a) $\frac{-4}{9}$.3+$\frac{7}{6}$. $\frac{-15}{14}$
b) $\frac{12}{14}$ – $\frac{4}{14}$ – $\frac{6}{7}$ : $\frac{15}{11}$
c) $\frac{-3}{7}$ . $\frac{5}{13}$ + $\frac{-3}{2}$ . $\frac{8}{13}$
d) ($\frac{1}{9}$ – $\frac{9}{17}$)+$\frac{3}{6}$ – ($\frac{8}{17}$ – $\frac{1}{2}$)
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Đáp án:
`a)-31/12`
`b)-2/35`
`c)-99/91`
`d)1/9`
Giải thích các bước giải:
`a)-4/(9).3+7/(6).(-15)/14`
`=-12/9+7/(6).(-15)/14`
`=-12/9+(7.(-15))/(6.14)`
`=-12/9+(-105)/84`
`=-12/9+(-105:21)/(84:21)`
`=-12/9+(-5)/4`
`=(-48)/36+(-45)/36`
`=(-48-45)/36`
`=-93/36`
`=(-93:3)/(36:3)`
`=-31/12`
`b)12/14-4/14-6/7:15/11`
`=12/14-4/14-6/7.(11)/15`
`=(12-4)/14-(6.11)/(7.15)`
`=8/14-66/105`
`=4/7-22/35`
`=20/35-22/35`
`=(20-22)/35`
`=-2/35`
`c)-3/7.(5)/13+(-3)/2.(8)/13`
`=(-3.5)/(7.13)+(-3.8)/(2.13)`
`=-15/91+(-24)/(26)`
`=-15/91+(-12)/13`
`=-15/91+(-12.7)/(91)`
`=-15/91+(-84)/91`
`=(-15-84)/91`
`=-99/91`
`d)(1/9-9/17)+3/6-(8/17-1/2)`
`=(1/9-9/17)+1/2-(8/17-1/2)`
`=1/9-9/17+1/2-8/17+1/2`
`=1/9+(-9/17-8/17)+(1/2+1/2)`
`=1/9+(-9-8)/17+(1+1)/2`
`=1/9+(-17)/17+2/2`
`=1/9+(-1)+1`
`=1/9+0`
`=1/9`
Đáp án:
\(d)\dfrac{1}{9}\)
Giải thích các bước giải:
\(\begin{array}{l}
a) – \dfrac{4}{9}.3 – \dfrac{7}{6}.\dfrac{{15}}{{14}}\\
= – \dfrac{4}{3} – \dfrac{5}{4} = \dfrac{{ – 16 – 15}}{{12}} = – \dfrac{{31}}{{12}}\\
b)\dfrac{{12 – 4}}{{14}} – \dfrac{6}{7}.\dfrac{{11}}{{15}}\\
= \dfrac{8}{{14}} – \dfrac{{22}}{{35}}\\
= \dfrac{4}{7} – \dfrac{{22}}{{35}} = \dfrac{{20 – 22}}{{35}} = \dfrac{-2}{{35}}\\
c) – \dfrac{3}{7}.\dfrac{5}{{13}} – \dfrac{3}{2}.\dfrac{8}{{13}} = – \dfrac{3}{{13}}\left( {\dfrac{5}{7} + \dfrac{8}{2}} \right)\\
= – \dfrac{3}{{13}}.\dfrac{{33}}{7} = – \dfrac{{99}}{{91}}\\
d)\dfrac{1}{9} – \dfrac{9}{{17}} + \dfrac{1}{2} – \dfrac{8}{{17}} + \dfrac{1}{2}\\
= \dfrac{1}{9} – \dfrac{{9 + 8}}{{17}} + 1\\
= \dfrac{1}{9} – 1 + 1 = \dfrac{1}{9}
\end{array}\)