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a) \(\frac{3}{2}.\frac{7}{2}+\frac{5}{3}.\frac{1}{2}=\frac{21}{2}+\frac{5}{6}=\frac{63}{6}+\frac{5}{6}=\frac{68}{6}=\frac{34}{3}\)
b) \(\frac{1}{9}.\frac{2}{145}-\frac{13}{3}.\frac{2}{145}+\frac{2}{145}=\frac{2}{145}\left(\frac{1}{9}-\frac{39}{9}+\frac{9}{9}\right)=\frac{2}{145}\left(-29\right)=-0.4\)
c) \(\left(-\frac{91}{12}\right):\frac{15}{7}-\frac{1}{18}:\frac{15}{7}+\frac{20}{9}:\frac{15}{7}=\frac{7}{15}\left(-\frac{91}{12}-\frac{1}{18}+\frac{20}{9}\right)=\frac{7}{15}\left(-\frac{65}{12}\right)=-\frac{91}{36}\)
1/ -7264 + (1543 + 7264)
=-7264 + 1543 + 7264=1543
2/ (144 – 97) – 144
=144-97-144=-97
3/ (-145) – (18 – 145)(Vì có dấu trừ ở trước ngoặc nên p đổi dấu)
=-145-18+145=-18
4/ 111 + (-11 + 27)
=111-11+27=137
a: =2/3+2/7=14/21+6/21=20/21
b: =17/18-33/18=-16/18=-8/9
c: =7/12-3/14=49/84-18/84=31/84
d: =-1/4-1/8=-3/8
\(\dfrac{1}{2}+\dfrac{3}{4}-\left(\dfrac{3}{4}-\dfrac{4}{5}\right)\)
=\(\dfrac{1}{2}+\dfrac{3}{4}-\dfrac{3}{4}+\dfrac{4}{5}\)
=\(\left(\dfrac{1}{2}+\dfrac{4}{5}\right)+\left(\dfrac{3}{4}-\dfrac{3}{4}\right)\)
=\(\left(\dfrac{5}{10}+\dfrac{8}{10}\right)+0\)
=\(\dfrac{13}{10}\)
\(-\dfrac{7}{25}.\dfrac{11}{13}+\left(-\dfrac{7}{25}\right).\dfrac{2}{13}-\dfrac{18}{25}\)
=\(-\dfrac{7}{25}.\cdot\left(\dfrac{11}{13}+\dfrac{2}{13}\right)-\dfrac{18}{25}\)
=\(-\dfrac{7}{25}.1-\dfrac{18}{25}\)
=\(-\dfrac{7}{25}-\dfrac{18}{25}\)
=\(-\dfrac{25}{25}\) = \(-1\)
4S = 4/(5x5) + 4/(9x9) + … + 1/(409x409)
Ta thấy:
4/(5x5) < 4/(3x7) = 1/3 – 1/7
4/(9x9) < 4/(7x11) = 1/7 – 1/11
…………
4/(409x409) < 4/(407x411) = 1/407 – 1/411
Mà :
4/(3x7) + 4/(7x11) + …. + 4/(407x411) = 1/3 – 1/411 = 136/411
4S < 136/411
S < 34/411 < 34/408 = 1/12
Hay S < 1/12
`@` `\text {Ans}`
`\downarrow`
`a.`
`A=(1/2-7/13-1/3)+(-6/13+1/2+1 1/3)`
`= 1/2 - 7/13 - 1/3 - 6/13 + 1/2 + 1 1/3`
`= (1/2 + 1/2) + (-7/13 - 6/13) + (-1/3 + 1 1/3) `
`= 1 - 1 + 1`
`= 1`
`b.`
`B=0,75+2/5+(1/9-1 1/2+5/4)`
`= 3/4 + 2/5 + 1/9 - 3/2 + 5/4`
`= (3/4+5/4)+ 1/9 + 2/5 - 3/2`
`= 2 + 1/9 - 11/10`
`= 19/9 - 11/10`
`= 91/90`
`c.`
`(-5/9).3/11+(-13/18).3/11`
`= 3/11*[(-5/9) + (-13/18)]`
`= 3/11*(-23/18)`
`= -23/66`
`d.`
`(-2/3).3/11+(-16/9).3/11`
`= 3/11* [(-2/3) + (-16/9)]`
`= 3/11*(-22/9)`
`= -2/3`
`e.`
`(-1/4).(-2/13)-7/24.(-2/13)`
`= (-2/13)*(-1/4-7/24)`
`= (-2/13)*(-13/24)`
`= 1/12`
`f.`
`(-1/27).3/7+(5/9).(-3/7)`
`= 3/7*(-1/27 - 5/9)`
`= 3/7*(-16/27)`
`= -16/63`
`g.`
`(-1/5+3/7):2/11+(-4/5+4/7):2/11`
`=[(-1/5+3/7)+(-4/5+4/7)] \div 2/11`
`= (-1/5+3/7 - 4/5 + 4/7) \div 2/11`
`= [(-1/5-4/5)+(3/7+4/7)] \div 2/11`
`= (-1+1) \div 2/11`
`= 0 \div 2/11 = 0`
a,\(\frac{3}{2}\cdot\frac{7}{3}+\frac{4}{3}\cdot\frac{1}{2}\)=\(\frac{7}{2}+\frac{2}{3}\)=\(\frac{25}{6}\)
b,\(\frac{2}{145}\cdot\left(\frac{1}{9}-\frac{13}{3}+1\right)\)=\(\frac{2}{145}.-\frac{29}{9}=-\frac{2}{45}\)
c.\(\frac{15}{7}:\left(-\frac{31}{12}-\frac{1}{18}-\frac{20}{9}\right)\)=\(\frac{15}{7}:\left(-\frac{175}{36}\right)=-\frac{108}{245}\)
\(1\frac{1}{2}.2\frac{1}{3}+1\frac{1}{3}.\frac{1}{2}\)
\(=\frac{3}{2}.\frac{7}{3}+\frac{4}{3}.\frac{1}{2}\)
\(=\frac{7}{2}+\frac{2}{3}\)
\(=\frac{25}{6}\)
\(\frac{1}{9}.\frac{2}{145}-4\frac{1}{3}.\frac{2}{145}+\frac{2}{145}\)
\(=\frac{2}{1305}-\frac{13}{3}.\frac{2}{145}+\frac{2}{145}\)
\(=\frac{2}{1305}-\frac{26}{435}+\frac{2}{145}\)
\(=\frac{-2}{45}\)
\(\left(-2\frac{7}{12}\right):2\frac{1}{7}-\frac{1}{18}:2\frac{1}{7}+2\frac{2}{9}:2\frac{1}{7}\)
\(=\frac{-17}{12}:\frac{15}{7}-\frac{1}{18}:\frac{15}{7}+\frac{20}{9}:\frac{15}{7}\)
\(=\left(\frac{-17}{2}-\frac{1}{18}+\frac{20}{9}\right):\frac{15}{7}\)
\(=\frac{-19}{3}.\frac{7}{15}\)
\(=\frac{-133}{45}\)
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