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\(\dfrac{3}{4}.\dfrac{2}{3}-\dfrac{1}{6}.\dfrac{3}{4}-\dfrac{3}{4}.\dfrac{1}{2}\)
= \(\dfrac{3}{4}.\left(\dfrac{2}{3}-\dfrac{1}{6}-\dfrac{1}{2}\right)\)
= \(\dfrac{3}{4}.0\)
= 0
\(\dfrac{3}{4}\cdot\dfrac{2}{3}-\dfrac{1}{6}\cdot\dfrac{3}{4}-\dfrac{3}{4}\cdot\dfrac{1}{2}\)
\(=\dfrac{3}{4}\left(\dfrac{2}{3}-\dfrac{1}{6}-\dfrac{1}{2}\right)\)
\(=\dfrac{3}{4}\cdot\left(\dfrac{4}{6}-\dfrac{1}{6}-\dfrac{3}{6}\right)\)
=0
\(\frac{5}{5}x\)\(\frac{17}{21}+\frac{17}{21}x\)\(\frac{2}{5}\)
=(\(\frac{5}{5}+\frac{2}{5}\)) x\(\frac{17}{21}\)
=\(\frac{7}{5}x\)\(\frac{17}{21}\)
\(\frac{119}{105}\)
\(\frac{5}{9}\times\frac{8}{17}+\frac{4}{9}\times\frac{8}{17}\)
\(=\left(\frac{5}{9}+\frac{4}{9}\right)\times\frac{8}{17}\)
\(=1\times\frac{8}{17}\)
\(=\frac{8}{17}\)
\(\frac{4}{5}\cdot\frac{3}{7}+\frac{4}{5}\cdot\frac{6}{7}-\frac{4}{5}\cdot\frac{4}{14}\)
\(=\frac{4}{5}\cdot\left(\frac{3}{7}+\frac{6}{7}-\frac{4}{14}\right)\)
\(=\frac{4}{5}\cdot1=\frac{4}{5}\)
#Louis
\(\dfrac{3}{4}\cdot\dfrac{2}{5}-\dfrac{3}{4}\cdot\dfrac{2}{7}\)
= \(\dfrac{3}{4}\cdot\left(\dfrac{2}{5}-\dfrac{2}{7}\right)\)
= \(\dfrac{3}{4}\cdot\left(\dfrac{14}{35}-\dfrac{10}{35}\right)\)
= \(\dfrac{3}{4}\cdot\dfrac{4}{35}\)
= \(\dfrac{3}{35}\)
\(\frac{1}{3}x\)\(\frac{1}{2}-\frac{1}{5}x\)\(\frac{1}{2}\)
=(\(\frac{1}{3}-\frac{1}{5}\)) x \(\frac{1}{2}\)
=\(\frac{2}{15}x\)\(\frac{1}{2}\)
=\(\frac{1}{15}\)
1/3 * 1/2 - 1/5 * 1/2
= (1/3 + 1/5) * 1/2
=8/15*1/2
=4/15