1/15+...+1/22+1/23 = (1/12+1/13+1/14+...+1/17)+(1/18+1/19+...+1/23)

đặt A=1/12+1/13+1/14+...+1/17

ta có

1/13<1/12

1/14<1/12

..........................

.........................

1/17<1/12

=>A<1/12+1/12+1/12+....+1/12 (có 6 phân số)

=>A<1x6/12

=>A<1/2 (1)

Đặt B=1/18+1/19+...+11/23

ta có

1/19<1/18

1/20<1/18

...........................

..........................

1/23<1/18

=> B<1/18+1/18+1/18+...+1/18 (có 6 phân số)

=>B<1x 6/18

=>B<1/3      (2)

từ 1 và 2 =>S=A+B<1/2+1/3

=>S<5/6 (dpcm)

k cho mình nhé

Đặt S=1/12+1/13+1/14+1/15+...+1/23

ta có 1/12+1/13+1/14+1/15+...+1/22+1/23 = (1/12+1/13+1/14+...+1/17)+(1/18+1/19+...+1/23)

đặt A=1/12+1/13+1/14+...+1/17

ta có

1/13<1/12

1/14<1/12

..........................

.........................

1/17<1/12

=>A<1/12+1/12+1/12+....+1/12 (có 6 phân số)

=>A<1x6/12

=>A<1/2 (1)

Đặt B=1/18+1/19+...+11/23

ta có

1/19<1/18

1/20<1/18

...........................

..........................

1/23<1/18

=> B<1/18+1/18+1/18+...+1/18 (có 6 phân số)

=>B<1x 6/18

=>B<1/3      (2)

từ 1 và 2 =>S=A+B<1/2+1/3

=>S<5/6 (dpcm)

k cho mình nhé

ta có :

ts của a=tử số của b

mà ms của a<ms của b

suy ra a>b

sai bét

a)\(\frac{-10}{13}+\frac{8}{17}-\frac{3}{13}+\frac{12}{17}-\frac{11}{20}\)                

= \(\frac{-10}{13}+\frac{8}{17}+\frac{-3}{13}+\frac{12}{17}+\frac{-11}{20}\)     

=\(\left(\frac{-10}{13}+\frac{-3}{13}\right)+\left(\frac{8}{17}+\frac{12}{17}\right)+\frac{-11}{20}\)

=\(\frac{-13}{13}+\frac{20}{17}+\frac{-11}{20}\)

= \(\frac{-127}{340}\)

b) \(\frac{3}{4}+\frac{-5}{6}-\frac{11}{-12}\)

= \(\frac{3}{4}+\frac{-5}{6}+\frac{11}{12}\)

= \(\frac{9}{12}+\frac{-10}{12}+\frac{11}{12}\)

=\(\frac{10}{12}=\frac{5}{6}\)

c) \(\left[13.\frac{4}{9}+2.\frac{1}{9}\right]-3.\frac{4}{9}\)

= \(13+2.\left(\frac{4}{9}+\frac{1}{9}\right)-3.\frac{4}{9}\)

=\(15.\frac{5}{9}-3.\frac{4}{9}\)

=\(\left[15-3.\left(\frac{5}{9}-\frac{4}{9}\right)\right]\)

=\(12.\frac{1}{9}\)

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

Chúc bạn học tốt nhea. k mik nha ! ♥☺☺

\(3\frac{14}{19}+\frac{13}{17}+\frac{35}{43}+6\)

\(=\frac{71}{19}+\frac{13}{17}+\frac{35}{43}+6\)

\(=\frac{1454}{323}+\frac{35}{43}+6\)

\(=5,...+6\)

\(=11,...\)

\(Bai2a\)\(A=\frac{\sqrt{3}-\sqrt{6}}{1-\sqrt{2}}-\frac{2+\sqrt{8}}{1+\sqrt{2}}\)

\(=\frac{\sqrt{3}\left(1-\sqrt{2}\right)}{1-\sqrt{2}}-\frac{2\left(1+\sqrt{2}\right)}{1+\sqrt{2}}\)

\(=\sqrt{3}-2\) 

\(VayA=\sqrt{3}-2\)