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a)Ta thấy:
45 chia hết 9
99 chia hết 9
180 chia hết 9
=>45+99+180 chia hết 9
b)Ta thấy:
125 chia hết 5
350 chia hết 5
235 chia hết 5
=>125+350+235 chia hết 5
c)Ta thấy:
5124 chia hết 4
504 chia hết 4
=>5124-504 chia hết 4
d)Ta thấy:
9226 chia hết 7
1435 chia hết 7
=>9226-1435 chia hết 7
b: \(A=5\left(\dfrac{5}{1\cdot6}+\dfrac{5}{6\cdot11}+...+\dfrac{5}{26\cdot31}\right)\)
\(=5\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{26}-\dfrac{1}{31}\right)\)
\(=5\cdot\dfrac{30}{31}=\dfrac{150}{31}\)
c: \(C=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}\)
=1-1/16=15/16
1)
a)-24+3(x-4)=111
3(x-4)=111-(-24)
3(x-4)=111+24
3(x-4)=135
x-4=135:3
x-4=45
x =45+4
x =49
b)(2x-4)(3x+63)=0
\(\Rightarrow\)\(\orbr{\begin{cases}2x-4=0\\3x+63=0\end{cases}}\)\(\Rightarrow\)\(\orbr{\begin{cases}x=2\\x=-21\end{cases}}\)
Vậy x\(\in\){2;-21}
c)|x-7|-4=(-2)4
|x-7| =(-2)4+4
|x-7| =16+4
|x-7| =20
\(\Rightarrow\)\(\orbr{\begin{cases}x-7=7\\x-7=-7\end{cases}}\)\(\Rightarrow\)\(\orbr{\begin{cases}x=14\\x=0\end{cases}}\)
Vậy x\(\in\){14;0}
d)(x-1)2=144
(x-1)2=122
\(\Rightarrow\)x-1=12
x =12+1
x =13
e)(x+7)3=-8
(x+7)3=(-2)3
\(\Rightarrow\)x+7=-2
x =-2-7
x =-9
2)
a)Ta có:
\(3n+12⋮n-3\)
\(\Rightarrow3n-9+21⋮n-3\)
\(\Rightarrow3\left(n-3\right)+21⋮n-3\)
\(\Rightarrow21⋮n-3\)
\(\Rightarrow n-3\inƯ\left(21\right)\)
\(\Rightarrow n-3\in\left\{1;3;7;21\right\}\)
Ta có bảng sau:
n-3 | 1 | 3 | 7 | 21 |
n | 4 | 6 | 10 | 24 |
Vậy\(n\in\left\{4;6;10;24\right\}\)
b)Ta có:
\(n+9⋮n-1\)
\(\Rightarrow n-1+10⋮n-1\)
\(\Rightarrow10⋮n-1\)
\(\Rightarrow\)\(n-1\inƯ\left(10\right)\)
\(\Rightarrow n-1\in\left\{1;2;5;10\right\}\)
Ta có bảng sau:
n-1 | 1 | 2 | 5 | 10 |
n | 2 | 3 | 6 | 11 |
Vậy \(n\in\left\{2;3;6;11\right\}\)
Bài 2.
A = -3/5 + ( -2/5 + 2 )
A = -3/5 + ( -2/5 + 10/5 )
A = -3/5 + 8/5
A = 5/5
A = 1
--------------------------------------------------------
B = 3/7 + ( -1/5 + -3/7 )
B = 3/7 + ( -7/35 + -15/35 )
B = 3/7 + ( -22/35 )
B = 15/35 + ( -22/35 )
B = -1/5
-----------------------------------------------------
C = ( -5/24 + 0,75 + 7/12 ) : ( -2 . 1/8 )
C = ( -5/24 + 3/4 + 7/12 ) : ( -1/4 )
C = 9/8 : ( -1/4 )
C = 9/8 . ( -4 )
C = -9/2
Bài 3 .
a) 4/7 - x = 1/2 . x + 2/7
<=> -x - x = 1/2 - 4/7 + 2/7
<=> -2x = 3/14
<=> x = 3/14 . ( -1/2 )
<=> x = -3/28
Vậy x = -3/28
b) x : 3 1/5 = 1 1/2
<=> x : 16/5 = 3/2
<=> x = 3/2 . 16/5
<=> x = 24/5
Vậy x = 24/5
c) x . 3/4 = -1 5/8
<=> x . 3/4 = -13/8
<=> x = -13/8 . 4/3
<=> x = -13/6
Vậy x = -13/6
A=1−3+5−7+...+2001−2003+2005S=1−3+5−7+...+2001−2003+2005
=(1−3)+(5−7)+...+(2001−2003)+2005=(1−3)+(5−7)+...+(2001−2003)+2005(Có 1002 cặp)
=(−2).1002+2005=(−2).1002+2005
=−2004+2005=−2004+2005
=1
a: \(=\dfrac{32}{9}+\dfrac{13}{6}=\dfrac{32\cdot2+13\cdot3}{18}=\dfrac{64+39}{18}=\dfrac{103}{18}\)
b: \(=\dfrac{43}{8}-\dfrac{43}{6}=\dfrac{-43}{24}\)
c:\(=4-2-\dfrac{1}{6}=2-\dfrac{1}{6}=\dfrac{11}{6}\)
d: \(=5+\dfrac{2}{3}+7+\dfrac{1}{2}-3-\dfrac{1}{2}+1+\dfrac{2}{3}\)
\(=10+\dfrac{4}{3}=\dfrac{34}{3}\)
\(a,\dfrac{7}{35},\dfrac{18}{54},\dfrac{-15}{125},\dfrac{-4}{25}\)
Các thừa số đã tối giản : \(\dfrac{-4}{25}\)
\(\dfrac{7}{35}=\dfrac{7:7}{35:7}=\dfrac{1}{5}\) , \(\dfrac{18}{54}=\dfrac{18:18}{54:18}=\dfrac{1}{3}\)
\(\dfrac{-15}{125}=\dfrac{-15:5}{125:5}=\dfrac{-3}{25}\)
\(b,\dfrac{27}{45},\dfrac{21}{28},\dfrac{8}{14},\dfrac{18}{-60},\dfrac{-270}{360}\)
Các thừa số đã tối giản là : ko có
\(\dfrac{27}{45}=\dfrac{27:9}{45:9}=\dfrac{3}{5}\) , \(\dfrac{21}{28}=\dfrac{21:7}{28:7}=\dfrac{3}{4}\)
\(\dfrac{8}{14}\)\(=\dfrac{8:2}{14:2}=\dfrac{4}{7}\) , \(\dfrac{18}{-60}=\dfrac{18:6}{-60:6}=\dfrac{3}{-10}=\dfrac{-3}{10}\)
\(\dfrac{-270}{360}=\dfrac{-270:90}{360:90}=\dfrac{-3}{4}\)
\(c,\dfrac{3.4+3.7}{6.5+9}\) = \(\dfrac{3.\left(4+7\right)}{30+9}\) = \(\dfrac{3.11}{39}\) = \(\dfrac{3.11}{3.13}=\dfrac{11}{13}\)
\(\dfrac{-63}{81},\dfrac{9.6}{9.35},\dfrac{7.2+8}{2.14.5}\)
Các p/s đã tối giản : ko có
\(\dfrac{-63}{81}=\dfrac{-63:9}{81:9}=\dfrac{-7}{9}\) , \(\dfrac{9.6}{9.35}=\dfrac{6}{35}\)
\(\dfrac{7.2+8}{2.14.5}=\dfrac{14+8}{28.5}=\dfrac{22}{140}=\dfrac{11}{70}\)
Đáp án là A