a: \(=\dfrac{5}{14}\left(\dfrac{2}{9}+\dfrac{7}{9}+1\right)=\dfrac{5}{14}\cdot2=\dfrac{5}{7}\)

b: \(=\dfrac{6}{8}\left(\dfrac{6}{7}-6\right)=\dfrac{6}{8}\cdot\dfrac{-36}{7}=\dfrac{-216}{56}=\dfrac{-27}{7}\)

A = \(\frac{1}{5\times6}+\frac{3}{6\times9}+\frac{5}{9\times14}+\frac{7}{14\times21}+\frac{9}{21\times30}\)

A = \(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+\frac{1}{14}-\frac{1}{21}+\frac{1}{21}-\frac{1}{30}\)

A = \(1-\frac{1}{30}\)

A = \(\frac{29}{30}\)

\(\dfrac{14}{7}>\dfrac{9}{7}\)

\(\dfrac{6}{13}< 1\)

\(\dfrac{7}{9}=\dfrac{14}{18}\)

\(\dfrac{4}{9}=\dfrac{20}{45}< \dfrac{26}{45}\)

\(\dfrac{11}{24}>\dfrac{9}{24}=\dfrac{3}{8}\)

\(\dfrac{42}{91}=\dfrac{42:7}{91:7}=\dfrac{6}{13}< \dfrac{7}{13}\)

\(\dfrac{34}{64}< \dfrac{52}{64}=\dfrac{13}{16}\)

\(\dfrac{17}{30}>\dfrac{16}{30}=\dfrac{8}{15}\)

9/14 .<.. 11/14           4/25 .<.. 4/23          5/6 ..<. 7/8         1 ..>. 14/15

8/9 ..=. 24/27             20/19 ..>. 20/27        8/7 .>.. 9/8        1 .<..15/14

\(\dfrac{9}{14}< \dfrac{11}{14};\dfrac{8}{9}=\dfrac{24}{27}\)

\(\dfrac{4}{25}< \dfrac{4}{23};\dfrac{20}{19}>\dfrac{20}{27}\)

\(\dfrac{5}{6}< \dfrac{7}{8};\dfrac{8}{7}>\dfrac{9}{8}\)

\(1>\dfrac{14}{15};1< \dfrac{15}{14}\)

9/14 .<.. 11/14           4/25 .<.. 4/23          5/6 ..<. 7/8         1 ..>. 14/15

8/9 ..=. 24/27             20/19 ..>. 20/27        8/7 .>.. 9/8        1 .<..15/14

Phương pháp giải:

Tính nhẩm rồi điền kết quả vào chỗ trống.

Lời giải chi tiết:

  (19/13+7/13)+(14/6+4/6)+(1/9+17/9)

=26/13+18/6+18/9

=2+3+2

=7

Bài 2. > , < ,  = ?

5/7 < 4/3             2/5 < 6/10            1/4 = 3/12                27/36 >

2/9           7/6 > 7/9

7/2 = 2/7        15/23 < 1                  27/9 > 2          14/15 < 1          51/17 < 4

sai rôi

\(\frac{14}{6}+\frac{1}{3}+\frac{14}{14}+\frac{14}{9}+\frac{7}{15}+\frac{6}{4}\)

\(=\frac{14}{6}+\frac{1}{3}+\frac{14}{9}+\frac{7}{15}+\frac{14}{14}+\frac{6}{4}\)

\(=\frac{42+6+28}{18}+\frac{7}{15}+\frac{2}{2}+\frac{3}{2}\)

\(=\frac{76}{18}+\frac{7}{15}+\frac{5}{2}\)

\(=\frac{76}{18}+\frac{5}{2}+\frac{7}{15}\)

\(=\frac{76+45}{18}+\frac{7}{15}\)

\(=\frac{121}{18}+\frac{7}{15}\)

\(=\frac{605+42}{90}\)

\(=\frac{647}{90}\)

\(\frac{14}{6}+\frac{1}{3}+\frac{14}{14}+\frac{14}{9}+\frac{7}{15}+\frac{6}{4}\)

\(=(\frac{7}{3}+\frac{1}{3})+1+(\frac{14}{9}+\frac{7}{15})+\frac{3}{2}\)

\(=\frac{8}{3}+1+\frac{91}{45}+\frac{3}{2}\)

\(=2+\frac{2}{3}+1+2+\frac{1}{45}+1+\frac{1}{2}\)

\(=\left(\frac{2}{3}+\frac{1}{45}+\frac{1}{2}\right)+\left(2+1+2+1\right)\)

\(=1+\frac{17}{90}+6\)

\(=7+\frac{17}{90}\)

\(=7\frac{17}{90}\)