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1/9 x 4/11 + 3/4 +7/11 x 1/9
= 1/9 x (4/11 + 7/11) + 3/4
= 1/9 x 1 + 3/4
=1/9 + 3/4
= 31/36
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ĐẶt A = 2,(4)
10A = 24 + 0,(4)
10 A - A = 24 + 0,(4) - 2,(4) = 24 + 0,(4) - 2 - 0,(4) = 22
9A = 22
=> A = 22/9
Đặt B = 2,(45)
100b = 245,(45)
100b- b = 245,(45) - 2,(45)
99b = 243
b = 243 /99
= 27/11
Thay vào bt ta có
\(3,5\cdot\frac{4}{49}-\left[\frac{22}{9}\cdot\frac{27}{11}\right]:\left(-8,4\right)\)
\(=\frac{7}{2}\cdot\frac{4}{49}-6:-\frac{42}{5}\)
\(=\frac{2}{7}-6\cdot-\frac{5}{42}=\frac{2}{7}+\frac{5}{7}=1\)
\(\frac{10^3+2.5^3+5^3}{55}-\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)\(=\frac{2^3.5^3+2.5^3+5^3}{5.11}-\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\frac{5^3\left(2^3+2+1\right)}{5.11}-\frac{2^{12}.3^{10}.\left(1+5\right)}{2^{11}.3^{11}.\left(2.3-1\right)}=\frac{5^2.11}{11}-\frac{2.6}{3.5}=25-\frac{4}{5}=\frac{121}{5}\)
\(\dfrac{16^3.3^{10}+120.6^9}{4^6.3^{12}+6^{11}}=\dfrac{\left(2^4\right)^3.3^{10}+3.5.2^3.\left(2.3\right)^9}{\left(2^2\right)^6.3^{12}+\left(2.3\right)^{11}}\)
\(=\dfrac{2^{12}.3^{10}+3.5.2^3.2^9.3^9}{2^{12}.3^{12}+2^{11}.3^{11}}=\dfrac{2^{12}.3^{10}+5.2^{12}.3^{10}}{2^{12}.3^{12}+2^{11}.3^{11}}\)
\(=\dfrac{2^{12}.3^{10}\left(1+5\right)}{2^{11}.3^{11}.\left(2.3+1\right)}\)\(=\dfrac{2^{12}.3^{10}.6}{2^{11}.3^{11}.7}=\dfrac{2.2}{7}=\dfrac{4}{7}\)