1 . tính giá trị biểu thức a. -4/9×3/7+4/7x -4/9+17/9 b. (4-5/12):2+5/24 c.-7/3×4/5 x 10 x3/7×9/32 d.1/3×5 + 1/5×7 + 1/7×9 + …. + 1/97×99 gấp lắm ;

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1. Đáp án:

    $a) \frac{13}{9}\\
   b) 2\\
   c) \frac{-9}{4}\\
   d) \frac{16}{99}$

   Giải thích các bước giải:

   $a) \frac{-4}{9}.\frac{3}{7}+\frac{4}{7}.\frac{-4}{9}+\frac{17}{9}\\
   =\frac{-4}{9}\left ( \frac{3}{7}+\frac{4}{7} \right )+\frac{17}{9}\\
   =\frac{-4}{9}.\frac{3+4}{7}+\frac{17}{9}\\
   =\frac{-4}{9}+\frac{17}{9}\\
   =\frac{-4+17}{9}=\frac{13}{9}\\
   b) (4-\frac{5}{12}):2+\frac{5}{24}\\
   =2-\frac{5}{12}:2+\frac{5}{24}\\
   =2-\frac{5}{12}.\frac{1}{2}+\frac{5}{24}\\
   =2-\frac{5}{24}+\frac{5}{24}\\
   =2\\
   c) \frac{-7}{3}.\frac{4}{5}.10.\frac{3}{7}.\frac{9}{32}\\
   =\left ( \frac{-7}{3}.\frac{3}{7} \right ).\frac{4.10}{5}.\frac{9}{32}\\
   =(-1).8.\frac{9}{32}\\
   =\frac{-9}{4}\\
   d) \frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+…+\frac{1}{97.99}\\
   =\frac{1}{2}.\left (\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+…+\frac{2}{97.99}  \right )
   =\frac{1}{2}.\left ( \frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+….+\frac{1}{97}-\frac{1}{99} \right )\\
   =\frac{1}{2}.\left ( \frac{1}{3}-\frac{1}{99} \right )\\
   =\frac{1}{6}-\frac{1}{198}\\
   =\frac{33}{198}-\frac{1}{198}\\
   =\frac{32}{198}\\
   =\frac{16}{99}$

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