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a) \(\dfrac{3}{7}\)
b)\(\dfrac{9}{4}\)
c)\(\dfrac{1}{3}\)
d)\(\dfrac{41}{32}\)
e)\(\dfrac{73}{60}\)
\(=\dfrac{3}{7}\left(\dfrac{8}{5}-\dfrac{3}{5}\right)-\dfrac{1}{7}\cdot3=\dfrac{3}{7}\cdot1-\dfrac{3}{7}=0\)
\(\frac{1}{3}x\)\(\frac{1}{2}-\frac{1}{5}x\)\(\frac{1}{2}\)
=(\(\frac{1}{3}-\frac{1}{5}\)) 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
\(2-\dfrac{3}{4}x\dfrac{8}{5}+\dfrac{1}{2}\)
\(=2-\dfrac{24}{20}+\dfrac{1}{2}\)
\(=2-\dfrac{24+10}{20}\)
\(=\dfrac{2}{1}-\dfrac{34}{20}=\dfrac{40-34}{20}=\dfrac{6}{20}=\dfrac{3}{10}\)
\(2-\dfrac{3}{4}\times\dfrac{8}{5}+\dfrac{1}{2}=\dfrac{2\times20}{1\times20}-\dfrac{24}{20}+\dfrac{1\times10}{2\times10}\\ =\dfrac{40-24+10}{20}=\dfrac{26}{20}=\dfrac{13}{10}\)
\(\dfrac{3}{4}.\dfrac{2}{3}-\dfrac{1}{6}.\dfrac{3}{4}-\dfrac{3}{4}.\dfrac{1}{2}\)
= \(\dfrac{3}{4}.\left(\dfrac{2}{3}-\dfrac{1}{6}-\dfrac{1}{2}\right)\)
= \(\dfrac{3}{4}.0\)
= 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
\(\dfrac{1}{2}-\dfrac{1}{3}< \dfrac{1}{2}\cdot3;\dfrac{1}{3}-\dfrac{1}{5}< \dfrac{2}{3}\cdot5\)
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