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a) \(\dfrac{-15}{-2023}=\dfrac{15}{2023}>0\)
\(\dfrac{3}{-4}< 0\)
\(\Rightarrow\dfrac{-15}{-2023}>\dfrac{3}{-4}\)
b) \(\dfrac{2014}{-2015}< 0\)
\(\dfrac{-5}{-7}=\dfrac{5}{7}>0\)
\(\Rightarrow\dfrac{2014}{-2015}< \dfrac{-5}{-7}\)
c) \(\dfrac{-4162}{3976}< 0\)
\(\dfrac{1}{2}>0\)
\(\Rightarrow\dfrac{-4162}{3976}< \dfrac{1}{2}\)
d) \(\dfrac{-2401}{7693}< 0\)
\(\dfrac{-4}{-7}=\dfrac{4}{7}>0\)
\(\Rightarrow\dfrac{-2401}{7693}< \dfrac{4}{7}\)
a: \(\dfrac{-15}{-2023}=\dfrac{15}{2023}>0\)
\(\dfrac{3}{-4}< 0\)
Do đó: \(\dfrac{-15}{-2023}>\dfrac{3}{-4}\)
b: \(\dfrac{2014}{-2015}< 0\)
\(\dfrac{-5}{-7}=\dfrac{5}{7}>0\)
Do đó: \(\dfrac{2014}{-2015}< \dfrac{-5}{-7}\)
c: \(-\dfrac{4162}{3976}< 0\)
\(0< \dfrac{1}{2}\)
Do đó: \(-\dfrac{4162}{3976}< \dfrac{1}{2}\)
d: \(\dfrac{-2401}{7693}< 0\)
\(0< \dfrac{4}{7}=\dfrac{-4}{-7}\)
Do đó: \(-\dfrac{2401}{7693}< \dfrac{-4}{-7}\)
e: -17<-4
=>\(\dfrac{-17}{2019}< \dfrac{-4}{2019}\)
=>\(\dfrac{17}{-2019}< \dfrac{-4}{2019}\)
g: \(\dfrac{-15}{-43}=\dfrac{15}{43}\)
mà 15>7
nên \(\dfrac{-15}{-43}=\dfrac{15}{43}>\dfrac{7}{43}\)
h: \(\dfrac{-15}{60}=\dfrac{-15\cdot3}{60\cdot3}=\dfrac{-45}{180}\)
\(\dfrac{-20}{45}=\dfrac{-20\cdot4}{45\cdot4}=\dfrac{-80}{180}\)
Ta có: -45>-80
=>\(-\dfrac{45}{180}>-\dfrac{80}{180}\)
=>\(-\dfrac{15}{60}>-\dfrac{20}{45}\)
k: \(\dfrac{11}{45}>0\)
\(0>-\dfrac{14}{30}\)
Do đó: \(\dfrac{11}{45}>-\dfrac{14}{30}\)
m: \(-\dfrac{17}{15}< -\dfrac{15}{15}=-1\)
\(-1< -\dfrac{5}{18}=\dfrac{5}{-18}\)
Do đó: \(\dfrac{-17}{15}< \dfrac{5}{-18}\)
n: \(-\dfrac{14}{42}< 0\)
\(0< \dfrac{-56}{-28}\)
Do đó: \(\dfrac{-14}{42}< \dfrac{-56}{-28}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Câu 2:
1: \(\Leftrightarrow x\cdot\dfrac{7}{2}=\dfrac{9}{2}+3=\dfrac{15}{2}\)
hay x=15/7
2: \(\Leftrightarrow x=\dfrac{5}{2}\cdot\dfrac{8}{5}=4\)
3: \(\Leftrightarrow x=\dfrac{-11\cdot10}{5}=-11\cdot2=-22\)
4: =>2x=90
hay x=45
![](https://rs.olm.vn/images/avt/0.png?1311)
2:
a: \(8^{10}-8^9-8^8\)
\(=8^8\cdot8^2-8^8\cdot8-8^8\cdot1\)
\(=8^8\left(8^2-8-1\right)=8^8\cdot55⋮55\)
b: \(7^6+7^5-7^4\)
\(=7^4\cdot49+7^4\cdot7-7^4\)
\(=7^4\left(49+7-1\right)=7^4\cdot55⋮11\)
c: \(81^7-27^9-9^{13}\)
\(=3^{28}-3^{27}-3^{26}\)
\(=3^{26}\cdot3^2-3^{26}\cdot3-3^{26}\cdot1\)
\(=3^{26}\left(3^2-3-1\right)=3^{26}\cdot5=3^{24}\cdot45⋮45\)
d: \(10^9+10^8+10^7\)
\(=10^7\cdot100+10^7\cdot10+10^7\)
\(=10^7\left(100+10+1\right)\)
\(=10^7\cdot111=10^6\cdot1110⋮555\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 2
a) 60%.x – x + \(\dfrac{1}{3}\) = 2
\(\dfrac{3}{5}\).x - x + = 2
(\(\dfrac{3}{5}\) - 1).x = 2 -
- \(\dfrac{2}{5}\).x =
x = \(\dfrac{5}{3}\)
.
x = \(\dfrac{25}{-6}\)
b) x + \(\dfrac{1}{7}\) =
x = \(\dfrac{1}{2}\) -
x = \(\dfrac{5}{14}\)
Bài 3:
Số học sinh khá là
(30/125)×100=24 (học sinh)
Số học sinh giỏi là
24×(2/3)=16 (học sinh)
Số học sinh trung bình là:
(24/100)×50=12 (học sinh)
Tổng số học sinh của lớp 6A là:
24 + 16 + 12 = 52 (học sinh)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a.\dfrac{2}{3}-\dfrac{5}{7}.\dfrac{14}{25}=\dfrac{2}{3}-\dfrac{2}{5}=\dfrac{10}{15}-\dfrac{6}{15}=\dfrac{14}{15}\)
\(b.\dfrac{-2}{5}.\dfrac{5}{8}+\dfrac{5}{8}.\dfrac{3}{5}=\dfrac{5}{8}.\left(\dfrac{-2}{5}+\dfrac{3}{5}\right)=\dfrac{5}{8}.\dfrac{1}{5}=\dfrac{1}{8}\)
\(c.25\%-1\dfrac{1}{2}+0,5.\dfrac{12}{5}=\dfrac{1}{4}-\dfrac{3}{2}+\dfrac{6}{5}=-\dfrac{1}{20}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 3:
a) \(159-\left(25-x\right)=43\)
\(\Rightarrow25-x=159-43\)
\(\Rightarrow25-x=116\)
\(\Rightarrow x=25-116\)
\(\Rightarrow x=-91\)
b) \(\left(79-x\right)-43=-\left(17-52\right)\)
\(\Rightarrow\left(79-x\right)-43=-\left(-35\right)\)
\(\Rightarrow79-x=35+43\)
\(\Rightarrow79-x=78\)
\(\Rightarrow x=79-78\)
\(\Rightarrow x=1\)
c) \(-\left(-x+13-142\right)+18=55\)
\(\Rightarrow-\left(-x+13-142\right)=55-18\)
\(\Rightarrow x-13+142=37\)
\(\Rightarrow x+129=37\)
\(\Rightarrow x=37-129\)
\(\Rightarrow x=-92\)
a: \(4167+235=4167+33+202=4200+202=4402\)
b: \(4167+\left(-235\right)=4167-235\)
=(4000+167)-(200+35)
=4000+167-200-35
=4000-200+167-35
=3800+132
=3932
c: \(\left(-4167\right)+\left(-245\right)\)
\(=-\left(4167+245\right)\)
\(=-\left(4167+33+212\right)\)
\(=-\left(4200+212\right)\)
=-4412
d: \(3219-415\)
\(=3219-15-400\)
=3204-400
=2804
e: \(2986-195\)
\(=\left(2900+86\right)-\left(200-5\right)\)
\(=2900+86-200+5\)
\(=2700+81=2781\)
g: \(415-\left(-37\right)=415+37=452\)
h: \(\left(-29\right)-475=-29-475\)
\(=-\left(29+475\right)=-504\)
k: \(\left(-125\right)-\left(-3195\right)\)
=-125+3195
=3195-125
=3070
m: \(1976-48675=-\left(48675-1976\right)=-46699\)
n: \(215-\left(-3456\right)=3456+415=3871\)
o: \(\left(-2195\right)-\left(-468\right)=-2195+468\)
\(=-\left(2195-468\right)=-1727\)
p: \(\left(-7615\right)+429=-\left(7615-429\right)=-7186\)