thực hiện phép tính bằng cách hợp lí ( nếu có thể )
a.(1 2/9+11/6) x 27/11 - 0.5
b.(1+2+3+4+...+2014) x (127x126126-127127x126)
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a) \(=\left(13\dfrac{2}{7}+2\dfrac{5}{7}\right):\left(-\dfrac{8}{9}\right)\)
\(=16:\dfrac{-8}{9}=\dfrac{-8\cdot\left(-2\right)\cdot9}{-8}=-18\)
b)
\(=\left(\dfrac{-6}{11}\cdot\dfrac{11}{-6}\right)\cdot\dfrac{7\cdot10\cdot\left(-2\right)}{10}\)
\(=-14\)
c) \(=\dfrac{-1}{2}\cdot\dfrac{4}{3}\cdot\dfrac{-7}{2}\)
\(=\dfrac{-1\cdot2\cdot2\cdot\left(-7\right)}{2\cdot3\cdot2}=\dfrac{7}{3}\)
\(\dfrac{16^3.3^{10}+120.6^9}{4^6.3^{12}+6^{11}}=\dfrac{\left(2^4\right)^3.3^{10}+3.5.2^3.\left(2.3\right)^9}{\left(2^2\right)^6.3^{12}+\left(2.3\right)^{11}}\)
\(=\dfrac{2^{12}.3^{10}+3.5.2^3.2^9.3^9}{2^{12}.3^{12}+2^{11}.3^{11}}=\dfrac{2^{12}.3^{10}+5.2^{12}.3^{10}}{2^{12}.3^{12}+2^{11}.3^{11}}\)
\(=\dfrac{2^{12}.3^{10}\left(1+5\right)}{2^{11}.3^{11}.\left(2.3+1\right)}\)\(=\dfrac{2^{12}.3^{10}.6}{2^{11}.3^{11}.7}=\dfrac{2.2}{7}=\dfrac{4}{7}\)
\(a.\left[-\dfrac{6}{11}.\dfrac{11}{-6}\right].\dfrac{7}{10}.\left(-20\right)=1.7.\left(-2\right)=-14\)
\(b.\dfrac{-1}{2}:\dfrac{3}{4}.\dfrac{-7}{2}=\dfrac{7}{4}:\dfrac{3}{4}=\dfrac{7}{3}\)
\(c.\dfrac{93}{7}:-\dfrac{8}{9}+\dfrac{19}{7}:\dfrac{-8}{9}=\left(\dfrac{93}{7}+\dfrac{19}{7}\right):-\dfrac{8}{9}=\dfrac{-9}{8}.\dfrac{112}{7}=-18\)
a) 2/9 - (1/20 + 2/9)
= 2/9 - 1/20 - 2/9
= (2/9 - 2/9) - 1/20
= 0 - 1/20
= -1/20
b) -3/14 + 2/13 + (-25/14) + (-15/13)
= (-3/14 - 25/14) + (2/13 - 15/13)
= -2 - 1
= -3
c) -3/11 + 11/8 - 3/8 + (-8/11)
= (-3/11 - 8/11) + (11/8 - 3/8)
= -1 + 1
= 0
d) 3/8 + (-1/4) - (7/12 - 1/6)
= 1/8 - 5/12
= -7/24
e) (1/3 + 12/67 + 13/41) - (79/67 - 28/41)
= 1/3 + 12/67 + 13/41 - 79/67 + 28/41
= 1/3 + (12/67 - 79/67) + (13/41 + 28/41)
= 1/3 - 1 + 1
= 1/3
bài 2
1,35-x=-16-(-7)
35-x=-9
x=35-(-9)=44
2,/x-2/=9 suy ra x-2=9 hoặc =-9 rồi tự tính
3, suy ra 4-2x=0 hoặc x-3 =0 tụ tính x
4, (x-2)^2=64 = 8^2 suy ra x-2 =8 hoặc -8
Bài 2: Thực hiện phép tính (tính bằng cách hợp lí nếu có thể)
-16 - (35 - x) = -7
-16 - 35 + x = -7
-51 + x = -7
x = -7 - (-51)
x = 44
lx - 2l = 9
=> \(\orbr{\begin{cases}x-2=9\\x-2=-9\end{cases}}\)
=> \(\orbr{\begin{cases}x=9+2\\x=-9+2\end{cases}}\)
=> \(\orbr{\begin{cases}x=11\\x=-7\end{cases}}\)
(4 - 2x) . (x - 3) = 0
=> \(\orbr{\begin{cases}4-2x=0\\x-3=0\end{cases}}\)
=> \(\orbr{\begin{cases}2x=4-0\\x=0+3\end{cases}}\)
=> \(\orbr{\begin{cases}2x=4\\x=3\end{cases}}\)
=> \(\orbr{\begin{cases}x=4\div2\\x=3\end{cases}}\)
=> \(\orbr{\begin{cases}x=2\\x=3\end{cases}}\)
(x - 2)2 - 64 = 0
=> (x - 2)2 = 0 + 64
=> (x - 2)2 = 64
=> (x - 2)2 = 82
=> x - 2 = 8
=> x = 8 + 2
=> x = 10