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a) \(4.5^2-32:2^5\)
\(=4.25-2^5:2^5\)
\(=100-1\)
\(=99.\)
b) \(9.8.14+6.\left(-17\right)\left(-12\right)+19.\left(-4\right).18\)
\(=9.2.4.14+6.3.\left(-4\right)\left(-17\right)+76.18\)
\(=18.56+18.68+18.76\)
\(=18\left(56+68+76\right)\)
\(=18\left(132+68\right)\)
\(=18.200\)
\(=3600.\)
c) \(\left(\dfrac{-1}{2}\right)^3-2.\left(\dfrac{-1}{2}\right)^2+3.\left(\dfrac{-1}{2}\right)+1\)
\(=\left(\dfrac{-1}{2}\right)\left[\left(\dfrac{-1}{2}\right)^2+2.\dfrac{-1}{2}+3\right]+1\)
\(=\left(\dfrac{-1}{2}\right)\left[\dfrac{1}{4}+\left(-1\right)+3\right]+1\)
\(\)\(=\left(\dfrac{-1}{2}\right)\left[\dfrac{1}{4}+2\right]+1\)
\(=\left(\dfrac{-1}{2}\right).\dfrac{9}{4}+1\)
\(=\dfrac{-9}{8}+1\)
\(=\dfrac{-1}{8}\)
\(A=\dfrac{12n+1}{30n+2}\)
Gọi \(d\)là \(UCLN\left(12n+1;30n+2\right)\)
\(\left\{{}\begin{matrix}12n+1⋮d\\30n+2⋮d\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}60n+5⋮d\\60n+4⋮d\end{matrix}\right.\)
\(\Rightarrow\left(60n+5\right)-\left(60n+4\right)⋮d\)
\(1⋮d\Rightarrow d=1\)
Vậy phân số trên tối giản
b tương tự
1,Gọi a là ƯCLN(12n+1;30n+2).Nên ta có:
12n+1 chia hết cho d và 30n+2 chia hết cho d
<=>5.(12n+1) chia hết cho d và 2.(30n+2) chia hết cho d
<=>60n+5 chia hết cho d và 60n+4 chia hết cho d
=>(60n+5)-(60n+4) chia hết cho d
=>1 chia hết cho d =>d = 1
Vậy d=1 =>\(\dfrac{12n+1}{30n+2}\) là phân số tối giảm (đpcm )
1: \(\dfrac{1}{2}+\dfrac{9}{10}+\dfrac{5}{6}-\dfrac{11}{14}-\dfrac{1}{3}+\dfrac{-4}{35}\)
\(=\left(\dfrac{1}{2}+\dfrac{5}{6}-\dfrac{1}{3}\right)+\dfrac{9}{10}-\left(\dfrac{11}{14}+\dfrac{4}{35}\right)\)
\(=\dfrac{3+5-2}{6}+\dfrac{9}{10}-\dfrac{55+8}{70}\)
\(=1+\dfrac{9}{10}-\dfrac{9}{10}\)
=1
f: \(=\dfrac{7}{19}\left(\dfrac{8}{11}+\dfrac{3}{11}\right)-\dfrac{12}{19}=\dfrac{7}{19}-\dfrac{12}{19}=\dfrac{-5}{19}\)
i: \(=\left(\dfrac{9}{24}-\dfrac{18}{24}+\dfrac{14}{24}\right)\cdot\dfrac{6}{5}+\dfrac{1}{2}=\dfrac{5}{24}\cdot\dfrac{6}{5}+\dfrac{1}{2}\)
=1/4+1/2=3/4
` 7/19 . 8/11 + 3/11 . 7/19 + (-12)/19 `
`= 7/19 . ( 8/11 + 3/11 ) + (-12)/19 `
`= 7/19 . 11/11 + (-12)/19`
`= 7/19 . 1 + (-12)/19 `
`= 7/19 + (-12)/19 `
`= -5/19 `
`( 3/8 + (-3)/4 + 7/12 ) : 5/6 + 1/2`
`= 3/8 + (-3)4 + 7/12 . 6/5 + 1/2`
`= ( 9+(-18) + 14)/24 . 6/5 + 1/2`
`= 5/24 . 6/5 + 1/2`
`= 1/4 + 1/2 `
`= 3/4`
a: =35/17-18/17-9/5+4/5
=1-1=0
b: =-7/19(3/17+8/11-1)
=7/19*18/187=126/3553
c: =26/15-11/15-17/3-6/13
=1-6/13-17/3
=7/13-17/3=-200/39
Bài 1.
Đặt (12n + 1; 30n + 2) = d
\(\Rightarrow\) \(\left\{{}\begin{matrix}12n+1⋮d\\30n+2⋮d\end{matrix}\right.\) \(\Rightarrow\) \(\left\{{}\begin{matrix}5\left(12n+1\right)⋮d\\2\left(30n+2\right)⋮d\end{matrix}\right.\) \(\Rightarrow\) \(\left\{{}\begin{matrix}60n+5⋮d\\60+4⋮d\end{matrix}\right.\)
\(\Rightarrow\) (60n + 5) - (60n + 4) \(⋮\) d
\(\Rightarrow\) 1 \(⋮\) d
\(\Rightarrow\) d = 1
\(\Rightarrow\) (12n + 1; 30n + 2) = 1
Vậy phân số \(\dfrac{12n+1}{30n+2}\) là phân số tối giản