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a) 5/9 + 4/9 . 3/7 + 4/9 . 4/7
= 5/9 + 4/9 . (3/7 + 4/7)
= 5/9 + 4/9 . 1
= 5/9 + 4/9
= 1
a) 4 + ( -1 ) 3 = 4 + ( -1 ) = 3
b ) \(\left(-\frac{1}{4}+\frac{5}{8}\right)+\left(-\frac{3}{8}\right)=\left(-\frac{2}{8}+\frac{5}{8}\right)-\frac{3}{8}=\frac{3}{8}-\frac{3}{8}=0\)
c) { [ ( -3 )2 . 10 - 2.5 - 100 ] + | -10 |: ( -2 ) } : ( -5 )
={ [ ( -9 . 10 - 10 - 100 ] + 10: ( -2 ) } : ( -5 )
={ [ -90 - 10 - 100 ] + (-5) } : ( -5 )
={ [ -100 - 100 ] + ( -5 ) } : ( -5 )
={ -200 + ( -5 ) } : ( -5 )
= -205 : ( -5 )
= 41
a; - \(\dfrac{2}{3}\) + \(\dfrac{3}{4}\) - (- \(\dfrac{1}{6}\)) + (- \(\dfrac{2}{5}\))
= - \(\dfrac{2}{3}\) + \(\dfrac{3}{4}\) + \(\dfrac{1}{6}\) - \(\dfrac{2}{5}\)
= \(-\dfrac{40}{60}\) + \(\dfrac{45}{60}\) + \(\dfrac{10}{60}\) - \(\dfrac{24}{60}\)
= \(\dfrac{5}{60}\) + \(\dfrac{10}{60}\) - \(\dfrac{24}{60}\)
= \(\dfrac{15}{60}\) - \(\dfrac{24}{60}\)
= - \(\dfrac{3}{20}\)
b; (- \(\dfrac{2}{3}\)) + (- \(\dfrac{1}{5}\)) + \(\dfrac{3}{4}\) - \(\dfrac{5}{6}\) - \(\dfrac{-7}{10}\)
= - \(\dfrac{2}{3}\) - \(\dfrac{1}{5}\) + \(\dfrac{3}{4}\) - \(\dfrac{5}{6}\) + \(\dfrac{7}{10}\)
= - \(\dfrac{40}{60}\) - \(\dfrac{12}{60}\) + \(\dfrac{45}{60}\) - \(\dfrac{50}{60}\) + \(\dfrac{42}{60}\)
= - \(\dfrac{52}{60}\) + \(\dfrac{45}{60}\) - \(\dfrac{50}{60}\) + \(\dfrac{42}{60}\)
= - \(\dfrac{7}{60}\) - \(\dfrac{50}{60}\) + \(\dfrac{42}{60}\)
= - \(\dfrac{57}{60}\) + \(\dfrac{42}{60}\)
= - \(\dfrac{1}{4}\)
\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.....\frac{9999}{10000}\)
\(=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}......\frac{99.101}{100.100}\)
\(=\frac{1.2.3...99}{2.3.4....100}.\frac{3.4.5....101}{2.3.4....100}\)
\(=\frac{1}{100}.\frac{101}{2}\)
\(=\frac{101}{200}\)
a ) 2 1 5 + 3 4 5 = 2 + 3 + 1 5 + 4 5 = 6
b ) 4 1 2 + 3 4 5 = 4 + 3 + 1 2 + 4 5 = 7 + 13 10 = 8 3 10