Giải bài 1 trang 15 SGK Toán 7 tập 1 - Chân trời sáng tạo

Đề bài

Tính:

a) $\frac{2}{{15}} + \left( {\frac{{ - 5}}{{24}}} \right)$           

b) $\left( {\frac{{ - 5}}{9}} \right) - \left( { - \frac{7}{{27}}} \right);$           

c) $\left( { - \frac{7}{{12}}} \right) + 0,75$

d) $\left( {\frac{{ - 5}}{9}} \right) - 1,25$          

e) $0,34.\frac{{ - 5}}{{17}}$                       

g) $\frac{4}{9}:\left( { - \frac{8}{{15}}} \right);$

h) $\left( {1\frac{2}{3}} \right):\left( {2\frac{1}{2}} \right)$       

i) $\frac{2}{5}.\left( { - 1.25} \right)$                     

k) $\left( {\frac{{ - 3}}{5}} \right).\left( {\frac{{15}}{{ - 7}}} \right).3\frac{1}{9}$

Lời giải chi tiết

a) $\frac{2}{{15}} + \left( {\frac{{ - 5}}{{24}}} \right) = \frac{{16}}{{120}} + \left( {\frac{{ - 25}}{{120}}} \right) = \frac{{ - 9}}{{120}} = \frac{{ - 3}}{{40}}$          

b) $\left( {\frac{{ - 5}}{9}} \right) - \left( { - \frac{7}{{27}}} \right) = \left( {\frac{{ - 15}}{{27}}} \right) + \frac{7}{{27}} = \frac{{ - 8}}{{27}}$          

c) $\left( { - \frac{7}{{12}}} \right) + 0,75$ $= \left( { - \frac{7}{{12}}} \right) + \frac{75}{100}$ $= \left( { - \frac{7}{{12}}} \right) + \frac{3}{4}$ $= \left( { - \frac{7}{{12}}} \right) + \frac{9}{{12}}$ $= \frac{2}{{12}} = \frac{1}{6}$

d) $\left( {\frac{{ - 5}}{9}} \right) - 1,25$ $=\left( {\frac{{ - 5}}{9}} \right) - \frac{125}{100} = \left( {\frac{{ - 5}}{9}} \right) - \frac{5}{4}$ $= \left( {\frac{{ - 20}}{{36}}} \right) - \frac{{45}}{{36}} = \frac{{ - 65}}{{36}}$

e) $0,34.\frac{{ - 5}}{{17}} =\frac{{34}}{{100}}.\frac{{ - 5}}{{17}}$ $= \frac{{17}}{{50}}.\frac{{ - 5}}{{17}}$ $= \frac{{ - 1}}{{10}}$                       

g) $\frac{4}{9}:\left( { - \frac{8}{{15}}} \right)$ $= \frac{4}{9}.\left( { - \frac{{15}}{8}} \right)$ $= \frac{{ - 5}}{6}$

h) $\left( {1\frac{2}{3}} \right):\left( {2\frac{1}{2}} \right)$ $= \frac{5}{3}:\frac{5}{2}$ $= \frac{5}{3}.\frac{2}{5}$ $= \frac{2}{3}$       

i) $\frac{2}{5}.\left( { - 1,25} \right)$ $= \frac{2}{5}.\frac{{ - 125}}{100}$ $= \frac{2}{5}.\frac{{ - 5}}{4}$ $= \frac{{ - 1}}{2}$

k) $\left( {\frac{{ - 3}}{5}} \right).\left( {\frac{{15}}{{ - 7}}} \right).3\frac{1}{9}$ $= \left( {\frac{{ - 3}}{5}} \right).\left( {\frac{{15}}{{ - 7}}} \right).\frac{{28}}{9}$ $= \frac{{ - 3.3.5.7.4}}{{5.\left( { - 7} \right).3.3}} = 4$