Đề bài - bài 60 trang 31 sgk 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

\[\eqalign{
& a]\,\,\left[ {{1 \over 3}x} \right]:{2 \over 3} = 1{3 \over 4}:{2 \over 5} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,{x \over 3}:{2 \over 3} = {7 \over 4}:{2 \over 5} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,{x \over 3}.{3 \over 2} = {7 \over 4}.{5 \over 2} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,{x \over 2} = {{35} \over 8} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\;x = {{35.2} \over 8} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\;x = {{35} \over 4} \cr} \].

Vậy \[x={{35} \over 4} \]

\[\begin{array}{l}
b]\;4,5:0,3 = 2,25:\left[ {0,1.x} \right]\\
\;\;\;15 = 2,25:\left[ {0,1.x} \right]\\
\;\;\;0,1.x = 2,25:15\\
\;\;\;0,1x = 0,15\\\;\;\;x=0,15:0,1\\
\;\;\;x = 1,5
\end{array}\]

Vậy x=1,5

\[\eqalign{
& c]\,\,8:\left[ {{1 \over 4}.x} \right] = 2:0,02 \cr
& \,\,\,\,\,\,\,8:\left[ {{1 \over 4}.x} \right] = 100 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{1 \over 4}x = 8:100 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{1 \over 4}x = 0,08 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x = 0,08:{1 \over 4} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x = 0,08.4 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x = 0,32 \cr} \]

Vậy x=0,32

\[\begin{array}{l}
d]\,3:2\dfrac{1}{4} = \dfrac{3}{4}:\left[ {6.x} \right]\\
3:\dfrac{9}{4} = \dfrac{3}{4}:\left[ {6.x} \right]\\
3.\dfrac{4}{9} = \dfrac{3}{4}:\left[ {6.x} \right]\\
\dfrac{4}{3} = \dfrac{3}{4}:\left[ {6.x} \right]\\
6.x = \dfrac{3}{4}:\dfrac{4}{3}\\
6.x = \dfrac{3}{4}.\dfrac{3}{4}\\
6.x = \dfrac{9}{{16}}\\
x = \dfrac{9}{{16}}:6\\
x = \dfrac{9}{{16}}.\dfrac{1}{6}\\
x = \dfrac{3}{{32}}
\end{array}\]

Vậy \[x = \frac{3}{{32}}\]