\(\dfrac{1}{7}+\dfrac{2}{7}+\dfrac{3}{7}+\dfrac{4}{7}+\dfrac{5}{7}+\dfrac{6}{7}\)

\(=\dfrac{1+2+3+4+5+6}{7}=3\)

\(\dfrac{1}{7}+\dfrac{2}{7}+\dfrac{3}{7}+\dfrac{4}{7}+\dfrac{5}{7}+\dfrac{6}{7}\)

\(=\left(\dfrac{1}{7}+\dfrac{6}{7}\right)+\left(\dfrac{2}{7}+\dfrac{5}{7}\right)+\left(\dfrac{3}{7}+\dfrac{4}{7}\right)\)

\(=1+1+1\)

\(=3\)

\(a,\dfrac{5}{13}\times\dfrac{4}{15}\times13=\dfrac{5\times4\times13}{13\times5\times3}=\dfrac{4}{3}\\ b,\left(\dfrac{3}{7}+\dfrac{5}{2}\right)\times\dfrac{7}{5}=\dfrac{3}{7}\times\dfrac{7}{5}+\dfrac{5}{2}\times\dfrac{7}{5}=\dfrac{3}{5}+\dfrac{7}{2}=\dfrac{6}{10}+\dfrac{35}{10}=\dfrac{41}{10}\\ c,\dfrac{1}{5}\times\dfrac{11}{18}+\dfrac{11}{18}\times\dfrac{3}{5}=\dfrac{11}{18}\times\left(\dfrac{1}{5}+\dfrac{3}{5}\right)=\dfrac{11}{18}\times\dfrac{4}{5}=\dfrac{22}{45}\)

a, 4/3  b, 41/10   c,22/45

\(=\dfrac{3}{7}\left(\dfrac{5}{4}-\dfrac{2}{9}\right)=\dfrac{3}{7}\cdot\dfrac{45-8}{36}=\dfrac{3}{36}\cdot\dfrac{37}{7}=\dfrac{37}{84}\)

\(\dfrac{3}{7}:\dfrac{4}{5}-\dfrac{3}{7}:\dfrac{9}{2}\)
\(=\dfrac{3}{7}\times\dfrac{5}{4}-\dfrac{3}{7}\times\dfrac{2}{9}\)
\(=\dfrac{3}{7}\times\left(\dfrac{5}{4}-\dfrac{2}{9}\right)\)
\(=\dfrac{3}{7}\times\left(\dfrac{45}{36}-\dfrac{8}{36}\right)\)
\(=\dfrac{3}{7}\times\dfrac{37}{36}\)
\(=\dfrac{37}{84}\)
#DatNe

\(\dfrac{7}{6}\times\dfrac{3}{4}+\dfrac{3}{4}\times\dfrac{5}{6}-\dfrac{3}{4}\\ =\left(\dfrac{7}{6}+\dfrac{5}{6}-1\right)\times\dfrac{3}{4}\\ =1\times\dfrac{3}{4}=\dfrac{3}{4}\\ \dfrac{6\times7\times15\times8}{4\times21\times10\times3}\\ =\dfrac{2\times3\times7\times5\times3\times4\times2}{4\times7\times3\times5\times2\times3}\\ =2\)

a)=2

b)=1/3

a,2

b,1/3

Bài 3

a,26/100+0,009+41/100+0,24

0,26+0,09+0,41+0,24

(0,26+0,24)+(0,09+0,41)

0,5+0,5

=1

b,9+1/4+6+2/7+7+3/5+8+2/3+2/5+1/3+5/7+3/4

(9+6+7+8)+(2/7+5/7)+(1/4+3/4)+(3/5+2/5)+(2/3+1/3)

30+1+1+1+1

=34

Bài 4,5 khó quá mik ko bít lamf^^))

Bài 5: vì \(\dfrac{3}{11}\) = \(\dfrac{3\times5}{11\times5}\) = \(\dfrac{15}{55}\)

Vậy Khi giữ nguyên tử số thì số cần thêm vào mẫu số là: 

              55 - 39 = 16

Đáp số: 16 

Bài 4: a, \(\dfrac{2008}{2009}\) < 1; \(\dfrac{10}{9}\) > 1

           \(\dfrac{2008}{2009}\) < \(\dfrac{10}{9}\)

         b, \(\dfrac{1}{a+1}\) và \(\dfrac{1}{a-1}\)

Ta có: a + 1 > a - 1 ⇒ \(\dfrac{1}{a+1}\) < \(\dfrac{1}{a-1}\)

 60x [7/12+4/15]

60x153/180

=9180/180

b 1/2x2/3x3/4x4/5x5/6x6/7x7/8x8/9=40320/4032

\(B=\dfrac{1+\dfrac{1}{7}+\dfrac{1}{7^2}-\dfrac{1}{7^3}}{4+\dfrac{4}{7}+\dfrac{4}{7^2}-\dfrac{4}{7^3}}\cdot\dfrac{858585}{313131}\cdot\left(-1\dfrac{14}{17}\right)\)

\(=\dfrac{1}{4}\cdot\dfrac{85}{31}\cdot\dfrac{-31}{17}\)

\(=\dfrac{-5}{4}\)

Ta có: \(B=\dfrac{1+\dfrac{1}{7}+\dfrac{1}{7^2}-\dfrac{1}{7^3}}{4+\dfrac{4}{7}+\dfrac{4}{7^2}-\dfrac{4}{7^3}}.\dfrac{858585}{313131}.\left(-1\dfrac{14}{17}\right)\)

             \(=\dfrac{1+\dfrac{1}{7}+\dfrac{1}{7^2}-\dfrac{1}{7^3}}{4\left(1+\dfrac{1}{7}+\dfrac{1}{7^2}-\dfrac{1}{7^3}\right)}.\dfrac{85.10101}{32.10101}.\dfrac{-31}{17}=\dfrac{1}{4}.\dfrac{85}{31}.\dfrac{-31}{17}=-\dfrac{5}{4}\)

 \(\dfrac{2}{3}\times\dfrac{3}{4}\times\dfrac{4}{5}\) \(=\dfrac{2\times3\times4}{3\times4\times5}\) \(=\) \(\dfrac{2}{5}\)

\(\dfrac{2}{3}x\dfrac{3}{4}x\dfrac{4}{5}=\dfrac{2}{5}\)

\(\dfrac{2}{3}\)x\(\dfrac{3}{5}\)^{=\(\dfrac{2}{5}\)}