Tính hợp lí
\(2\frac{5}{12}-99\frac{213}{9115}:\frac{12}{5}+97\frac{213}{9115}:\frac{12}{5}\)
Ai làm nhanh và đúng mình tick cho
K
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29 tháng 6 2017
a) \(\frac{5}{1.4}+\frac{5}{4.7}+\frac{5}{7.10}+.....+\frac{5}{27.30}\)
\(=\frac{5}{3}\left(\frac{1}{1.4}+\frac{1}{4.7}+........+\frac{1}{27.30}\right)\)
\(=\frac{5}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+.....+\frac{1}{27}-\frac{1}{30}\right)\)
\(=\frac{5}{3}\left(1-\frac{1}{30}\right)\)
\(=\frac{5}{3}.\frac{29}{30}=\frac{29}{36}\)
DL
1 tháng 7 2017
Đặt \(A=\frac{12}{3\cdot5}+\frac{12}{5\cdot7}+\frac{12}{7\cdot9}+....+\frac{12}{97\cdot99}\)
\(2A=\frac{12}{3}-\frac{12}{5}+\frac{12}{5}-\frac{12}{7}+...+\frac{12}{97}-\frac{12}{99}\)
\(2A=\frac{12}{3}-\frac{12}{99}\)
\(A=\frac{128}{33}\cdot\frac{1}{2}=\frac{64}{33}\)
KN
28 tháng 3 2019
\(B=\frac{3+\frac{8}{12}+\frac{9}{13}-\frac{12}{17}}{4+\frac{8}{12}+\frac{12}{13}-\frac{16}{17}}+\frac{4+\frac{16}{60}-\frac{24}{213}-\frac{32}{11}}{5+\frac{20}{61}-\frac{36}{213}-\frac{40}{11}}\)
\(\Leftrightarrow B=\frac{3\left(1+\frac{8}{12}+\frac{3}{13}-\frac{4}{17}\right)}{4\left(1+\frac{8}{12}+\frac{3}{13}-\frac{4}{17}\right)}+\frac{4\left(1+\frac{4}{60}-\frac{6}{213}-\frac{8}{11}\right)}{5\left(1+\frac{4}{60}+\frac{6}{213}-\frac{8}{11}\right)}\)
\(\Leftrightarrow B=\frac{3}{4}+\frac{4}{5}\)
\(\Leftrightarrow B=\frac{15}{20}+\frac{16}{20}\)
\(\Leftrightarrow B=\frac{31}{20}\)
5 tháng 3 2020
\(B=81.\left(\frac{12-\frac{12}{7}-\frac{12}{7}-\frac{12}{289}-\frac{12}{85}}{4-\frac{4}{7}-\frac{4}{289}-\frac{4}{85}}:\frac{5+\frac{5}{13}+\frac{5}{169}+\frac{5}{91}}{6+\frac{6}{13}+\frac{6}{169}+\frac{6}{91}}\right).\frac{158158158}{711711711}\)
\(\Leftrightarrow B=81.\left(\frac{12\left(1-\frac{1}{7}-\frac{1}{289}-\frac{1}{85}\right)}{4\left(1-\frac{1}{7}-\frac{1}{289}-\frac{1}{85}\right)}:\frac{5\left(1+\frac{1}{13}+\frac{1}{169}+\frac{1}{91}\right)}{6\left(1+\frac{1}{13}+\frac{1}{169}+\frac{1}{91}\right)}\right).\frac{158\left(1001001\right)}{711\left(1001001\right)}\)
\(\Leftrightarrow B=81\left(\frac{12}{3}:\frac{5}{6}\right).\frac{158}{711}\)
\(\Leftrightarrow B=81\left(3.\frac{6}{5}\right).\frac{2}{9}\)
\(\Leftrightarrow B=81.\frac{18}{5}.\frac{2}{9}\)
\(\Leftrightarrow B=\frac{324}{5}\)
Hok tốt!!
VH
4
17 tháng 6 2019
\(\frac{5}{12}.\left(\frac{-3}{4}\right)-\frac{7}{12}.\frac{3}{4}\)
\(=\left(\frac{-5}{12}-\frac{7}{12}\right).\frac{3}{4}\)
\(=\left(-1\right).\frac{3}{4}=\frac{-3}{4}\)
~ Hok tốt ~
17 tháng 6 2019
\(\frac{5}{12}.\left(-\frac{3}{4}\right)-\frac{7}{12}.\frac{3}{4}\)
\(=\frac{3}{4}.\left(-\frac{5}{12}-\frac{7}{12}\right)\)
\(=\frac{3}{4}.\left(-1\right)\)
\(=-\frac{3}{4}\)
KT
12 tháng 10 2018
\(B=\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{...89}{90}\)
\(=1-\frac{1}{2}+1-\frac{1}{6}+1-\frac{1}{12}+1-\frac{1}{20}+...+1-\frac{1}{90}\)
\(=9-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\right)\)
\(=9-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)\)
\(=9-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(=9-\left(1-\frac{1}{10}\right)\)
\(=9-\frac{9}{10}=8\frac{1}{10}\)
30 tháng 4 2018
\(I=\frac{5}{6}+\frac{5}{12}+\frac{5}{20}+...+\frac{5}{90}\)( viết tắt )
\(I=\frac{5}{2.3}+\frac{5}{3.4}+\frac{5}{4.5}+...+\frac{5}{9.10}\)
\(I=5\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)\)
\(I=5\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(I=5\left(\frac{1}{2}-\frac{1}{10}\right)\)
\(I=5\times\frac{2}{5}\)
\(I=2\)
Vậy \(I=2\)
Tk nha bn ~~
30 tháng 4 2018
\(I=\frac{5}{6}+\frac{5}{12}+\frac{5}{20}+\frac{5}{30}+\frac{5}{42}+\frac{5}{56}+\frac{5}{72}+\frac{5}{90}\)
\(I=\frac{5}{2\cdot3}+\frac{5}{3\cdot4}+\frac{5}{4\cdot5}+\frac{5}{5\cdot6}+\frac{5}{6\cdot7}+\frac{5}{7\cdot8}+\frac{5}{8\cdot9}+\frac{5}{9\cdot10}\)
\(I=5\left(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}\right)\)
Theo tính chất của toán HSG lớp 6, ta được
\(I=5\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)
\(I=5\left(\frac{1}{2}-\frac{1}{10}\right)\)
\(I=5\left(\frac{5}{10}-\frac{1}{10}\right)\)
\(I=5\cdot\frac{4}{10}=5\cdot\frac{2}{5}=\frac{10}{5}=2\)
Bài làm
\(2\frac{5}{12}-99\frac{213}{9115}:\frac{12}{5}+98\frac{213}{9115}:\frac{12}{5}\)
\(=2\frac{5}{12}-\left(99\frac{213}{9115}+98\frac{214}{9115}\right):\frac{12}{5}\)
\(=2\frac{5}{12}-197:\frac{12}{5}\)
\(=2\frac{5}{12}-197.\frac{5}{12}\)
\(=2\frac{5}{12}-197\frac{5}{12}\)
\(=\left(2-197\right)\frac{5}{12}\)
\(=-195\frac{5}{12}\)
\(=-2335\)
~ Chắc đúng ~
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Bài làm
Mik sai mất rồi. Mik sửa nè:
\(=-195\frac{5}{12}\)
\(=-\frac{2335}{12}\)
~ Thế mới đúng nha ~
# Chúc bạn học tốt #