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a) \(0,2 + 2,5:\frac{7}{2} = \frac{2}{{10}} + \frac{25}{10}:\frac{7}{2} = \frac{1}{5} + \frac{25}{10}.\frac{2}{7} \\= \frac{1}{5} + \frac{5}{7} = \frac{7}{{35}} + \frac{{25}}{{35}} = \frac{{32}}{{35}}\)
b)
\(\begin{array}{l}9.{\left( {\frac{{ - 1}}{3}} \right)^2} - {\left( { - 0,1} \right)^3}:\frac{2}{{15}}\\ = 9.\frac{1}{9} - {\left( {\frac{{ - 1}}{{10}}} \right)^3}:\frac{2}{{15}}\\ = 1 - \frac{{ - 1}}{{1000}}:\frac{2}{{15}}\\ = 1 - \frac{{ - 1}}{{1000}}.\frac{{15}}{2}\\ = 1 + \frac{3}{{400}}\\=\frac{400}{400}+\frac{3}{400}\\ = \frac{{403}}{{400}}\end{array}\)
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0,1(6):x=0,(33)
=>[0,1+0,0(6)]:x=33/99=1/3
=>(1/10+1/15):1/3=x
=>1/6.3=x
=>x=3/6=1/2=0,5
/HT\
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\(\begin{array}{l}a)\sqrt {0,49} + \sqrt {0,64} = 0,7 + 0,8 = 1,5;\\b)\sqrt {0,36} - \sqrt {0,81} = 0,6 - 0,9 = - 0,3;\\c)8.\sqrt 9 - \sqrt {64} = 8.3 - 8 = 24 - 8 = 16;\\d)0,1.\sqrt {400} + 0,2.\sqrt {1600} = 0,1.20 + 0,2.40 = 2 + 8 = 10\end{array}\)
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\(A=1,\left(35\right)-\frac{0,1\left(35\right)}{2,2}\)
\(\Rightarrow10A=13,\left(53\right)-\frac{1,\left(35\right)}{2,2}\)
\(\Rightarrow10A=13+0,\left(53\right)-\frac{1+0,\left(35\right)}{2,2}\)
\(\Rightarrow10A=13+\frac{53}{99}-\frac{1+\frac{53}{99}}{2,2}\)
\(\Rightarrow10A=\frac{1340}{99}-\frac{\frac{152}{99}}{2,2}\)
\(\Rightarrow10A=\frac{1340}{99}-\frac{152.2,2}{99}\)
\(\Rightarrow10A=\frac{1340}{99}-\frac{152.22:10}{99}\)
\(\Rightarrow10A=\frac{1340}{99}-\frac{152.2:10}{9}\)
\(\Rightarrow10A=\frac{1340-304}{9.10}\)
\(\Rightarrow10A=\frac{1036}{90}\)\(\Rightarrow A=\frac{1036}{900}=\frac{259}{225}\)
\(0,1\left(7\right)+0,2\left(6\right)=\dfrac{8}{45}+\dfrac{4}{45}=\dfrac{12}{45}=\dfrac{4}{15}\)
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