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Cách 1 ở tất cả các câu: Tính bình thường như đề cho

 a)   Cách 2: \(\frac{5}{7}\times\frac{3}{4}+\frac{5}{7}\times\frac{1}{2}\)

 b) Cách 2: \(\frac{13}{21}\times\left(\frac{5}{7}+\frac{2}{7}\right)\)

c) Cách 2: \(\frac{2}{5}\times\frac{1}{2}+\frac{2}{5}\times\frac{1}{3}\)

d) Cách 2: \(\frac{17}{21}\times\left(5+\frac{2}{5}\right)\)

A = 4/1.3 + 4/3.5 + 4/5.7 + ... + 4/11.13

A = 2.(2/1.3 + 2/3.5 + 2/5.7 + ... + 2/11.13)

A = 2.(1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/11 - 1/13)

A = 2.(1 - 1/13)

A = 2.12/13

A = 24/13

24/13 đúng 100%

giải giúp mình nhé

\(\frac{4}{3.7}+\frac{5}{7.12}+\frac{1}{12.13}+\frac{7}{13.20}+\frac{3}{20.23}\)

\(=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{12}+...+\frac{1}{20}-\frac{1}{23}\)

\(=\frac{1}{3}-\frac{1}{23}+0+0+0\)

\(=\frac{20}{69}\)

Dấu "." là dấu nhân nha

Đặt \(A=\frac{4}{3\cdot7}+\frac{5}{7\cdot12}+\frac{1}{12\cdot13}+\frac{7}{13\cdot20}+\frac{3}{20\cdot23}\)

\(A=\frac{7-3}{3\cdot7}+\frac{12-7}{7\cdot12}+\frac{13-12}{12\cdot13}+\frac{20-13}{13\cdot20}+\frac{23-20}{20\cdot23}\)

\(A=\frac{1}{3}-\frac{1}{7}+....+\frac{1}{20}-\frac{1}{23}\)

\( A=\frac{1}{3}-\frac{1}{23}=\frac{20}{69}\)

= 20/69

5) Ta có: \(\dfrac{\left(5\sqrt{3}+\sqrt{50}\right)\left(5-\sqrt{24}\right)}{\sqrt{75}-5\sqrt{2}}\)

\(=\dfrac{5\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}-\sqrt{2}\right)^2}{5\left(\sqrt{3}-\sqrt{2}\right)}\)

=1

a) \(\frac{3}{5}:\left(-\frac{1}{15}-\frac{1}{6}\right)+\frac{3}{5}:\left(-\frac{1}{3}-1\frac{1}{15}\right)\)

\(=\frac{3}{5}:\left(-\frac{1}{15}-\frac{1}{6}-\frac{2}{6}-1+\frac{1}{15}\right)\)

\(=\frac{3}{5}:\left(-\frac{1}{2}-1\right)\)

\(=\frac{3}{5}:\left(-\frac{3}{2}\right)\)

\(=-\frac{2}{5}\)

b) \(\left(-\frac{3}{4}+\frac{5}{13}\right):\frac{2}{7}-\left(2\frac{1}{4}+\frac{8}{13}\right):\frac{2}{7}\)

\(=\left(-\frac{3}{4}+\frac{5}{13}-2+\frac{1}{4}+\frac{8}{13}\right):\frac{2}{7}\)

\(=\left(-\frac{1}{2}+1-2\right):\frac{2}{7}\)

\(=\left(-\frac{1}{2}-1\right):\frac{2}{7}\)

\(=-\frac{3}{2}:\frac{2}{7}\)

\(=-\frac{21}{4}\)

c) \(\left(\frac{1}{2}-\frac{13}{14}\right):\frac{5}{7}-\left(-\frac{2}{21}+\frac{1}{7}\right):\frac{5}{7}\)

\(=\left(\frac{7}{14}-\frac{13}{14}+\frac{2}{21}-\frac{3}{21}\right):\frac{5}{7}\)

\(=\left(-\frac{3}{7}-\frac{1}{21}\right):\frac{5}{7}\)

\(=\left(-\frac{9}{21}-\frac{1}{21}\right):\frac{5}{7}\)

\(=-\frac{10}{21}:\frac{5}{7}\)

\(=-\frac{2}{3}\)

a.\(\dfrac{27}{8}\)

b.\(\dfrac{37}{40}\)
c.\(\dfrac{5}{2}\)

d.\(\dfrac{7}{3}\)

e.5

g.\(\dfrac{53}{16}\)

Bài 1 :

a) \(\dfrac{3}{2}+\dfrac{5}{4}+\dfrac{5}{8}=\dfrac{12}{8}+\dfrac{10}{8}+\dfrac{5}{8}=\dfrac{12+10+5}{8}=\dfrac{27}{8}\)

b) \(\dfrac{4}{5}-\dfrac{3}{8}+\dfrac{2}{4}=\dfrac{32}{40}-\dfrac{15}{40}+\dfrac{20}{40}=\dfrac{32-15+20}{40}=\dfrac{37}{40}\)

c) \(3+\dfrac{6}{8}-\dfrac{5}{4}=\dfrac{3}{1}+\dfrac{6}{8}-\dfrac{5}{4}=\dfrac{24}{8}+\dfrac{6}{8}-\dfrac{10}{8}=\dfrac{20}{8}=\dfrac{5}{2}\)

d) \(\dfrac{5}{6}-\dfrac{1}{2}+2=\dfrac{5}{6}-\dfrac{1}{2}+\dfrac{2}{1}=\dfrac{5}{6}-\dfrac{3}{6}+\dfrac{12}{6}=\dfrac{14}{6}=\dfrac{7}{3}\)

e) \(\dfrac{3}{5}+\dfrac{6}{11}+\dfrac{7}{13}+\dfrac{2}{5}+\dfrac{16}{11}+\dfrac{19}{13}=\left(\dfrac{3}{5}+\dfrac{2}{5}\right)+\left(\dfrac{6}{11}+\dfrac{16}{11}\right)+\left(\dfrac{7}{13}+\dfrac{19}{13}\right)=1+2+2=5\)

g) \(\dfrac{75}{100}+\dfrac{18}{21}+\dfrac{29}{32}+\dfrac{1}{4}+\dfrac{3}{21}+\dfrac{13}{32}=\dfrac{3}{4}+\dfrac{6}{7}+\dfrac{29}{32}+\dfrac{1}{4}+\dfrac{1}{7}+\dfrac{13}{32}=\left(\dfrac{3}{4}+\dfrac{1}{4}\right)+\left(\dfrac{6}{7}+\dfrac{1}{7}\right)+\left(\dfrac{29}{32}+\dfrac{13}{32}\right)=1+1+\dfrac{21}{16}=2+\dfrac{21}{16}=\dfrac{53}{16}\)

a,3/2+5/4+5/8 = 12/8 + 10/8 + 5/8 = 27/8

b,4/5-3/8+2/4 = 32/40 - 15/40 + 20/40 = 37/40

c,3+6/8-5/4= 24/8 + 6/8 - 10/8 = 20/8 = 5/2

d,5/6-1/2+2 = 5/6 - 3/6 + 12/6 = 14/6 = 7/3

e,3/5+6/11+7/13+2/5+16/11+19/13 = ( 3/5+ 2/5) + ( 6/11 + 16/11) + ( 7/13 + 19/13) = 1 + 2 + 2 = 5

g,75/100+18/21+29/32+1/4+3/21+13/32 = 3/4 + 6/7 + 29/32 + 1/4 + 1/7 + 13/32=  ( 3/4 + 1/4) + ( 29/32 + 13/32) + ( 6/7 + 1/7)= 1 + 21/16 + 1 = 53/16

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