Ôn tập chương III

`\color {blue} \text {_Namm_}`

`c, = 3 3/29-3 1/5+2 7/11-2 2/29+3 4/11`

`= (3 3/29- 2 3/29)+(2 7/11+3 4/11)-3 1/5`

`= 1+6-3 1/5=7-3 1/5=19/5`

`d, =-1/4*(152/11- (-68/11))`

`=-1/4*(152/11+68/11)`

`=-1/4*20 = -5`

`2,`

`a, 5/6+(5x+3/2) \div 8/15=2 1/12`

`(5x+3/2) \div 8/15=2 1/12 - 5/6`

`(5x-3/2) \div 8/15=5/4`

`5x-3/2=5/4*8/15`

`5x-3/2=2/3`

`5x=2/3-3/2`

`5x=-5/6`

`x= -5/6 \div 5`

`x= -1/6`

`b, 2/3(x+9/5)-3/10*(5x-1/3)=7/15`

`(2/3*x+2/3*9/5) - (3/10*5x - 3/10*1/3)=7/15`

`2/3*x+6/5 - 3/10*5x -1/10=7/15`

`-5/6 *x= - 5/6`
`x=(-5/6) \div (-5/6)`

`x=1`

`c, 3/5*x-1/2=7/10`

`3/5*x=7/10+1/2`

`3/5*x=6/5`

`x=6/5 \div 3/5`

`x=2`

`d, 1/5+4/5 \div x=-1`

`4/5 \div x=-1 - 1/5`

`4/5 \div x=-6/5`

`x=4/5 \div (-6/5)`

`x=-2/3`

2:

a: =>(5x+3/2)*15/8=25/12-5/6=25/12-10/12=15/12=5/4

=>5x+3/2=5/4*8/15=40/60=2/3

=>5x=2/3-3/2=4/6-9/6=-5/6

=>x=-1/6

b: =>2/3x+6/5-3/2x+1/10=7/15

=>-5/6x=-5/6

=>x=1

c: =>3/5x=7/10+1/2=12/10=6/5

=>x=2

d: =>4/5:x=-1-1/5=-6/5

=>x=-4/5:6/5=-4/5*5/6=-20/30=-2/3

Bài 1:

a: \(=\dfrac{5}{18}\left(\dfrac{6}{13}+\dfrac{7}{13}\right)-\dfrac{1}{2}=\dfrac{5}{18}-\dfrac{1}{2}=\dfrac{-4}{18}=\dfrac{-2}{9}\)

b: \(=\dfrac{81}{20}\cdot\dfrac{4}{9}+\left(\dfrac{12}{15}-\dfrac{8}{15}\right)\cdot\dfrac{-7}{4}\)

\(=\dfrac{9}{5}+\dfrac{4}{15}\cdot\dfrac{-7}{4}=\dfrac{9}{5}-\dfrac{7}{15}=\dfrac{27-7}{15}=\dfrac{20}{15}=\dfrac{4}{3}\)

\(=\dfrac{15}{37}\cdot\dfrac{38}{41}-\dfrac{15}{37}\cdot\dfrac{74}{45}-\dfrac{38}{41}\cdot\dfrac{15}{37}-\dfrac{38}{41}\cdot\dfrac{82}{76}\)

\(=\dfrac{-1}{3}\cdot2-\dfrac{1}{2}\cdot2=-\dfrac{2}{3}-1=-\dfrac{5}{3}\)

\(1-\dfrac{1}{1.2}-\dfrac{1}{2.3}-...-\dfrac{1}{9.10}\\ =1-\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{9.10}\right)\\ =1-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)\\ =1-\left(1-\dfrac{1}{10}\right)\\ =1-\dfrac{9}{10}\\ =\dfrac{1}{10}\\ Vì\dfrac{1}{10}< \dfrac{1}{9}\\ Vậy1-\dfrac{1}{1.2}-\dfrac{1}{2.3}-...-\dfrac{1}{9.10}< \dfrac{1}{9}\)

=1-(1-1/2+1/2-1/3+...+1/9-1/10)

=1-1+1/10

=1/10<1/9

Lời giải:

a. Với $x$ nguyên, để biểu thức có giá trị nguyên thì $x-1$ là ước của $2$

$\Rightarrow x-1\in\left\{1; -1; 2;-2\right\}$

$\Rightarrow x\in\left\{2; 0; 3; -1\right\}$

b. 

$\frac{x-2}{x-1}=\frac{(x-1)-1}{x-1}=1-\frac{1}{x-1}$

Để biểu thức nhận giá trị nguyên thì $\frac{1}{x-1}$ nguyên

$\Rightarrow x-1$ là ước của $1$

$\Rightarrow x-1\in\left\{1; -1\right\}$

$\Rightarrow x\in\left\{2; 0\right\}$

TK :

1-4+7-10+...-208+301-304+307
=(1-4)+(7-10)+...+(205-208)+(301-304)+307  (có tất cả 51 cặp)
=(-3)+(-3)+...+(-3)+(-3)+307
=(-3).51+307
=(-153)+307=154

\(\left(-23\right)+15+23+\left(-25\right)\)
\(=\left(-23+23\right)+\left(15+-25\right)=0+-10=-10\)

=>(x+1)(y-1)=11

=>\(\left(x+1;y-1\right)\in\left\{\left(1;11\right);\left(11;1\right);\left(-1;-11\right);\left(-11;-1\right)\right\}\)

=>\(\left(x,y\right)\in\left\{\left(0;12\right);\left(10;2\right);\left(-2;-10\right);\left(-12;0\right)\right\}\)

1-2+3-4...+99-100

= (1-2)+(3-4)...+(99-100)

= -1.(100/2)

= -50

Giúp mik vs ạaaa