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a) 67+135+33
= ( 67+33)+135
= 100 + 135
= 235
b) 146+121+54+379
= ( 146+54)+( 121+379)
= 200 + 500
= 700
c) 198+232-98-32
= ( 232-32)+(198-98)
= 200 + 100
= 300
d)1+2+3+4+.........+50
= ( 50+1) x 50:2 =1275
e)2+4+6+8+..........+100
= ( 100+2) x 50 : 2 =2550
f) 23 x 56 +56
= 1288 + 56
= 1344
g)32 x 19+32
= 608 + 32
= 640
\(a.67+135+33\)
\(=\left(67+33\right)+135\)
\(=100+135=235\)
\(b.141+121+54+379\)
\(=\left(146+54\right)+\left(121+379\right)\)
\(=200+500=700\)
\(c.198+232-98-32\)
\(=\left(232-32\right)+\left(198-98\right)\)
\(=200+100=300\)
\(f.23.56+56=1288+56=1344\)
\(g.32.19+32=608+32=640\)
1,
a,\(2020-\left(249+2020\right)+\left(249-573\right)\)
\(=2020-249-2020+249-573\)
\(=-573\)
b,\(\left|-257\right|+\left(-3\right)^0-\left(18+257\right)\)
\(=257+1-18-257\)
\(=1-18=-17\)
\(c,25.\left(85-47\right)-85.\left(47+25\right)\)
\(=25.85-25.47-47.85+85.25\)
\(=85.\left(25-47+25\right)-25.47\)
\(=85.3-25.47\)
\(=-920\)
2,
\(a,15-5.\left(x+2\right)=-30\)
\(=>5.\left(x+2\right)=15+30=45\)
\(=>x+2=\frac{45}{5}=9\)
\(=>x=7\)
\(b,\left(x+2\right)^2+5=105\)
\(=>\left(x+2\right)^2=100\)
\(=>\left(x+2\right)^2=10^2\)
\(=>x+2=10\)
\(=>x=8\)
\(c,\left|2x-5\right|-\left(-6\right)=11\)
\(=>\left|2x-5\right|=11-6=5\)
\(=>\orbr{\begin{cases}2x-5=5\\2x-5=-5\end{cases}}\)
\(=>\orbr{\begin{cases}2x=5-5=0\\2x=-5+5=0\end{cases}=>x=0}\)
\(M=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{19}+2^{20}\right)\\ M=\left(2+2^2\right)+2\left(2+2^2\right)+...+2^{18}\left(2+2^2\right)\\ M=\left(2+2^2\right)\left(1+2+...+2^{18}\right)\\ M=6\left(1+2+...+2^{18}\right)⋮6\)
Câu 1: Giải
\(\frac{a}{b}< 1\Leftrightarrow a< b\)
\(\Leftrightarrow am< bm\)
\(\Leftrightarrow ab+am< ab+bm\)
\(\Leftrightarrow a\left(b+m\right)< b\left(a+m\right)\)
\(\Leftrightarrow\frac{a}{b}< \frac{a+m}{b+m}\left(đpcm\right)\)
Câu 2: Giải
Ta có : \(\hept{\begin{cases}\frac{437}{564}=1-\frac{127}{564}\\\frac{446}{573}=1-\frac{127}{573}\end{cases}}\)
Vì \(\frac{127}{564}>\frac{127}{573}\) nên \(\frac{437}{564}>\frac{446}{573}\)
`a)25/(x+1)-1 1/6=-1/3-0,5`
`=>25/(x+1)=-1/3-1/2+1+1/6`
`=>25/(x+1)=1/3`
`=>75=x+1`
`=>x=74`
Vậy `x=74`
`b)(2x+25 3/5)^2-9/25=0`
`=>(2x+128/5)=9/25`
`**2x+128/5=3/5`
`=>2x=-125/5=-25`
`=>x=-25/2`
`**2x+128/5=-3/5`
`=>2x=-131/5`
`=>x=-131/10`
\(a,573+67-\left(573-23\right)\\ =573+67-573+23\\=\left(573-573\right)+\left(67+23\right)\\ =0+90\\ =90\\ b,\left(-73\right)-\left[2^3.5-6\right].2\\ =\left(-73\right)-\left[8.5-6\right].2\\ =\left(-73\right)-\left[40-6\right].2\\ =\left(-73\right)-34.2\\ =\left(-73\right)-68\\ =-141\)
\(573+67-\left(573-23\right)\)
\(=573+67-573+23\)
\(=\left(573-573\right)+\left(67+23\right)\)
\(=0+90=90\)
\(------------\)
\(\left(-73\right)-\left(2^3.5-6\right).2\)
\(=\left(-73\right)-\left(8.5-6\right).2\)
\(\left(-73\right)-34.2\)
\(=\left(-73\right)-68=-141\)