Rút gọn phân số sau: \(\dfrac{320}{15}\)
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![](https://rs.olm.vn/images/avt/0.png?1311)
Giải:
a) \(\dfrac{5^3.90.4^3}{25^2.3^2.2^{13}}\)
\(=\dfrac{5^3.5.3^2.2.\left(2^2\right)^3}{\left(5^2\right)^2.3^2.2^{13}}\)
\(=\dfrac{5^4.3^2.2.2^6}{5^4.3^2.2^{13}}\)
\(=\dfrac{5^4.3^2.2^7}{5^4.3^2.2^{13}}\)
\(=\dfrac{1}{2^6}=\dfrac{1}{64}\)
b) \(\dfrac{15^2.16^4-15^3.16^3}{12^2.20^3-20^2.12^3}\)
\(=\dfrac{15^2.16^3.16-15^2.16^3.15}{12^2.20^2.20-20^2.12^2.12}\)
\(=\dfrac{15^2.16^3.\left(16-15\right)}{12^2.20^2.\left(20-12\right)}\)
\(=\dfrac{\left(3.5\right)^2.\left(2^4\right)^3.1}{\left(3.2^2\right)^2.\left(2^2.5\right)^2.8}\)
\(=\dfrac{3^2.5^2.2^{12}}{3^2.\left(2^2\right)^2.\left(2^2\right)^2.5^2.2^3}\)
\(=\dfrac{3^2.5^2.2^{12}}{3^2.5^2.2^4.2^4.2^3}\)
\(=\dfrac{3^2.5^2.2^{12}}{3^2.5^2.2^{11}}\)
\(=2\)
c) \(\dfrac{2.3+4.6+14.21}{3.5+6.10+21.35}\)
\(=\dfrac{2.3+2.3.2.2+2.3.7.7}{3.5+3.5.2.2+3.5.7.7}\)
\(=\dfrac{2.3+2.3.4+2.3.49}{3.5+3.5.4+3.5.49}\)
\(=\dfrac{2.3.\left(1+4+49\right)}{3.5.\left(1+4+49\right)}\)
\(=\dfrac{2.3}{3.5}\)
\(=\dfrac{2}{5}\)
Chúc bạn học tốt!
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{-334}{320}=\frac{-334\div2}{320\div2}=\frac{-167}{160}\)
\(\frac{451}{200}=\frac{451}{200}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
a: Các phân số tối giản là \(\dfrac{1}{3};\dfrac{4}{7};\dfrac{72}{73}\) vì ƯCLN(1;3)=1; ƯCLN(4;7)=1; ƯCLN(72;73)=1
b:
Các phân số rút gọn được là
\(\dfrac{8}{12}=\dfrac{8:4}{12:4}=\dfrac{2}{3}\)
\(\dfrac{30}{36}=\dfrac{30:6}{36:6}=\dfrac{5}{6}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{-8}{12}=\dfrac{-8:4}{12:4}=\dfrac{-2}{3}\\ \dfrac{15}{-60}=\dfrac{15:15}{-60:15}=\dfrac{1}{-4}\\ \dfrac{-16}{-72}=\dfrac{-16:\left(-8\right)}{-72:\left(-8\right)}=\dfrac{2}{9}\\ \dfrac{35}{14.15}=\dfrac{5.7}{7.2.5.3}=\dfrac{1}{2.3}=\dfrac{1}{6}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{15}{25}=\dfrac{15:5}{25:5}=\dfrac{3}{5}\\ \dfrac{24}{28}=\dfrac{24:4}{28:4}=\dfrac{6}{7}\\ \dfrac{18}{33}=\dfrac{18:3}{33:3}=\dfrac{6}{11}\\ \dfrac{12}{36}=\dfrac{12:12}{36:12}=\dfrac{1}{3}.\)
\(\dfrac{64}{3}\)
\(\dfrac{64}{3}\)