Tính nhanh:
\(\frac{10-\frac{1}{10}-\frac{2}{11}-\frac{3}{12}-...-\frac{10}{19}}{\frac{1}{60}+\frac{1}{66}+\frac{1}{72}+...+\frac{1}{114}}\)
Những câu hỏi liên quan
1 , \(c=\frac{10\frac{1}{3}.\left(26\frac{1}{3}-\frac{176}{7}\right)-\frac{12}{11}.\left(\frac{10}{3}-1,75\right)}{\frac{5}{\left(91-0,25\right).\frac{60}{11}-1}}\)
2 , \(A=\frac{0,375-0,3+\frac{3}{11}+\frac{3}{12}}{-0,265+0,5-\frac{5}{11}-\frac{5}{12}}+\frac{1,5+1-0,75}{2,5+\frac{5}{3}-1,25}\)
cac ban giai nhanh giup minh nha! ai nhanh minh k!
Tính giá trị biểu thức
\(\frac{10-\frac{1}{9}-\frac{2}{10}-\frac{3}{11}-\frac{4}{12}-...-\frac{10}{18}}{\frac{1}{45}+\frac{1}{50}+\frac{1}{55}+\frac{1}{60}+...+\frac{1}{90}}\)
B=\(\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+...+10}\)
C=\(\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}+\frac{55}{56}+\frac{71}{72}+\frac{89}{90}\)
Ta có công thức : \(1+2+3+...+n=\frac{n.\left(n+1\right)}{2}\)
\(\Rightarrow B=\frac{1}{1+2}+\frac{1}{1+2+3}+...+\frac{1}{1+2+...+10}\)
\(=\frac{1}{\frac{\left(1+2\right).2}{2}}+\frac{1}{\frac{\left(1+3\right).3}{2}}+...+\frac{1}{\frac{\left(1+10\right)10}{2}}\)
\(=\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{10.11}\)
\(=2.\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}\right)\)
\(=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\right)\)
\(=2.\left(\frac{1}{2}-\frac{1}{11}\right)=2.\frac{9}{22}=\frac{9}{11}\)
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Tính nhanh:
\(\frac{9-\frac{1}{11}-\frac{2}{12}-\frac{3}{13}-...-\frac{91}{101}}{\frac{1}{55}+\frac{1}{60}+\frac{1}{65}+...+\frac{1}{505}}\)
\(\frac{\left(\frac{3}{10}-\frac{4}{15}-\frac{7}{20}\right).\frac{5}{19}}{\left(\frac{1}{14}+\frac{1}{7}-\frac{-3}{5}\right).\frac{-4}{3}}\)
Giúp mik vs :< mai mik học r
Bài 1:So sánh(bằng 2 cách):
\(A=\frac{10^{11}-1}{10^{12}-1}\)\(B=\frac{10^{10}+1}{10^{11}+1}\)
Bài 2:Chứng minh:
\(\frac{3}{5}< \frac{1}{31}+\frac{1}{32}+\frac{1}{33}+..........+\frac{1}{59}+\frac{1}{60}< \frac{4}{5}\)
Câu hỏi của Quỳnh Anh - Toán lớp 6 - Học toán với OnlineMath
Em tham khảo câu 1 2 cách 2 bạn hướng dẫn nhé!
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\(\frac{\frac{3}{8}-\frac{3}{10}+\frac{3}{11}+\frac{3}{12}}{\frac{-5}{6}+\frac{5}{10}+\frac{5}{11}+\frac{5}{12}}+\frac{\frac{3}{2}+1+\frac{3}{4}}{\frac{5}{2}+\frac{5}{3}+\frac{5}{4}}\)
-5/6 là -5/8
Tính nhanh
\(\frac{\frac{3}{8}-\frac{3}{10}+\frac{3}{11}+\frac{3}{12}}{\frac{5}{8}-\frac{5}{10}+\frac{5}{11}+\frac{5}{12}}+\frac{\frac{3}{2}+1+\frac{3}{4}}{\frac{5}{2}+\frac{5}{3}+\frac{5}{4}}\)
\(=\frac{3.\left(\frac{1}{8}-\frac{1}{10}+\frac{1}{11}+\frac{1}{12}\right)}{5.\left(\frac{1}{8}-\frac{1}{10}+\frac{1}{11}+\frac{1}{12}\right)}+\frac{3.\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}\right)}{5.\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}\right)}\)
\(=\frac{3}{5}+\frac{3}{5}\)
\(=\frac{6}{5}\)
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Bài 1. Tính giá trị của biểu thức sau:
A=\(\frac{7}{4}.\left(\frac{3333}{1212}+\frac{3333}{2020}+\frac{3333}{3030}+\frac{3333}{4242}\right)\)
Bài 2. So sánh
A=\(\frac{20^{10}+1}{20^{10}-1}\)
B=\(\frac{20^{10}-1}{20^{10}-3}\)
Bài 3.Tính nhanh
P=\(\frac{\frac{2}{3}-\frac{1}{4}+\frac{5}{11}}{\frac{5}{12}+1-\frac{7}{11}}\)
Bài 1:
\(A=\frac{3333}{101}\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)=\frac{3333}{101}\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)\)
\(A=\frac{3333}{101}\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)\)
\(A=\frac{3333}{101}\left(\frac{1}{3}-\frac{1}{7}\right)=\frac{3333}{101}.\frac{4}{21}=\frac{1111.4}{101.7}=\frac{4444}{707}\)
Bài 2
\(A=\frac{2^{10}+1}{2^{10}-1}=\frac{2^{10}-1+2}{2^{10}-1}=1+\frac{2}{2^{10}-1}\)
\(B=\frac{2^{10}-1}{2^{10}-3}=\frac{2^{10}-3+4}{2^{10}-3}=1+\frac{4}{2^{10}-3}\)
Ta thấy \(2^{10}-1>2^{10}-3\Rightarrow\frac{2}{2^{10}-1}< \frac{2}{2^{10}-3}< \frac{4}{2^{10}-3}\)
Từ đó \(\Rightarrow1+\frac{2}{2^{10}-1}< 1+\frac{4}{2^{10}-3}\Rightarrow A< B\)
Bài 3\(P=\frac{\left(\frac{2}{3}-\frac{1}{4}\right)+\frac{5}{11}}{\frac{5}{12}+\left(1-\frac{7}{11}\right)}=\frac{\frac{5}{12}+\frac{5}{11}}{\frac{5}{12}+\frac{4}{11}}=\frac{\frac{55+60}{11.12}}{\frac{55+48}{12.11}}=\frac{115}{103}\)
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\(\frac{10\frac{1}{3}.\left(26\frac{1}{3}-\frac{176}{7}\right)-\frac{12}{11}\left(\frac{10}{3}-1.75\right)}{\frac{5}{\left(91-0.25\right).\frac{60}{11}-1}}\)
\(\frac{10\frac{1}{3}\left(26\frac{1}{3}-\frac{176}{7}\right)-\frac{12}{11}\left(\frac{10}{3}-1,75\right)}{\frac{5}{\left(91-0,25\right).\frac{60}{11}-1}}\)
\(\Leftrightarrow\left(\frac{31}{3}.\frac{25}{21}-\frac{12}{11}.\frac{19}{12}\right):\left(5:495-1\right)\)
\(\Leftrightarrow\left(\frac{775}{63}-\frac{19}{11}\right):\left(-\frac{98}{99}\right)\)
\(\Leftrightarrow x=-\frac{3664}{343}\)
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Tính : \(A=\frac{10\frac{1}{3}\left(26\frac{1}{3}-\frac{176}{7}\right)-\frac{12}{11}\left(\frac{10}{3}-1,75\right)}{\frac{5}{\left(91-0,25\right).\frac{60}{11}-1}}\)
mk ko viết lại đề đâu
A=\(\frac{\frac{31}{3}.\frac{25}{21}-\frac{12}{11}.\frac{19}{12}}{\frac{5}{90,75.\frac{60}{11}-1}}=\frac{\frac{775}{63}-\frac{19}{11}}{\frac{5}{495-1}}=\frac{7328}{693}:\frac{5}{494}=\frac{7328}{693}.\frac{494}{5}=\)
có máy tính thì tính được hết
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