227 x 65 = ?
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a, 4 x 113 x 8 - 32 x 13
= (4 x 8) x 113 - 32 x 13
= 32 x 113 - 32 x 13
= 32 x (113 - 13)
= 32 x 100 = 3200
b , 54 x 227 + 45 x 227 + 227
= 227 x (54+45+1)
= 227 x 100
= 22 700
c, ( 145 x 99 + 145 ) - ( 143 x101 - 143 )
= 145 x (99+1) - 143 x (101 - 1)
= 145 x 100 - 143 x 100
= 100 x (145 - 143)
= 100 x 2
= 200
a) \(4\times113\times8-32\times13\)
\(=4\times8\times113-32\times13\)
\(=32\times113-32\times13\)
\(=32\times\left(113-13\right)\)
\(=32\times100\)
\(=3200\)
b) \(54\times227+45\times227+227\)
\(=227\times\left(54+45+1\right)\)
\(=227\times100\)
\(=22700\)
c) \(\left(145\times99+145\right)-\left(143\times101-143\right)\)
\(=145\times\left(99+1\right)-143\left(101-1\right)\)
\(=145\times100-143\times100\)
\(=14500-14300\)
\(=200\)
a) \(227+50+23=\left(227+23\right)+50=250+50=300\)
b) \(135+360+65+40=\left(135+65\right)+\left(360+40\right)=200+400=600\)
c) \(1+2+3+4+5+...+97+98+99+100\)
\(=\left(100+1\right)+\left(99+2\right)+...+\left(50+51\right)\)
\(=101+101+101+...+101\)
\(=101\cdot50\)
\(\Leftrightarrow5050\)
d) \(115\cdot13-13\cdot15=13\cdot\left(115-15\right)=13\cdot100=1300\)
e) \(50-49+48-47+...+4-3+2-1\)
\(=\left(50-49\right)+\left(48-47\right)+...+\left(2-1\right)\)
\(=1+1+1+1+..+1\)
\(=1\cdot25\)
\(=25\)
f) \(30\cdot40\cdot50\cdot60=10\cdot3+10\cdot4+10\cdot5+10\cdot6\)
\(=10\cdot10\cdot10\cdot10\cdot3\cdot4\cdot5\cdot6\)
\(=10000\cdot360\)
\(=3600000\)
g) \(27\cdot36+27\cdot64=27\cdot\left(36+64\right)=27\cdot100=2700\)
h) \(5\cdot2^2-18:3=5\cdot4-18:3=20-6=14\)
i) \(13\cdot17-256:16+14:7-2021^0\)
\(=13\cdot17-4^4:4^2+2-1\)
\(=13\cdot17-16+2-1\)
\(=13\cdot17-17\)
\(=17\cdot\left(13-1\right)\)
\(=204\)
j) \(7^2-36:3=49-12=37\)
\(\frac{x+115}{15}+\frac{x+119}{19}=\frac{x+217}{117}+\frac{x+327}{227}\)
\(\Leftrightarrow\left(\frac{x+115}{15}-1\right)+\left(\frac{x+119}{19}-1\right)=\left(\frac{x+217}{117}-1\right)+\left(\frac{x+327}{227}-1\right)\)
\(\Leftrightarrow\frac{x+100}{15}+\frac{x+100}{19}=\frac{x+100}{117}+\frac{x+100}{227}\)
\(\Leftrightarrow\frac{x+100}{15}+\frac{x+100}{19}-\frac{x+100}{117}-\frac{x+100}{227}=0\)
\(\Leftrightarrow\left(x+100\right)\left(\frac{1}{15}+\frac{1}{19}-\frac{1}{117}-\frac{1}{227}\right)=0\)
\(\Leftrightarrow x+100=0\)
\(\Leftrightarrow x=-100\)
\(227-5.\left(x+8\right)=2187:9\)
\(277-5.\left(x+8\right)=243\)
\(5.\left(x+8\right)=34\)
\(\left(x+8\right)=6,8\)
\(x=-1,2\)