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\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\)= \(\frac{2-1}{2}.\frac{3-1}{3}.\frac{4-1}{4}\)= \(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}\)= \(\frac{1.2.3}{2.3.4}=\frac{1}{4}\)
\(\left(1+\frac{1}{2}\right):\left(1+\frac{1}{3}\right):\left(1+\frac{1}{4}\right)\)= \(\frac{2+1}{2}:\frac{3+1}{3}:\frac{4+1}{4}\)= \(\frac{3}{2}:\frac{4}{3}:\frac{5}{4}=\frac{3}{2}.\frac{3}{4}.\frac{4}{5}=\frac{3.3.4}{2.4.5}=\frac{3.3}{2.5}=\frac{9}{10}\)
\(\frac{6}{5}-\frac{4}{5}.\frac{4}{8}+1=\frac{6}{5}+1-\frac{4.4}{5.8}=\frac{6+5}{5}-\frac{4}{5.2}=\frac{11}{5}-\frac{2}{5}=\frac{9}{5}\)
x < \(\frac{3}{4}+\frac{4}{5}=\frac{15}{20}+\frac{16}{20}=\frac{31}{20}=\frac{20}{20}+\frac{11}{20}=1\frac{11}{20}\)=> x = 0 ; 1
\(\frac{1}{2}+\frac{2}{3}< x< 4-\frac{5}{4}\)<=> \(\frac{3}{6}+\frac{4}{6}< x< \frac{16}{4}-\frac{5}{4}\)<=> \(\frac{7}{6}< x< \frac{11}{4}\)=> \(\frac{14}{12}< \frac{12x}{12}< \frac{33}{12}\)
=> 14 < 12x < 33 => 12x = 24 => x = 24 : 12 = 2
\(\frac{2}{5}+1=\frac{2}{5}+\frac{5}{5}=\frac{7}{5}\) ;\(\frac{6}{7}.4=\frac{24}{7}\);\(\frac{3}{7}:2=\frac{3}{7}.\frac{1}{2}=\frac{3}{14}\);\(2:\frac{2}{4}=2.\frac{4}{2}=2.2=4\);\(\frac{3}{4}.4+\frac{1}{3}=\frac{12}{4}+\frac{1}{3}=3+\frac{1}{3}=\frac{10}{3}\);\(\frac{1}{4}:\frac{1}{3}-\frac{1}{2}=\frac{1}{4}.\frac{3}{1}-\frac{1}{2}=\frac{3}{4}-\frac{1}{2}=\frac{1}{4}\)
\(\frac{2}{5}+1=\frac{2}{5}+\frac{5}{5}=\frac{7}{5}\)
\(\frac{6}{7}\times4=\frac{6\times4}{7}=\frac{24}{7}\)
\(\frac{3}{7}\div2=\frac{3}{7}\times\frac{1}{2}=\frac{3\times1}{7\times2}=\frac{3}{14}\)
\(2\div\frac{2}{4}=2\times\frac{4}{2}=2\times2=4\)
\(\frac{3}{4}\times4+\frac{1}{3}=\frac{3\times4}{4}+\frac{1}{3}=3+\frac{1}{3}=\frac{9}{3}+\frac{1}{3}=\frac{10}{3}\)
\(\frac{1}{4}\div\frac{1}{3}-\frac{1}{2}=\frac{1}{4}\times3-\frac{1}{2}=\frac{1\times3}{4}-\frac{1}{2}=\frac{3}{4}-\frac{1}{2}=\frac{3}{4}-\frac{2}{4}=\frac{1}{4}\)
\(\frac{1}{2}\times\frac{1}{3}\times\frac{1}{4}=\frac{1\times1\times1}{2\times3\times4}=\frac{1}{24}\)
\(\frac{1}{2}\times\frac{1}{3}\div\frac{1}{4}=\frac{1}{2}\times\frac{1}{3}\times\frac{4}{1}=\frac{1\times1\times4}{2\times3\times1}=\frac{4}{6}=\frac{2}{3}\)
\(\frac{1}{2}\div\frac{1}{3}\times\frac{1}{4}=\frac{1}{2}\times\frac{3}{1}\times\frac{1}{4}=\frac{1\times3\times1}{2\times1\times4}=\frac{3}{8}\)
1/4 = 0,25
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tick mik
1/4 = 0,25