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Dùng tích chất kết hợp cho nó lẹ
a/\(\left(\frac{-2}{3}+\frac{3}{7}\right):\frac{4}{5}+\left(\frac{-1}{3}+\frac{4}{7}\right):\frac{4}{5}=\left(\frac{-2}{3}+\frac{3}{7}+\frac{-1}{3}+\frac{4}{7}\right):\frac{4}{5}=\left(-1+1\right):\frac{4}{5}=0\)
b/\(\frac{5}{9}:\left(\frac{1}{11}-\frac{5}{22}\right)+\frac{5}{9}:\left(\frac{1}{15}-\frac{2}{3}\right)=\frac{5}{9}:\left(\frac{1}{11}-\frac{5}{22}+\frac{1}{15}-\frac{2}{3}\right)=\frac{5}{9}:\left(\frac{-3}{22}+\frac{-3}{5}\right)=\frac{-5}{3\left(\frac{1}{22}+\frac{1}{5}\right)}=\frac{-550}{81}\)
Mà hình như câu b mình làm sai
b/\(\frac{5}{9}:\left(\frac{1}{11}-\frac{5}{22}\right)+\frac{5}{9}:\left(\frac{1}{15}-\frac{2}{3}\right)=\frac{5}{9}:\frac{-3}{22}+\frac{5}{9}:\frac{-3}{5}=\frac{5.22}{9.-3}+\frac{5.5}{9.-3}=\frac{-\left(5.22+5.5\right)}{27}=-5\)
a) \(\frac{\left(17\frac{2}{9}-15\frac{2}{15}\right):5\frac{2}{9}}{\left(18+3,75\right):0,25}.25\%=\frac{\left(17+\frac{2}{9}-15-\frac{2}{15}\right):\frac{47}{9}}{\left(18+3,75\right).4}.\frac{1}{4}\)
\(=\frac{\left(2+\frac{4}{45}\right).\frac{9}{47}}{\left(18+3,75\right).16}=\frac{\frac{94}{45}.\frac{9}{47}}{288+60}=\frac{\frac{2}{5}}{348}=\frac{2}{5}.\frac{1}{348}=\frac{174}{5}=34,8\)
b) \(\frac{\frac{5}{3}-\frac{5}{7}+\frac{5}{9}}{\frac{10}{3}-\frac{10}{7}+\frac{10}{9}}=\frac{5\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{9}\right)}{10\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{9}\right)}=\frac{1}{2}\)
b) \(\frac{\frac{5}{3}-\frac{5}{7}+\frac{5}{9}}{\frac{10}{3}-\frac{10}{7}+\frac{10}{9}}=\frac{5.\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{9}\right)}{10.\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{9}\right)}=\frac{5}{10}=\frac{1}{2}\)
\(A = {1\over2}-{3\over4}+{5\over6}-{7\over12}={6\over12}-{9\over12}+{10\over12}-{7\over12}\)\(={0\over12}=0\)
Gửi tạm trước 2 câu !
\(a,\text{ }3^2\cdot\frac{1}{243}\cdot81^2\cdot3^{-3}=3^2\cdot\frac{1}{3^5}\cdot\left(3^4\right)^2\cdot\frac{1}{3^3}=3^2\cdot\frac{1}{3^5}\cdot3^8\cdot\frac{1}{3^3}=3^2=9\)\(b,\text{ }\frac{\left(-3\right)^{10}\cdot15^5}{25^3\cdot\left(-9\right)^7}=\frac{3^{10}\cdot\left(3\cdot5\right)^5}{\left(5^2\right)^3\cdot\left(-3\cdot3\right)^7}=\frac{3^{10}\cdot3^5\cdot5^5}{5^6\cdot3^7\cdot\left(-3\right)^7}=\frac{3^{15}\cdot5^5}{5^6\cdot3^7\cdot\left(-3\right)^7}=\frac{3}{-5}\)
Trả lời :
\(a,\text{ }3^2\cdot\frac{1}{243}\cdot81^2\cdot3^{-3}=3^2\cdot\frac{1}{3^5}\cdot\left(3^4\right)^2\cdot\frac{1}{3^3}=3^2\cdot\frac{1}{3^5}\cdot3^8\cdot\frac{1}{3^3}=3^2=9\)\(b,\text{ }\frac{\left(-3\right)^{10}\cdot15^5}{25^3\cdot\left(-9\right)^7}=\frac{3^{10}\cdot\left(3\cdot5\right)^5}{\left(5^2\right)^3\cdot\left(-3\cdot3\right)^7}=\frac{3^{10}\cdot3^5\cdot5^5}{5^6\cdot3^7\cdot\left(-3\right)^7}=\frac{3^{15}\cdot5^5}{5^6\cdot3^7\cdot\left(-3\right)^7}=\frac{3}{-5}\)
Bài 1
\(a,\left(\frac{3}{5}\right)^2-\left[\frac{1}{3}:3-\sqrt{16}.\left(\frac{1}{2}\right)^2\right]-\left(10.12-2014\right)^0\)
\(=\frac{9}{25}-\left[\frac{1}{9}-4.\frac{1}{4}\right]-1\)
\(=\frac{9}{25}-\left(-\frac{8}{9}\right)-1\)
\(=\frac{9}{25}+\frac{8}{9}-1\)
\(=\frac{56}{225}\)
\(b,|-\frac{100}{123}|:\left(\frac{3}{4}+\frac{7}{12}\right)+\frac{23}{123}:\left(\frac{9}{5}-\frac{7}{15}\right)\)
\(=\frac{100}{123}:\left(\frac{4}{3}\right)+\frac{23}{123}:\frac{4}{3}\)
\(=\left(\frac{100}{123}+\frac{23}{123}\right):\frac{4}{3}\)
\(=1:\frac{4}{3}=\frac{3}{4}\)
Phần c đăng riêng vì mk chưa tìm đc cách giải bt mỗi đáp án :v
\(c,\frac{\left(-5\right)^{32}.20^{43}}{\left(-8\right)^{29}.125^{25}}\)
\(=\frac{\left(-5\right)^{32}.\left(4.5\right)^{43}}{\left[4.\left(-2\right)\right]^{29}.\left(-5^3\right)^{25}}\)
\(=\frac{-5^{32}.4^{43}.5^{43}}{4^{29}.\left(-2\right)^{29}.\left(5\right)^{75}}\)
\(=\frac{\left(-5^4\right)^8.4^{43}.5^{43}}{4^{29}.\left(-2\right)^{29}.\left(5^3\right)^{25}}\)
\(=-\frac{1}{2}\)
a)\(=\frac{27}{23}+\frac{5}{21}-\frac{4}{23}+\frac{1}{2}\)+\(\frac{16}{21}\)
\(=\left(\frac{27}{23}-\frac{4}{23}\right)+\left(\frac{5}{21}+\frac{16}{21}\right)\)+\(\frac{1}{2}\)
\(=1+1+\frac{1}{2}\)
\(=2+\frac{1}{2}\)=\(\frac{5}{2}\)
Bài 2
| x - \(\frac{1}{3}\)| + \(\frac{4}{5}\)= | ( -3,2) + \(\frac{2}{5}\)|
=> | x - \(\frac{1}{3}\)| + \(\frac{4}{5}\)= | -2,8|
=> | x - \(\frac{1}{3}\)| + \(\frac{4}{5}\)= -2,8
=> | x - \(\frac{1}{3}\)| = -2,8 - \(\frac{4}{5}\)
=> | x - \(\frac{1}{3}\)| = - 3,6
=> x - \(\frac{1}{3}\)= -3,6
=> x = -3,6 + \(\frac{1}{3}\)
=> x = \(\frac{-49}{15}\)
Bài 3 :
Áp dụng tính chất dãy tỉ số bằng nhau ta có :
\(\frac{a_1-1}{9}=\frac{a_2-2}{8}=...=\frac{a_9-9}{1}=\frac{a_1-1+a_2-2+...+a_9-9}{9+8+...+1}\)
\(=\frac{\left[a_1+a_2+...+a_9\right]-\left[1+2+...+9\right]}{9+8+...+1}=\frac{90-45}{45}=1\)
Ta có : \(\frac{a_1-1}{9}=1\Rightarrow a_1=10\)
Tương tự : \(a_1=a_2=....=a_9=10\)
a)\(\frac{3}{7}\left(-\frac{5}{2}\right)+\left(-\frac{3}{7}\right)\)
\(=\left(-\frac{15}{17}\right)+\left(-\frac{3}{7}\right)\)
\(=-\frac{156}{119}\)
b) \(\frac{2}{3}+\frac{3}{4}\left(-\frac{4}{9}\right)\)
\(=\frac{2}{3}+-\frac{1}{3}=\frac{1}{3}\)
(-3)^10.15^5/25^3.(-9)^7 = 3^10.3^5.5^5/5^6.3^14.(-1) = 3^15.5^5/5^6.3^14.(-1)= 3/5(-1) = -3/5