Bài 1: Thực hiện phép tính                                        a) \(\frac{3}{5}+\left(-\frac{2}{3}\right)-\left(-\frac{5}{2}\right)\)                            b) \(2\frac{2}{9}:1\frac{1}{9}-\frac{46}{5}:4\frac{3}{5}\)                     c) \(\left(\frac{2}{3}\right)^{^2}+\frac{5}{9}+\left(\frac{2}{3}:\frac{-2}{3}\right)\)               d) \(\frac{5^2\cdot5^3}{\left(-5\right)^4}\)
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{
"content1": {
"a": "a) \(\frac{3}{5}+\left(-\frac{2}{3}\right)-\left(-\frac{5}{2}\right) = \frac{3}{5} -\frac{2}{3} +\frac{5}{2} = \frac{9}{15} - \frac{10}{15} + \frac{15}{15} = \frac{14}{15}\)",
"b": "b) \(2\frac{2}{9}:1\frac{1}{9}-\frac{46}{5}:4\frac{3}{5} = \frac{20}{9}:\frac{10}{9} - \frac{46}{5}:\frac{23}{5} = 2 - 2 = 0\)",
"c": "c) \(\left(\frac{2}{3}\right)^{^2}+\frac{5}{9}+\left(\frac{2}{3}:\frac{-2}{3}\right) = \frac{4}{9} + \frac{5}{9} + \frac{-2}{3} = \frac{7}{9} - \frac{2}{3} = \frac{1}{9}\)",
"d": "d) \(\frac{5^2\cdot5^3}{\left(-5\right)^4} = \frac{5^{2+3}}{(-5)^4} = \frac{5^5}{(-5)^4} = \frac{3125}{625} = 5\)"
},
"content2": {
"a": "a) \(\frac{3}{5}+\left(-\frac{2}{3}\right)-\left(-\frac{5}{2}\right) = \frac{3}{5} -\frac{2}{3} +\frac{5}{2} = \frac{9}{15} - \frac{10}{15} + \frac{15}{15} = \frac{14}{15}\)",
"b": "b) \(2\frac{2}{9}:1\frac{1}{9}-\frac{46}{5}:4\frac{3}{5} = 2\frac{2}{9}:\frac{10}{9} - \frac{46}{5}:\frac{23}{5} = 2 - 2 = 0\)",
"c": "c) \(\left(\frac{2}{3}\right)^{^2}+\frac{5}{9}+\left(\frac{2}{3}:\frac{-2}{3}\right) = \frac{4}{9} + \frac{5}{9} + \frac{-2}{3} = \frac{7}{9} - \frac{2}{3} = \frac{1}{9}\)",
"d": "d) \(\frac{5^2\cdot5^3}{\left(-5\right)^4} = \frac{5^{2+3}}{(-5)^4} = \frac{5^5}{(-5)^4} = \frac{3125}{625} = 5\)"
},
"content3": {
"a": "a) \(\frac{3}{5}+\left(-\frac{2}{3}\right)-\left(-\frac{5}{2}\right) = \frac{3}{5} -\frac{2}{3} +\frac{5}{2} = \frac{9}{15} - \frac{10}{15} + \frac{15}{15} = \frac{14}{15}\)",
"b": "b) \(2\frac{2}{9}:1\frac{1}{9}-\frac{46}{5}:4\frac{3}{5} = 2\frac{2}{9}:\frac{10}{9} - \frac{46}{5}:\frac{23}{5} = 2 - 2 = 0\)",
"c": "c) \(\left(\frac{2}{3}\right)^{^2}+\frac{5}{9}+\left(\frac{2}{3}:\frac{-2}{3}\right) = \frac{4}{9} + \frac{5}{9} + \frac{-2}{3} = \frac{7}{9} - \frac{2}{3} = \frac{1}{9}\)",
"d": "d) \(\frac{5^2\cdot5^3}{\left(-5\right)^4} = \frac{5^{2+3}}{(-5)^4} = \frac{5^5}{(-5)^4} = \frac{3125}{625} = 5\)"
},
"content4": {
"a": "a) \(\frac{3}{5}+\left(-\frac{2}{3}\right)-\left(-\frac{5}{2}\right) = \frac{3}{5} -\frac{2}{3} +\frac{5}{2} = \frac{9}{15} - \frac{10}{15} + \frac{15}{15} = \frac{14}{15}\)",
"b": "b) \(2\frac{2}{9}:1\frac{1}{9}-\frac{46}{5}:4\frac{3}{5} = 2\frac{2}{9}:\frac{10}{9} - \frac{46}{5}:\frac{23}{5} = 2 - 2 = 0\)",
"c": "c) \(\left(\frac{2}{3}\right)^{^2}+\frac{5}{9}+\left(\frac{2}{3}:\frac{-2}{3}\right) = \frac{4}{9} + \frac{5}{9} + \frac{-2}{3} = \frac{7}{9} - \frac{2}{3} = \frac{1}{9}\)",
"d": "d) \(\frac{5^2\cdot5^3}{\left(-5\right)^4} = \frac{5^{2+3}}{(-5)^4} = \frac{5^5}{(-5)^4} = \frac{3125}{625} = 5\)"
},
"content5": {
"a": "a) \(\frac{3}{5}+\left(-\frac{2}{3}\right)-\left(-\frac{5}{2}\right) = \frac{3}{5} -\frac{2}{3} +\frac{5}{2} = \frac{9}{15} - \frac{10}{15} + \frac{15}{15} = \frac{14}{15}\)",
"b": "b) \(2\frac{2}{9}:1\frac{1}{9}-\frac{46}{5}:4\frac{3}{5} = 2\frac{2}{9}:\frac{10}{9} - \frac{46}{5}:\frac{23}{5} = 2 - 2 = 0\)",
"c": "c) \(\left(\frac{2}{3}\right)^{^2}+\frac{5}{9}+\left(\frac{2}{3}:\frac{-2}{3}\right) = \frac{4}{9} + \frac{5}{9} + \frac{-2}{3} = \frac{7}{9} - \frac{2}{3} = \frac{1}{9}\)",
"d": "d) \(\frac{5^2\cdot5^3}{\left(-5\right)^4} = \frac{5^{2+3}}{(-5)^4} = \frac{5^5}{(-5)^4} = \frac{3125}{625} = 5\)"
},
"content6": {
"a": "a) \(\frac{3}{5}+\left(-\frac{2}{3}\right)-\left(-\frac{5}{2}\right) = \frac{3}{5} -\frac{2}{3} +\frac{5}{2} = \frac{9}{15} - \frac{10}{15} + \frac{15}{15} = \frac{14}{15}\)",
"b": "b) \(2\frac{2}{9}:1\frac{1}{9}-\frac{46}{5}:4\frac{3}{5} = 2\frac{2}{9}:\frac{10}{9} - \frac{46}{5}:\frac{23}{5} = 2 - 2 = 0\)",
"c": "c) \(\left(\frac{2}{3}\right)^{^2}+\frac{5}{9}+\left(\frac{2}{3}:\frac{-2}{3}\right) = \frac{4}{9} + \frac{5}{9} + \frac{-2}{3} = \frac{7}{9} - \frac{2}{3} = \frac{1}{9}\)",
"d": "d) \(\frac{5^2\cdot5^3}{\left(-5\right)^4} = \frac{5^{2+3}}{(-5)^4} = \frac{5^5}{(-5)^4} = \frac{3125}{625} = 5\)"
}
}

{
"answer1": "a) \(\frac{3}{5}+\left(-\frac{2}{3}\right)-\left(-\frac{5}{2}\right) = \frac{3}{5} - \frac{2}{3} + \frac{5}{2} = \frac{9}{15} - \frac{10}{15} + \frac{15}{10} = \frac{-1}{15} + \frac{15}{10} = \frac{-1}{15} + \frac{9}{5} = \frac{-1 \cdot 3}{15 \cdot 3} + \frac{9 \cdot 3}{5 \cdot 3} = \frac{-3}{45} + \frac{27}{15} = -\frac{1}{15} + \frac{9}{5} = \frac{-1}{15} + \frac{27}{15} = \frac{26}{15}\n",
"answer2": "b) \(2\frac{2}{9}:1\frac{1}{9}-\frac{46}{5}:4\frac{3}{5} = \frac{20}{9}: \frac{10}{9} - \frac{46}{5}: \frac{23}{5} = \frac{20}{9} \cdot \frac{9}{10} - \frac{46}{5} \cdot \frac{5}{23} = 2 - 2 = 0\n",
"answer3": "c) \(\left(\frac{2}{3}\right)^{^2}+\frac{5}{9}+\left(\frac{2}{3}:\frac{-2}{3}\right) = \frac{2^2}{3^2} + \frac{5}{9} + \frac{2}{3} \cdot \frac{3}{-2} = \frac{4}{9} + \frac{5}{9} + \frac{2}{-2} = \frac{9}{9} + \frac{2}{-2} = 1 - 1 = 0\n",
"answer4": "d) \(\frac{5^2 \cdot 5^3}{\left(-5\right)^4} = \frac{5^5}{(-5)^4} = \frac{3125}{625} = 5\n"
}