Câu hỏi:

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Tự luận

1. Thực hiện phép tính (tính nhanh nếu có thể):

a) 1514\frac{1}{5} - \frac{1}{4};                                                   b) 27.815+27.11527\frac{2}{7}.\frac{8}{{15}} + \frac{2}{7}.\frac{1}{{15}} - \frac{2}{7}.

2. Tìm xx:

a) 79x=312\frac{{ - 7}}{9}x = 3\frac{1}{2};                                                 b) 35  .  (x+112)=0,4\frac{3}{5}\,\,.\,\,\left( {x + \frac{{11}}{2}} \right) = 0,4.

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Lời giải

Hướng dẫn giải:

1.

a) 1514  =  420520  =  4520  =  120\frac{1}{5} - \frac{1}{4}\; = \;\frac{4}{{20}} - \frac{5}{{20}}\; = \;\frac{{4 - 5}}{{20}}\; = \;\frac{{ - 1}}{{20}};

b) 211118+911+38  =  211+911+(118+38)=1+(1)=0\frac{2}{{11}} - \frac{{11}}{8} + \frac{9}{{11}} + \frac{3}{8}\; = \;\frac{2}{{11}} + \frac{9}{{11}} + \left( { - \frac{{11}}{8} + \frac{3}{8}} \right) = 1 + ( - 1) = 0.

2.

a) 79x=312\frac{{ - 7}}{9}x = 3\frac{1}{2}

79x=72\frac{{ - 7}}{9}x = \frac{7}{2}

x=72:(79)x = \frac{7}{2}:\left( {\frac{{ - 7}}{9}} \right)

x=92x = \frac{{ - 9}}{2}

Vậy x=92x = \frac{{ - 9}}{2}.

 

 

b) 35(x+112)=0,4\frac{3}{5}\left( {x + \frac{{11}}{2}} \right) = 0,4

35(x+112)=25\frac{3}{5}\left( {x + \frac{{11}}{2}} \right) = \frac{2}{5}

 x+112=25:35x + \frac{{11}}{2} = \frac{2}{5}:\frac{3}{5}

x+112=23x + \frac{{11}}{2} = \frac{2}{3}

x=23112x = \frac{2}{3} - \frac{{11}}{2}

x=296x = \frac{{ - 29}}{6}

Vậy x=296x = \frac{{ - 29}}{6}.

 

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