Bài tập 1 trang 27 toán 7 tập 1 CTST

Thực hiện phép tính

a) $\frac{2}{5}+\frac{3}{5}:\left ( -\frac{3}{2} \right )+\frac{1}{2}$

b) $2\frac{1}{3} + \left ( -\frac{1}{3} \right )^{2}-\frac{3}{2}$

c) $\left ( \frac{7}{8}-0,25 \right ) :  \left ( \frac{5}{6}-0,75 \right )^{2}$

d) $(-0,75) - \left [ (-2) +  \frac{3}{2} \right ]:1,5 + \left ( \frac{-5}{4} \right )$

Hướng dẫn giải:

a) $\frac{2}{5}+\frac{3}{5}:\left ( -\frac{3}{2} \right )+\frac{1}{2}$

= $\frac{2}{5} + \frac{-2}{5} + \frac{1}{2}$

= $0+ \frac{1}{2}$

=  $\frac{1}{2}$

b) $2\frac{1}{3} + \left ( -\frac{1}{3} \right )^{2}-\frac{3}{2}$

= $\frac{7}{3} + \frac{1}{9} -\frac{3}{2}$

= $\frac{21}{9} + \frac{1}{9} -\frac{3}{2}$

= $\frac{22}{9}  -\frac{3}{2}$

= $\frac{44}{18}  -\frac{27}{18}$

= $\frac{17}{18}$

 c) $\left ( \frac{7}{8}-0,25 \right ) :  \left ( \frac{5}{6}-0,75 \right )^{2}$

= $\left ( \frac{7}{8}-\frac{1}{4} \right ) : \left ( \frac{5}{6}-\frac{3}{4} \right )^{2}$

= $\left ( \frac{7}{8}-\frac{2}{8} \right ) : \left ( \frac{10}{12}-\frac{9}{12} \right )^{2}$

= $\frac{5}{8} : \frac{1}{144} $

= 90

d) $(-0,75) - \left [ (-2) +  \frac{3}{2} \right ]:1,5 + \left ( \frac{-5}{4} \right )$

= $\frac{-3}{4} - \left [ \frac{-4}{2} +  \frac{3}{2} \right ]: \frac{3}{2} + \left ( \frac{-5}{4} \right )$

= $\frac{-3}{4} - \left [ \frac{-4}{2} +  \frac{3}{2} \right ]: \frac{3}{2} + \left ( \frac{-5}{4} \right )$

= $\frac{-3}{4} - \left [ \frac{-1}{2}  \right ] : \frac{3}{2} + \left ( \frac{-5}{4} \right )$

= $\frac{-3}{4} + \frac{1}{3} + \left ( \frac{-5}{4} \right )$

= $\frac{-9}{12} +  \frac{4}{12} - \frac{15}{12}$

= $\frac{-20}{12}$

= $\frac{-5}{3}$

Bài tập 2 trang 27 toán 7 tập 1 CTST

Thực hiện phép tính (bằng cách hợp lí nếu có thể)

a) $\frac{5}{23}+\frac{7}{17}+0,25-\frac{5}{23}+\frac{10}{17}$

b) $\frac{3}{7}.2\frac{2}{3}-\frac{3}{7}.1\frac{1}{2}$

c) $13\frac{1}{4}:\left ( \frac{-4}{7} \right )-17\frac{1}{4}:\left (\frac{-4}{7}  \right )$

d) $\frac{100}{123} : \left ( \frac{3}{4}+\frac{7}{12} \right )+\frac{23}{123}:\left ( \frac{9}{5} -\frac{7}{15}\right )$

Hướng dẫn giải:

a) $\frac{5}{23}+\frac{7}{17}+0,25-\frac{5}{23}+\frac{10}{17}$

= $\frac{5}{23}+\frac{7}{17}+\frac{1}{4}-\frac{5}{23}+\frac{10}{17}$

= $\frac{5}{23} -\frac{5}{23} + \frac{7}{17} +\frac{10}{17} +\frac{1}{4}$

= 0 + 1 + $\frac{1}{4}$

= $\frac{5}{4}$

b) $\frac{3}{7}.2\frac{2}{3}-\frac{3}{7}.1\frac{1}{2}$

= $\frac{3}{7}. [\frac{8}{3} -\frac{3}{2}]$

= $\frac{3}{7}. \frac{7}{6}$

= $\frac{1}{2}$

c) $13\frac{1}{4}:\left ( \frac{-4}{7} \right )-17\frac{1}{4}:\left (\frac{-4}{7}  \right )$

= $(13\frac{1}{4} - 17\frac{1}{4}) :\left ( \frac{-4}{7} \right )$ 

= $-4 : \left ( \frac{-4}{7} \right )$ 

= 7

d) $\frac{100}{123} : \left ( \frac{3}{4}+\frac{7}{12} \right )+\frac{23}{123}:\left ( \frac{9}{5} -\frac{7}{15}\right )$

= $\frac{1}{123} : [100.\left ( \frac{3}{4}+\frac{7}{12} \right ) + 23.\left ( \frac{9}{5} -\frac{7}{15} \right )]$

= $\frac{1}{123} : [100. \frac{4}{3} + 23.\frac{4}{3} ]$

 = $\frac{4}{369}$ : 123

= $\frac{4}{45387}$

Bài tập 3 trang 27 toán 7 tập 1 CTST

Thực hiện phép tính

a) $\frac{5^{16}.27^{7}}{125^{5}.9^{11}}$

b) $(-0,2)^{2}.5-\frac{2^{13}.27^{3}}{4^{6}.9^{5}}$

c) $\frac{5^{6}+2^{2}.25^{3}+2^{3}.125^{2}}{26.5^{6}}$

Hướng dẫn giải:

) $\frac{5^{16}.27^{7}}{125^{5}.9^{11}}$ = $\frac{5^{16}.(3^{3})^{7}}{(5^{3})^{5}.(3^{2})^{11}}$ = $\frac{5^{16}.3^{21}}{5^{15}.3^{22}}$ = $\frac{5}{3}$

b) $(-0,2)^{2}.5-\frac{2^{13}.27^{3}}{4^{6}.9^{5}}$ = $(\frac{1}{5})^{2}.5-\frac{2^{13}.(3^{3})^{3}}{(2^{2})^{6}.(3^{2})^{5}}$ =$\frac{1}{5}-\frac{2^{13}.3^{9}}{2^{12}.3^{10}}$ = $\frac{1}{5}-\frac{2}{3}$ = $\frac{1}{5}-\frac{2}{3}$ =  $-\frac{7}{15}$

c) $\frac{5^{6}+2^{2}.25^{3}+2^{3}.125^{2}}{26.5^{6}}$ = $\frac{5^{6}+2^{2}.(5^{2})^{3}+2^{3}.(5^{3})^{2}}{26.5^{6}}$ = $\frac{5^{6}+2^{2}.5^{6}+2^{3}.5^{6}}{26.5^{6}}$= $\frac{5^{6} .(1 + 2^{2}+2^{3})}{26.5^{6}}$ =  $\frac {13}{26}$ = $\frac {1}{2}$

Bài tập 4 trang 27 toán 7 tập 1 CTST

Tính giá trị các biểu thức sau:

a) $A = \left [(-0,5)-\frac{3}{5}  \right ] : (-3) + \frac{1}{3}-\left (-\frac{1}{6}  \right ) : (-2)$

b) $B = \left ( \frac{2}{25} -0,036 \right ) : \frac{11}{50}-\left [ \left ( 3\frac{1}{4} - 2\frac{4}{9}  \right ) \right ].\frac{9}{29}$

Hướng dẫn giải:

a) $A = \left [(-0,5)-\frac{3}{5}  \right ] : (-3) + \frac{1}{3}-\left (-\frac{1}{6}  \right ) : (-2)$

$= \left [-\frac{1}{2} - \frac{3}{5}\right ] : (-3) + \frac{1}{3} - \frac{1}{12}$

$ =  \left [-\frac{5}{10} - \frac{6}{10}\right ] : (-3) + \frac{1}{3}. -\frac{1}{12}$

$ = \left [-\frac{11}{10}: (-3) + \frac{1}{4}\right ]$

$= \left [\frac{11}{30} + \frac{1}{4}\right ]$

$= \left [\frac{22}{60} + \frac{15}{60}\right ]$

$= \frac{22}{60}$

b) $B = \left ( \frac{2}{25} -0,036 \right ) : \frac{11}{50}-\left [ \left ( 3\frac{1}{4} - 2\frac{4}{9}  \right ) \right ].\frac{9}{29}$

$B = \left ( \frac{20}{250} -\frac{9}{250}\right ) .\frac{50}{11}-\left [ \left ( \frac{13}{4} - \frac{22}{9}  \right ) \right ].\frac{9}{29}$

$B = \frac{11}{250} .\frac{50}{11}-\left [ \left ( \frac{117}{36} - \frac{88}{36} \right ) \right ].\frac{9}{29}$

$B = \frac{1}{5} -\frac{29}{36}.\frac{9}{29}$

$B = \frac{1}{5} -\frac{29}{36}.\frac{9}{29}$

$B = \frac{1}{5} - \frac{1}{4}$

$B = \frac{4}{20} - \frac{5}{20}$

$B = -\frac{1}{20}$