Tính bằng cách thuận tiện \(\frac56*\frac37+\frac37*\frac76\)
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\(a,=\left(\dfrac{3}{5}+\dfrac{3}{5}+\dfrac{6}{5}\right)\times\left(\dfrac{6}{7}:7\right)=3\times\dfrac{6}{49}=\dfrac{18}{49}\)

9/5 + 4/7 + 6/5 + 3/7
= ( 9/5 + 6/5 ) + ( 4/7 + 3/7)
= 3 + 1
= 4
9/5 + 4/7 + 6/5 + 3/7 = (9/5 + 6/5) + (4/7 + 3/7)
= 15/5 + 7/7
= 3 + 1
= 4
1/2 x 45/33 x 1/9 x 11/6 = (1/2 x 1/9) x (45/33 x 11/6)
= 1/18 x 45/18
= 5/2

\(\dfrac{5}{6}\times\dfrac{7}{5}+\dfrac{5}{6}:\dfrac{15}{3}+\dfrac{5}{6}\times\dfrac{3}{5}-\dfrac{5}{6}\\ =\dfrac{5}{6}\times\dfrac{7}{5}+\dfrac{5}{6}\times\dfrac{1}{5}+\dfrac{5}{6}\times\dfrac{3}{5}-\dfrac{5}{6}\\ =\dfrac{5}{6}\times\left(\dfrac{7}{5}+\dfrac{1}{5}+\dfrac{3}{5}-1\right)\\ =\dfrac{5}{6}\times\dfrac{6}{5}=1\)

6/7 * 5/8*7/3*7/6*8/5
= 6*5*7*7*8 /7*8*3*6*5
=1*1*7*1*1/1*1*3*1*1
= 7/3

\(\dfrac{4}{5}\times\dfrac{3}{7}\times\dfrac{4}{5}\times\dfrac{6}{7}\times\dfrac{4}{14}=\dfrac{4}{5}\times\dfrac{3}{7}+\dfrac{4}{5}\times\dfrac{6}{7}-\dfrac{4}{5}\times\dfrac{2}{7}=\dfrac{4}{5}\times\left(\dfrac{6}{7}+\dfrac{3}{7}-\dfrac{2}{7}\right)=\dfrac{4}{5}\)
`5/6*3/7+3/7*7/6`
`=3/7*(5/6+7/6)`
`=3/7*(5+7)/6`
`=3/7*12/6`
`=3/7*2`
`=(3*2)/7`
`=6/7`
Vậy: ...
=\(\frac37*\left(\frac56+\frac76\right)\)
=\(\frac37*2\)
=6/7