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25 x 5 x 4 x 27 x 2
= ( 25 x 4 ) x ( 5 x 2 ) x 27
= 100 x 10 x 27
= 1000 x 27
= 27000

(111*222+444*888)/(222*444+333*666)=(111*111*2+444*444*2)/(222*222*2+333*333*2)=[(1112+4442)*2]/[(2222+3332)*2]=(1112+1112*42)/(1112*22+1112*32)=[(1112)(1+16)]/[(111)2(4+9)]=17/13


\(=5.22\left(3134+275\cdot2+1.079\cdot4\right)\)
\(=5.22\cdot3688.316=19253.00952\)

\(17.12.25+51.2.5+85.14\)
\(=17.12.25+17.3.2.5+17.5.14\)
\(=17.2.2.3.5.5+17.2.3.5+17.5.2.7\)
\(=17.2.5\left(2.3.5+3+7\right)\)
\(=170.40\)
\(=6800\)
17.12.25+51.2.5+85.14
=17.3.4.25+51.2.5+17.5.14
=17.3.(4.25)+51.10+17.5.14
=17.3.100+17.3.10+17.5.7.2
=17.3.100+17.3.10+17.7.10
=17.(3.100+3.10+7.10)
=17.(300+30+70)
=17.400=6800

(1200-60):12= 1200:12-60:12=100-5=95
213-98=215-2-98=215-2-98=215-100=115
( 1200 - 60) : 12 = 1200 : 12 - 60 : 12
= 100 - 5
= 95
213 - 98 = 115

25 . 6 + 25 . 4 + 25 . 18 + 25 . 12
= 25 . (6 + 4 + 18 + 12)
= 25 . 40
= 1000
25 x 6 + 25 x 4 + 25 x 18 + 25 x 12
= 25 x ( 6 + 4 + 18 + 12 )
= 25 x 40
= 1 000
\(\Rightarrow C=\left(-\dfrac{3}{4}\right)\cdot\left(-\dfrac{8}{9}\right)\cdot\left(-\dfrac{15}{16}\right)\cdot\cdot\cdot\cdot\left(-\dfrac{399}{400}\right)\)
\(=-\left(\dfrac{3}{4}\cdot\dfrac{8}{9}\cdot\dfrac{15}{16}\cdot\cdot\cdot\cdot\dfrac{399}{400}\right)\)
\(=-\left(\dfrac{1\cdot3}{2\cdot2}\cdot\dfrac{2\cdot4}{3\cdot3}\cdot\dfrac{3\cdot5}{4\cdot4}\cdot\cdot\cdot\cdot\dfrac{19\cdot21}{20\cdot20}\right)\)
\(=-\left(\dfrac{1\cdot2\cdot3\cdot4\cdot...\cdot19}{2\cdot3\cdot4\cdot...\cdot20}\cdot\dfrac{3\cdot4\cdot5\cdot...\cdot21}{2\cdot3\cdot4\cdot...\cdot20}\right)\)
\(=-\left(\dfrac{1}{20}\cdot\dfrac{21}{2}\right)=-\dfrac{21}{40}\)