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\(-\dfrac{3}{17}+\left(\dfrac{2}{3}+\dfrac{3}{17}\right)=\dfrac{-3}{17}+\dfrac{3}{17}+\dfrac{2}{3}=\dfrac{2}{3}\)
\(\dfrac{-5}{21}+\dfrac{-16}{21}+1=-1+1=0\)
\(\dfrac{-4}{11}\cdot\dfrac{5}{15}\cdot\dfrac{11}{-4}=\dfrac{5}{15}=\dfrac{1}{3}\)
a: =-1/3+1/3=0
b: \(=\dfrac{4}{11}\left(-\dfrac{2}{7}-\dfrac{4}{7}-\dfrac{1}{7}\right)=\dfrac{4}{11}\cdot\left(-1\right)=-\dfrac{4}{11}\)
c: \(=10+\dfrac{5}{9}-3-\dfrac{5}{7}-4-\dfrac{5}{9}=3-\dfrac{5}{7}=\dfrac{16}{7}\)
d: \(=\dfrac{1}{3}+\dfrac{7}{4}-\dfrac{7}{4}+\dfrac{4}{5}=\dfrac{1}{3}+\dfrac{4}{5}=\dfrac{5+12}{15}=\dfrac{17}{15}\)
a: =-1/3+1/3=0
b: =411(−27−47−17)=411⋅(−1)=−411=411(−27−47−17)=411⋅(−1)=−411
c: =10+59−3−57−4−59=3−57=167=10+59−3−57−4−59=3−57=167
d: =13+74−74+45=13+45=5+1215=1715
`a)1 4/23 + ( 5/21-4/23)+16/21-1/2`
`=27/23+5/21-4/23+16/21-1/2`
`=(27/23-4/23)+(5/21+16/21)-1/2`
`=23/23+21/21-1/2`
`=1+1-1/2`
`=2-1/2`
`=4/2-1/2`
`=3/2`
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`b)75%-(5/2+5/3)+(-1/2)^3`
`=3/4-5/2+5/3+(-1/8)`
`=(3/4-5/2-1/8)+5/3`
`=(6/8-20/8-1/8)+5/3`
`=-15/8+5/3`
`=-45/24+40/24`
`=-5/24`
___
`c)-3/4(-55/9).8/11`
`=-3/4.(-40/9)`
`=-10/3`
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`d)-3/8 . 6/13 + 7/13 . (-3/8) + 1 3/8`
`= -3/8 . (6/13 + 7/13) + 11/8`
`= -3/8 . 13/13 + 11/8`
`= -3/8 .1 + 11/8`
`= -3/8 + 11/8`
`= 8/8`
`=1`
a. \(C=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\)
\(=\frac{1}{11}-\frac{1}{66}=\frac{5}{66}\)
b. \(D=\frac{2}{3}.\left(\frac{3}{1.4}+\frac{4}{4.7}+...+\frac{3}{97.100}\right)\)
\(=\frac{2}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{100}\right)\)
\(=\frac{2}{3}.\left(1-\frac{1}{100}\right)=\frac{2}{3}.\frac{99}{100}=\frac{33}{50}\)
\(C=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-....-\frac{1}{66}\)
\(C=\frac{1}{11}-\frac{1}{66}=\frac{5}{66}\)
\(D=\frac{2}{3}.\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-....-\frac{1}{100}\right)\)
\(D=\frac{2}{3}.\left(1-\frac{1}{100}\right)=\frac{2}{3}.\frac{99}{100}=\frac{33}{50}\)
A = \(\dfrac{2}{5}:\dfrac{3}{4}+\dfrac{2}{5}.\dfrac{3}{6}+\dfrac{2}{5}\)
A=\(\dfrac{2}{5}.\dfrac{4}{3}+\dfrac{2}{5}.\dfrac{3}{6}+\dfrac{2}{5}\)
A=\(\dfrac{2}{5}.\left(\dfrac{4}{3}+\dfrac{3}{6}+1\right)\) =\(\dfrac{2}{5}.\dfrac{17}{6}\)= \(\dfrac{17}{5}\)
B = \(\dfrac{5}{21}.\dfrac{4}{11}+\dfrac{7}{11}.\dfrac{5}{21}-\dfrac{2}{3}\)
B =\(\dfrac{5}{21}\left(\dfrac{4}{11}+\dfrac{7}{11}\right)-\dfrac{2}{3}\)
B= \(\dfrac{5}{21}.1-\dfrac{2}{3}\) = \(\dfrac{5}{21}-\dfrac{2}{3}=\dfrac{-3}{7}\)
\(\dfrac{1}{21}+\dfrac{2}{21}+\dfrac{3}{21}+\dfrac{4}{21}+\dfrac{5}{21}+...+\dfrac{17}{21}+\dfrac{18}{21}+\dfrac{19}{21}+\dfrac{20}{21}\)
\(=\dfrac{1+2+3+4+5+...+17+18+19+20}{21}\)
\(=\dfrac{1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20}{21}\)
\(=\dfrac{210}{21}\)
\(=10\)
\(\dfrac{21}{4}\cdot\dfrac{-11}{4}+\dfrac{21}{4}\cdot\dfrac{1}{2}+\dfrac{21}{4}\cdot\dfrac{-1}{2}\)
\(=\dfrac{21}{4}\cdot\dfrac{-11}{4}\cdot\dfrac{21}{4}+\dfrac{2}{4}+\dfrac{21}{4}\cdot\dfrac{-2}{4}\)
\(=\dfrac{21}{4}\cdot\left(\dfrac{-11}{4}+\dfrac{2}{4}+\dfrac{-2}{4}\right)\)
\(=\dfrac{21}{4}\cdot\dfrac{-11}{4}\)
\(=\dfrac{-231}{16}\)