Tìm số nguyên thích hợp cho ô vuông:
a) \(\frac{7}{{25}}.\frac{{?}}{{28}} = \frac{{ - 3}}{{20}};\)
b) \(\frac{{46}}{{15}}.\frac{{ - 3}}{{?}} = \frac{{23}}{5};\)
c) \(\frac{{?}}{{ - 18}}.\frac{5}{2} = \frac{{ - 5}}{{12}}\)
Quy tắc nhân phân số:
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\(\frac{a}{b}.\frac{c}{d} = \frac{{a.c}}{{b.d}}\;\;(b \ne 0,d \ne 0);\;\;\;m.\frac{a}{b} = \frac{a}{b}.m = \frac{{a.m}}{b}\)
Lưu ý: Kết hợp với rút gọn phân số, hai phân số bằng nhau.
\(a)\frac{7}{{25}}.\frac{?}{{28}} = \frac{{ - 3}}{{20}} \Leftrightarrow \frac{?}{{28}} = \frac{{ - 3}}{{20}}:\frac{7}{{25}} \\\Leftrightarrow \frac{?}{{28}} = \frac{{ - 3}}{{20}}.\frac{{25}}{7} \Leftrightarrow \frac{?}{{28}} = \frac{{ - 15}}{{28}}\\ \Leftrightarrow ?.28 = ( - 15).28 \Leftrightarrow ? = - 15\)
\(b)\frac{{46}}{{15}}.\frac{{ - 3}}{?} = \frac{{23}}{5} \Leftrightarrow \frac{{ - 3}}{?} = \frac{{23}}{5}:\frac{{46}}{{15}} \\ \Leftrightarrow \frac{{ - 3}}{?} = \frac{{23}}{5}.\frac{{15}}{{46}} \Leftrightarrow \frac{{ - 3}}{?} = \frac{3}{2} \\ \Leftrightarrow ( - 3).2 = 3.? \Leftrightarrow ? = - 2\)
\(c)\frac{?}{{ - 18}}.\frac{5}{2} = \frac{{ - 5}}{{12}} \Leftrightarrow \frac{?}{{ - 18}} = \frac{{ - 5}}{{12}}:\frac{5}{2}\\ \Leftrightarrow \frac{?}{{ - 18}} = \frac{{ - 5}}{{12}}.\frac{2}{5} \Leftrightarrow \frac{?}{{ - 18}} = \frac{{ - 1}}{6}\\ \Leftrightarrow ?.6 = ( - 1).( - 18) \Leftrightarrow ? = 3\)