Bài 37 trang 32 Vở bài tập toán 7 tập 1

Đề bài

Tìm \(x\) trong các tỉ lệ thức sau:

\(\eqalign{
& a)\,\,\left( {{1 \over 3}x} \right):{2 \over 3} = 1{3 \over 4}:{2 \over 5} \cr 
& b)\,\,4,5:0,3{\rm{ }} = {\rm{ }}2.25:\left( {0,1.x} \right) \cr 
& c)\,\,8:\left( {{1 \over 4}.x} \right) = 2:0,02 \cr 
& d)\,\,3:2{1 \over 4} = {3 \over 4}:(6.x) \cr} \)

Lời giải chi tiết

\(\begin{array}{l}
a){\kern 1pt} {\kern 1pt} \left( {\dfrac{1}{3}x} \right):\dfrac{2}{3} = 1\dfrac{3}{4}:\dfrac{2}{5}\\
\Rightarrow \left( {\dfrac{1}{3}x} \right).\dfrac{2}{5} = \dfrac{2}{3}.1\dfrac{3}{4}\\
\Rightarrow \dfrac{1}{3}x = \dfrac{{\dfrac{2}{3}.\dfrac{7}{4}}}{{\dfrac{2}{5}}}\\
\Rightarrow \dfrac{1}{3}x = \dfrac{{35}}{{12}}\\
\Rightarrow x = \dfrac{{35}}{{12}}:\dfrac{1}{3} = \dfrac{{35}}{4}
\end{array}\)

\(\begin{array}{l}
b)\;\,4,5:0,3 = 2,25:\left( {0,1.x} \right)\\
\Rightarrow 4,5.\left( {0,1.x} \right) = 0,3.2,25\\
\Rightarrow 0,1.x = \dfrac{{0,3.2,25}}{{4,5}}\\
\Rightarrow x = \dfrac{{0,15}}{{0,1}} = 1,5
\end{array}\)

\(\begin{array}{l}
c){\kern 1pt} {\kern 1pt} \,8:\left( {\dfrac{1}{4}.x} \right) = 2:0,02\\
\Rightarrow 2.\left( {\dfrac{1}{4}.x} \right) = 8.0,02\\
\Rightarrow \dfrac{1}{4}x = \dfrac{{8.0,02}}{2}\\
\Rightarrow x = 0,08:\dfrac{1}{4} = 0,32
\end{array}\)

\(\begin{array}{l}
d)\,\,{\kern 1pt} {\kern 1pt} 3:2\dfrac{1}{4} = \dfrac{3}{4}:(6.x)\\
\Rightarrow 3.\left( {6.x} \right) = 2\dfrac{1}{4}.\dfrac{3}{4}\\
\Rightarrow 6.x = \dfrac{{\dfrac{9}{4}.\dfrac{3}{4}}}{3}\\
\Rightarrow x = \dfrac{9}{{16}}:6 = \dfrac{3}{{32}}
\end{array}\)

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