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1, a) ( 42 - 69 + 17 ) - ( 42 + 17 )
= 42 - 69 + 17 - 42 - 17
= - 69
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\begin{array}{l} - \left( { - \frac{3}{4}} \right) - \left( {\frac{2}{3} + \frac{1}{4}} \right)\\ = \frac{3}{4} - \frac{2}{3} - \frac{1}{4}\\ = \left( {\frac{3}{4} - \frac{1}{4}} \right) - \frac{2}{3}\\ = \frac{2}{4} - \frac{2}{3}\\= \frac{1}{2} - \frac{2}{3}\\ = \frac{3}{6} - \frac{4}{6}\\ = \frac{{ - 1}}{6}\end{array}\)
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a) Mẫu số chung = BCNN(11, 7) = 77
Thừa số phụ: 77: 11= 7; 77:7 = 11.
Ta có:
\(\begin{array}{l}\frac{7}{{11}} + \frac{5}{7} = \frac{{7.7}}{{11.7}} + \frac{{5.11}}{{7.11}}\\ = \frac{{49}}{{77}} + \frac{{55}}{{77}} = \frac{{104}}{{77}}\end{array}\).
b) Mẫu số chung = BCNN(20, 15)= 60
Thừa số phụ: 60:20 = 3; 60:15 = 4
Ta có:
\(\begin{array}{l}\frac{7}{{20}} - \frac{2}{{15}} = \frac{{7.3}}{{20.3}} - \frac{{2.4}}{{15.4}}\\ = \frac{{21}}{{60}} - \frac{8}{{60}} = \frac{{13}}{{60}}\end{array}\).
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\(\begin{array}{l}\frac{{ - 4}}{3} - \frac{{12}}{5} = \frac{{ - 4}}{3} + \frac{{ - 12}}{5}\\ = \frac{{ - 20}}{{15}} + \frac{{ - 36}}{{15}} = \frac{{ - 56}}{{15}}\end{array}\).
![](https://rs.olm.vn/images/avt/0.png?1311)
Sai đâu bỏ qua nhé, hơi to mới lại mk tính máy tính ra : \(\frac{77}{30}\)nên ko chắc nhé
\(2+\frac{1}{1+\frac{1}{1+\frac{1}{3+\frac{1}{4}}}}=2+\frac{1}{1+\frac{1}{1+\frac{1}{\frac{13}{4}}}}\)
\(=2+\frac{1}{1+\frac{1}{1+\frac{4}{13}}}=2+\frac{1}{1+\frac{1}{\frac{17}{3}}}\)
\(=2+\frac{1}{1+\frac{3}{17}}=2+\frac{1}{\frac{20}{17}}=2+\frac{17}{20}=\frac{57}{20}\)
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\(\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}+...+\frac{2}{899}\)
\(=\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+\frac{2}{9\cdot11}+...+\frac{2}{29\cdot31}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{29}-\frac{1}{31}\)
\(=\frac{1}{3}-\frac{1}{31}\)
\(=\frac{28}{93}\)
\(\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{899}\)
= \(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+....+\frac{2}{29.31}\)
= \(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{29}-\frac{1}{31}\)
= \(\frac{1}{3}-\frac{1}{31}+0+0+...+0\)
= \(\frac{29}{93}\)
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\(N=-2\frac{2}{3}-0,2+1,75-\frac{5}{6}+0,7\)
\(N=\frac{-8}{3}-\frac{1}{5}+\frac{7}{4}-\frac{5}{6}+\frac{7}{10}\)
\(N=\frac{-160}{60}-\frac{12}{60}+\frac{105}{60}-\frac{50}{60}+\frac{42}{60}\)
\(N=\frac{\left[\left(-160\right)-12+105-50=42\right]}{60}\)
\(N=\frac{-75}{60}=\frac{-5}{4}\)
\(\Rightarrow N=\frac{-5}{4}\)
= -8/3 - 1/5 + 7/4 - 5/6 + 7/10 =
= -43/15 + 11/12 + 7/10 =
= -39/20 + 7/10 =
= -5/4
tk cho mình nhé bạn
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\(\frac{6}{25}-\frac{81}{25}+\left|-4\right|\cdot\frac{2}{7}-(-2)^3\)
\(\Rightarrow\frac{6-81}{25}+4\cdot\frac{2}{7}-(-2)^3\)
\(=\frac{-75}{25}+\frac{8}{7}+8\)
\(=3+\frac{8}{7}+8=3+8+\frac{8}{7}=11+\frac{8}{7}=\frac{77+8}{7}=\frac{85}{7}\)
\(\frac{6}{25}-\frac{81}{25}+|-4|.\frac{2}{7}-\left(-2\right)^3\)
\(=\frac{6-81}{25}+4.\frac{2}{7}-\left(-8\right)\)
\(=\frac{-75}{25}+\frac{8}{7}+8\)
\(=-3+\frac{8}{7}+8\)
\(=5+\frac{8}{7}=\frac{35}{7}+\frac{8}{7}=\frac{35+8}{7}=\frac{43}{7}\)
\(\frac{1994.1993-2}{1992+1992.1994}=\frac{1994.1992+1994-2}{1992+1992.1994}=\frac{1994.1992+1992}{1992+1992.1994}=1\)
\(\frac{1994.1993-2}{1992+1991.1994}\)
= \(\frac{1994.1992-1994-2}{1992-1992.1994}\)
= \(\frac{1994.1992-1992}{1992-1992.1994}\)
= \(1\)