Tính.
\(\frac{5}{8} \times \frac{24}{25} =\) |
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\(\frac{3}{2^2}\times\frac{8}{3^2}\times\frac{15}{4^2}\times\frac{24}{5^2}\times...\times\frac{624}{25^2}\)
\(=\frac{1.3}{2.2}\times\frac{2.4}{3.3}\times\frac{3.5}{4.4}\times...\times\frac{24.26}{25.25}\)
\(=\frac{1\times2\times3\times...\times24}{2\times3\times4\times...\times25}\times\frac{3\times4\times5\times...\times26}{2\times3\times4\times...\times25}\)
\(=\frac{1}{25}\times13\)
\(=\frac{13}{25}\)
#)Giải :
\(A=\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times\frac{24}{25}\times...\times\frac{2499}{2500}\)
\(A=\frac{1.3}{2.2}\times\frac{2.4}{3.3}\times\frac{3.5}{4.4}\times\frac{4.6}{5.5}\times...\times\frac{49.51}{50.50}\)
\(A=\frac{1\times3\times2\times4\times3\times5\times...\times49\times51}{2\times2\times3\times3\times4\times4\times...\times50\times50}\)
\(A=\frac{1\times51}{2\times50}\)
\(A=\frac{51}{100}\)
\(A=\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times\frac{24}{25}\times...\times\frac{2499}{2500}\)
\(=\frac{1\times3}{2\times2}\times\frac{2\times4}{3\times3}\times\frac{3\times5}{4\times4}\times\frac{6\times4}{5\times5}\times...\times\frac{49.51}{50\times50}\)
\(=\frac{1}{2}\times\frac{51}{50}\)
\(=\frac{51}{100}\)
\(E=\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}.\frac{5^2}{4.6}...\frac{9^2}{8.10}=\frac{\left(2.3.4...9\right)^2}{1.2.\left(3.4...8\right)^2.9.10}=\frac{2^2.9^2}{1.2.9.10}=\frac{18}{10}=\frac{9}{5}\)
\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.\frac{24}{25}....\frac{899}{900}\)
\(A=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.\frac{4.6}{5.5}....\frac{29.31}{30.30}\)
\(A=\frac{1.2.3.4....29}{2.3.4....30}.\frac{3.4.5.6...31}{2.3.4...30}\)
\(A=\frac{1}{30}.\frac{31}{2}\) (Rút gọn theo chiều /// và \\\ nhé)
\(A=\frac{31}{60}\)
Chúc học tốt!~~
A=3/4x8/9x15/16x24/25x...x899/900
A=1.3/22 x 2.4/33 x 3.5/42 x 4.6/55 x ... x 29.31/302
A=1.2.3.4...29/2.3.4.5...30 x 3.4.5.6...31/2.3.4.5...30
A=1/30 x 31/2
A=31/60
\(\frac{-5}{8}X\frac{16}{25}-\frac{21}{35}\)
\(=\frac{-2}{5}-\frac{21}{35}\)
\(=\left(-1\right)\)
A = (4+\(\frac{1}{5}\)) . \(\frac{18}{19}\)+ (2+\(\frac{8}{5}\)) . \(\frac{21}{5}\)
A= \(\frac{21}{5}\).18/19 + 18/5 . 21/5
A= 21/5 (18/19 + 18/5)
A= 21/5 . 432/95
A= 9288/95
b= 25/2. (3+2/7) - 23/7. (5 + 1/2)
b= 25/2 . 23/7 - 23/7 . 11/2
b= 23/7 (25/2 -11/2)
b=23/7 . 7
b= 23
\(a,\frac{1}{2}\times\frac{4}{5}\div\frac{6}{10}\)
\(=\frac{2}{5}\div\frac{6}{10}\)
\(=\frac{2}{5}\times\frac{10}{6}\)
\(=\frac{2}{3}\)
\(b,\frac{24}{35}\div\left(\frac{4}{5}\times\frac{8}{7}\right)\)
\(=\frac{24}{35}\div\frac{32}{35}\)
\(=\frac{24}{35}\times\frac{35}{32}\)
\(=\frac{3}{4}\)
\(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.\frac{24}{25}.\frac{35}{36}\)
\(=\frac{3.2.4.3.5.4.6.5.7}{2.2.3.3.4.4.5.5.6.6}=\frac{7}{2.6}\)
\(=\frac{7}{12}\)
\(=\frac{1\cdot3\cdot2\cdot4\cdot3\cdot5\cdot4\cdot6\cdot5\cdot7}{2\cdot2\cdot3\cdot3\cdot4\cdot4\cdot5\cdot5\cdot6\cdot6}\)
\(=\frac{1\cdot7}{2\cdot6}\)
\(=\frac{7}{12}\)
Phan Hoàng Mai
Tính :
\(\left(-0,5-\frac{3}{5}\right):\left(-\frac{22}{25}\right)+\left(\frac{2}{25}-1,08\right).\frac{3}{8}-72:12^2\)
\(=\left(-\frac{5}{10}-\frac{3}{5}\right):\frac{-22}{25}+\left(\frac{2}{25}-\frac{108}{100}\right).\frac{3}{8}-72:144\)
\(=\left(-\frac{5}{10}-\frac{6}{10}\right).\frac{-25}{22}+\left(\frac{8}{100}-\frac{108}{100}\right).\frac{3}{8}-\frac{1}{2}\)
\(=\frac{-11}{10}.\frac{-25}{22}+\left(-1\right).\frac{3}{8}-\frac{1}{2}\)
\(=\frac{\left(-11\right).\left(-25\right)}{10.22}+\frac{-3}{8}-\frac{1}{2}\)
\(=\frac{5}{4}+\frac{-3}{8}-\frac{1}{2}\)
\(=\frac{10}{8}+\frac{-3}{8}-\frac{4}{8}\)
\(=\frac{3}{8}\)
Chúc bạn học tốt!!!
\(\left(-0,5-\frac{3}{5}\right):\left(-\frac{22}{25}\right)+\left(\frac{2}{25}-1,08\right)\cdot\frac{3}{8}-72:12^2\)
=\(\left(-\frac{1}{2}-\frac{3}{5}\right):\left(-\frac{22}{25}\right)+\left(\frac{2}{25}-\frac{27}{25}\right)\cdot\frac{3}{8}-\frac{72}{144}\)
=\(\left(-\frac{11}{10}.\left(-\frac{25}{22}\right)\right)-1\cdot\frac{3}{8}-\frac{1}{2}\)
= \(\frac{5}{4}-\frac{3}{8}-\frac{1}{2}\)
= \(\frac{10}{8}-\frac{3}{8}-\frac{4}{8}=\frac{3}{8}\)
5/8 x 24/25 = 3/5
\(\dfrac{5}{8}\times\dfrac{24}{25}=\dfrac{5\times24}{8\times25}=\dfrac{120}{200}=\dfrac{3}{5}\)