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99 + 87 + 99 + 13 + 99 + 45
= ( 99 + 99 + 99 ) + ( 87 + 13 ) + 45
= 297 + 100 + 45
= 397 + 45
= 442
\(\dfrac{x-13}{87}+\dfrac{x-27}{73}+\dfrac{x-67}{83}+\dfrac{x-73}{27}=4\)
<=>\(\dfrac{x-13}{87}-1+\dfrac{x-27}{73}-1+\dfrac{x-67}{83}-1+\dfrac{x-73}{27}-1=0\)
<=>\(\dfrac{x-100}{87}+\dfrac{x-100}{73}+\dfrac{x-100}{83}+\dfrac{x-100}{27}=0\)
<=>\(\left(x-100\right)\left(\dfrac{1}{87}+\dfrac{1}{73}+\dfrac{1}{83}+\dfrac{1}{27}\right)=0\)
Do \(\dfrac{1}{87}+\dfrac{1}{73}+\dfrac{1}{83}+\dfrac{1}{27}>0\)
=>x-100=0
<=>x=100
a)45.(13+78)+9.(87+22).5
=45.91+(9.5).109
=45.91+45.109
=45.(91+109)
=45.200
=9000
b) 16.(27+75)+8.(53+25).2
=16.102+(8.2).78
=16.102+16.78
=16.(102+78)
=16.180
=2880
(x-13)/87+(x-27)/73+(x-67)/33+(x-73)/27=4
=>(x-13-87)/87+(x-27-73)/73+(x-67-33)/33+(x-73-27)/27=4-1-1-1-1
=>(x-100)/87+(x-100)/73+(x-100)/33+(x-100)/27=0
=>(x-100)*(1/87+1/73+1/33+1/27)=0
=>x-100=0
=>x=100
5: \(=42\cdot\left(15+96+25+4\right)=42\cdot140=5880\)
6: \(=45\left(13+78+87+22\right)=45\cdot200=9000\)
87.(13 - 45) - 13.(87 + 45)
= 87.13 - 87.45 - 13.87 - 13.45
= (87.13 - 13.87) - (87.45 + 13.45)
= 0 - 45.(87+ 13)
= - 45.100
= - 4500