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a;
c; \(\dfrac{1}{10}\) + \(\dfrac{4}{20}\) + \(\dfrac{9}{30}\)+\(\dfrac{16}{40}+\dfrac{25}{50}+\dfrac{36}{60}+\dfrac{49}{70}+\dfrac{64}{80}+\dfrac{81}{90}\)
= \(\dfrac{1}{10}+\dfrac{2}{10}+\dfrac{3}{10}+\dfrac{4}{10}+\dfrac{5}{10}+\dfrac{6}{10}+\dfrac{7}{10}+\dfrac{8}{10}+\dfrac{9}{10}\)
= \(\dfrac{1+2+3+4+5+6+7+8+9}{10}\)
= \(\dfrac{\left(1+9\right)+\left(2+8\right)+\left(3+7\right)+\left(4+6\right)+5}{10}\)
= \(\dfrac{10+10+10+10+5}{10}\)
= \(\dfrac{\left(10+10+10+10\right)+5}{10}\)
= \(\dfrac{10\times4+5}{10}\)
= \(\dfrac{45}{10}\)
= \(\dfrac{9}{2}\)
4.
a. 1/2 + 1/4 + 1/5
= 1*10/20 + 1*5/20 + 1*4/20
= (10 + 5 + 4)/20
= 19/20
= 0,95
b.1/2 * 4/5 : 1/4
= (1*4/2*5) : 1/4
= 4/10 : 1/4
= 2/5 * 4
= 8/5
= 1,6
\(\frac{8}{9}\):\(\frac{3}{4}\).\(\frac{5}{8}\)
=\(\frac{8}{9}\).\(\frac{4}{3}\).\(\frac{5}{8}\)
=\(\frac{8.4.5}{9.3.8}\)
=\(\frac{160}{216}\)
=0,(740)
\(\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}=\frac{2}{5}\)
\(\frac{1}{2}:\frac{3}{4}:\frac{5}{6}=\frac{1}{2}\times\frac{4}{3}\times\frac{6}{5}=\frac{1\times2\times2}{5}=\frac{4}{5}\)