2/5 x 3/7 => 2 x 3/5 x 7 => 6/35
4/7 x 3/4 => 4 x 3/7 x 4 => 12/28 => 3/7
4/9 x 3/10 = 4 x 3/9 x 10 => 12/90
2 x 5/18 = 10/18 = 5/9
`2/5 xx 3/7= 6/35`
`4/7 xx 3/4=12/28= 3/7`
`4/9 xx 3/10=12/90=2/15`
`2 xx 5/18= 10/18= 5/6`
`3/8 : 7/5= 3/8 xx 5/7= 15/56`
`3/4 : 9/10 = 3/4 xx 10/9=30/36=5/6`
`7/8 : 2= 7/8 xx 1/2= 7/16`
`6 : 2/3= 6 xx 3/2= 18/2=9`
`1/3 xx 3/5 xx 5/9= (1xx3xx5)/(3xx5xx9)= 15/135=1/9`
`15/16 : 3/8 xx 3/4= 15/16 xx 8/3 xx 3/4= ( 15xx8xx3)/(16xx3xx4)= 360/192=15/8`
a) \(\dfrac{2}{5}\times\dfrac{3}{7}=\dfrac{6}{35}\); \(\dfrac{4}{7}\times\dfrac{3}{4}=\dfrac{3}{7}\); \(\dfrac{4}{9}\times\dfrac{3}{10}=\dfrac{12}{90}=\dfrac{2}{15}\); \(2\times\dfrac{5}{18}=\dfrac{10}{18}=\dfrac{5}{9}\).
b) \(\dfrac{3}{8}:\dfrac{7}{5}=\dfrac{3}{8}\times\dfrac{5}{7}=\dfrac{15}{56}\); \(\dfrac{3}{4}:\dfrac{9}{10}=\dfrac{3}{4}\times\dfrac{10}{9}=\dfrac{30}{36}=\dfrac{5}{6}\);
\(\dfrac{7}{8}:2=\dfrac{7}{8}\times\dfrac{1}{2}=\dfrac{7}{16}\); \(6:\dfrac{2}{3}=6\times\dfrac{3}{2}=\dfrac{18}{2}=9\)
c) \(\dfrac{1}{3}\times\dfrac{3}{5}\times\dfrac{5}{9}=\dfrac{1}{5}\times\dfrac{5}{9}=\dfrac{1}{9}\)
\(\dfrac{15}{16}:\dfrac{3}{8}\times\dfrac{3}{4}=\dfrac{15}{16}\times\dfrac{8}{3}\times\dfrac{3}{4}=\dfrac{120}{48}\times\dfrac{3}{4}=\dfrac{5}{2}\times\dfrac{3}{4}=\dfrac{15}{8}\)