Bài 1 trang 108 Vở bài tập toán 7 tập 2

Đề bài

Thực hiện các phép tính:

a) \(9,6.2\dfrac{1}{2} - \left( {2.125 - 1\dfrac{5}{{12}}} \right):\dfrac{1}{4}\)

b) \(\dfrac{5}{{18}} - 1,456:\dfrac{7}{{25}} + 4,5.\dfrac{4}{5}\);

c) \(\left( {\dfrac{1}{2} + 0,8 - 1\dfrac{1}{3}} \right).\left( {2,3 + 4\dfrac{7}{{25}} - 1,28} \right)\)

d) \(\left( { - 5} \right).12:\left[ {\left( { - \dfrac{1}{4}} \right) + \dfrac{1}{2}:\left( { - 2} \right)} \right] \)\(\,+ 1\dfrac{1}{3}\).

Lời giải chi tiết

a) 

\(\eqalign{
& 9,6.2{1 \over 2} - \left( {2.125 - 1{5 \over {12}}} \right):{1 \over 4} \cr 
& = 9,6.2,5 - \left( {250 - 1 - {{5} \over {12}}} \right) :{1 \over 4} \cr 
& = 24 - \left( {249 - {5 \over 12}}\right) :{1 \over 4}  \cr
&=24-\dfrac{249\times12-5}{12}:\dfrac{1}{4}\cr
& = 24 - {{2988 - 5} \over 12} \times 4  \cr
& = 24- {{2983} \over 3} \cr 
& =  {{24\times3-2983} \over 3} \cr 
& = {72-2983 \over 3} \cr 
& = - {2911 \over 3} \cr
&=-970\dfrac{1}{3}\cr}\)

b) \(\displaystyle{5 \over {18}} - 1,456:{7 \over {25}} + 4,5.{4 \over 5}\) \(=\displaystyle{5 \over {18}} - 1,456 :0,28 + 4,5.0,8 \)
\(=\displaystyle{5 \over {18}} - 5,2+ 3,6\) \(=\displaystyle{5 \over {18}} - 1,6\)

\(=\displaystyle{5 \over {18}} - {8 \over 5}\) \(=\displaystyle {{5.5 - 8.18} \over {90}}\) \(=\displaystyle{{ 25-144} \over {90}}\) \(=\displaystyle {{-119} \over {90}}\) \(=-1\displaystyle{{ 29} \over {90}}\).

c) \(\displaystyle\left( {{1 \over 2} + 0,8 - 1{1 \over 3}} \right).\left( {2,3 + 4{7 \over {25}} - 1,28} \right)\) 

\(\displaystyle= \left( 0,5 + 0,8 - {4 \over 3} \right).\left( 2,3 + 4,28 - 1,28 \right) \) 
\(\displaystyle= \left( 1,3-{4 \over 3}\right).\left( 2,3 + 3\right)\)
\( \displaystyle= \left( {13\over 10}-{4 \over 3} \right).5,3\) \(\displaystyle= {{13.3-4.10\over 30}}.{{53 \over 10}}\)  \(\displaystyle= {{-1\over 30}}.{{53 \over 10}}= {{ - 53} \over {300}}\)

d) \(\displaystyle\left( { - 5} \right).12:\left[ {\left( { - {1 \over 4}} \right) + {1 \over 2}:\left( { - 2} \right)} \right] + 1{1 \over 3} \) \(\displaystyle = - 60:\left[ \left( - {1 \over 4}\right) +\left( - {1 \over 4}\right) \right] + 1{1 \over 3} \) 

\(\displaystyle= - 60:\left( { - {1 \over 2}} \right) + 1{1 \over 3} \) \(\displaystyle= 120 + 1{1 \over 3} \) \(\displaystyle=121{1 \over 3}\)