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a) \(\dfrac{2}{3}\times\dfrac{4}{5}=\dfrac{4}{5}\times\dfrac{2}{3}\)
b) \(\left(\dfrac{1}{3}\times\dfrac{2}{5}\right)\times\dfrac{3}{4}=\dfrac{1}{3}\times\left(\dfrac{2}{5}\times\dfrac{3}{4}\right)\)
c) \(\left(\dfrac{1}{3}-\dfrac{2}{15}\right)\times\dfrac{3}{4}=\dfrac{1}{3}\times\dfrac{3}{4}+\dfrac{2}{15}\times\dfrac{3}{4}\)
\(\dfrac{1}{2}\times\dfrac{2}{3}\times\dfrac{3}{4}\times\dfrac{4}{5}=\dfrac{1}{5}\)
a) $\frac{3}{2} \times \frac{5}{8} + \frac{7}{4} = \frac{{15}}{{16}} + \frac{7}{4} = \frac{{15}}{{16}} + \frac{{28}}{{16}} = \frac{{43}}{{16}}$
b) $\frac{8}{5}:\left( {\frac{4}{3} - \frac{5}{6}} \right) = \frac{8}{5}:\left( {\frac{8}{6} - \frac{5}{6}} \right) = \frac{8}{5}:\frac{1}{2} = \frac{8}{5} \times 2 = \frac{{16}}{5}$
c) $\frac{3}{4} \times \frac{1}{5} - \frac{1}{{10}} = \frac{3}{{20}} - \frac{1}{{10}} = \frac{3}{{20}} - \frac{2}{{20}} = \frac{1}{{20}}$
a) \(\dfrac{3}{22}\times\dfrac{3}{11}\times22\)
\(=\dfrac{3}{22}\times\dfrac{3}{11}\times\dfrac{22}{1}\)
\(=\dfrac{3\times3\times22}{22\times11\times1}\)
\(=\dfrac{9}{11}\)
b) \(\left(\dfrac{1}{3}+\dfrac{1}{6}\right)\times\dfrac{2}{5}\)
\(=\left(\dfrac{2}{6}+\dfrac{1}{6}\right)\times\dfrac{2}{5}\)
\(=\dfrac{3}{6}\times\dfrac{2}{5}\)
\(=\dfrac{1}{2}\times\dfrac{2}{5}\)
\(=\dfrac{2}{10}\)
\(=\dfrac{1}{5}\)
a: =3/22*22*3/11
=3*3/11
=9/11
b: =(2/6+1/6)*2/5
=1/2*2/5
=1/5
a) $\frac{5}{2} \times \frac{4}{3} + \frac{1}{3} = \frac{{10}}{3} + \frac{1}{3} = \frac{{11}}{3}$
b) $\frac{7}{3} - \frac{2}{3}:\frac{5}{7} = \frac{7}{3} - \frac{2}{3} \times \frac{7}{5} = \frac{7}{3} - \frac{{14}}{{15}} = \frac{{35}}{{15}} - \frac{{14}}{{15}} = \frac{{21}}{{15}} = \frac{7}{5}$
c) $\frac{3}{4} \times \left( {\frac{5}{2} - \frac{3}{2}} \right) = \frac{3}{4} \times 1 = \frac{3}{4}$
a) \(\left(\dfrac{1}{4}+\dfrac{1}{12}\right):\dfrac{1}{13}\)
\(=\left(\dfrac{3}{12}+\dfrac{1}{12}\right):\dfrac{1}{13}\)
\(=\dfrac{4}{12}\times13\)
\(=\dfrac{1}{3}\times13\)
\(=\dfrac{13}{3}\)
b) \(\dfrac{3}{5}:\dfrac{2}{9}-\dfrac{1}{10}\)
\(=\dfrac{3}{5}\times\dfrac{9}{2}-\dfrac{1}{10}\)
\(=\dfrac{27}{10}-\dfrac{1}{10}\)
\(=\dfrac{26}{10}\)
\(=\dfrac{13}{5}\)
a: =2/5+3/8=16/40+15/40=31/40
b: =1/2x(25/10-6/10)=1/2x19/10=19/20
\(a)1-\dfrac{1}{2}\times1-\dfrac{1}{3}\times1-\dfrac{1}{4}\)
\(=\dfrac{1}{1}-\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{4}\)
\(=\dfrac{12}{12}-\dfrac{6}{12}-\dfrac{4}{12}-\dfrac{3}{12}\)
\(=\dfrac{-1}{12}\)
\(b)1+\dfrac{1}{2}:1+\dfrac{1}{3}:1+\dfrac{1}{4}\)
\(=\dfrac{1}{1}+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}\)
\(=\dfrac{12}{12}+\dfrac{6}{12}+\dfrac{4}{12}+\dfrac{3}{12}\)
\(=\dfrac{25}{12}\)
`(1-1/2)xx(1-1/3)xx(1-1/4)`
`=1/2 xx 2/3 xx 3/4`
`=(1xx2xx3)/(2xx3xx4)`
`=1/4`
`(1+1/2):(1+1/3):(1+1/4)`
`=3/2:4/3:5/4`
`=3/2 xx 3/4 xx 4/5`
`=(3xx3xx4)/(2xx4xx5)`
`=(3xx3)/(2xx5)`
`=9/10`