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Câu 1:
A = (4/9 + 5/6) : (7/8 - 7/12)
A = (8/18 + 15/18) :(21/24 - 14/24)
A = 23/18 : 7/24
A = 23/18 x 24/7
A = 92/21
Câu B = 3/4.8/9.15/16...9999/10000
B = \(\frac{1.3}{2.2}\).\(\frac{2.4}{3.3}\)....\(\frac{99.101}{100.100}\)
B = \(\frac{1.2.3\ldots99}{2.3\ldots100}\). \(\frac{3.4.\ldots101}{2.3\ldots100}\)
B = \(\frac{1}{100}\) x \(\frac{101}{2}\)
B = \(\frac{101}{200}\)
\(A=\left(9\frac{3}{4}:5,2+x.2\frac{7}{24}\right):1\frac{9}{16}=6\)
\(A=\left(9\frac{3}{4}:5,2+x.2\frac{7}{24}\right)=\frac{75}{8}\)
\(A=\left(2\frac{7}{24}.\frac{9}{11}+x.2\frac{7}{24}\right)=\frac{75}{8}\)
\(A=\left[2\frac{7}{24}.\left(\frac{9}{11}+x\right)\right]=\frac{75}{8}\)
\(A=\frac{9}{11}+x=\frac{45}{11}\)
\(x=\frac{45}{11}-\frac{9}{11}\)
\(x=\frac{36}{11}\)
\(a\)) Giải:
\(A=\frac{\frac{1}{3}+\frac{1}{9}-\frac{1}{27}}{\frac{5}{3}+\frac{5}{9}-\frac{5}{27}}=\frac{\frac{1}{3}+\frac{1}{9}-\frac{1}{27}}{5.\left(\frac{1}{3}+\frac{1}{9}-\frac{1}{27}\right)}=\frac{1}{5}\)
\(b\)) Giải:
\(B=\frac{\frac{2}{3}-\frac{1}{4}+\frac{5}{11}}{\frac{5}{12}+1-\frac{7}{11}}=\frac{\left(\frac{2}{3}-\frac{1}{4}+\frac{5}{11}\right).132}{\left(\frac{5}{12}+1-\frac{7}{11}\right).132}=\frac{88-33+60}{55+132-84}=\frac{115}{103}\)
\(\frac37+\frac{5}{13}+\frac{4}{13}\)
=\(\frac37+\left(\frac{5}{13}+\frac{4}{13}\right)\)
=\(\frac37+\frac{9}{13}\)
=\(\frac{39}{91}+\frac{63}{91}\)
=\(\frac{102}{91}\)
\(\left(\frac38+\frac{-3}{4}+\frac{7}{12}\right):\frac56+\frac12\)
=\(\left(\frac{9}{24}+\frac{-18}{24}+\frac{7}{24}\right)\times\frac65+\frac12\)
=\(\frac{5}{24}\times\frac65+\frac12\)
=\(\frac14+\frac12\)
=\(\frac14+\frac24\)
=\(\frac34\)