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

 \(\dfrac{8}{12}=\dfrac{8:4}{12:4}=\dfrac{2}{3}\)

\(\dfrac{30}{36}=\dfrac{30:6}{36:6}=\dfrac{5}{6}\)

\(\dfrac{{ - 12}}{{ - 4}} = \dfrac{{ - 12:\left( { - 4} \right)}}{{\left( { - 4} \right):\left( { - 4} \right)}} = 3\)

\(\dfrac{7}{{ - 35}} = \dfrac{{7:\left( { - 7} \right)}}{{ - 35:\left( { - 7} \right)}} = \dfrac{{ - 1}}{5}\)

\(\dfrac{{ - 9}}{{27}} = \dfrac{{ - 9:9}}{{27:9}} = \dfrac{{ - 1}}{3}\)

10/5=2

12/9=4/3

8/4=2

5/6 là PS tối giản

\(\frac{10}{5}=\frac{10:5}{5:5}=\frac{2}{1}\)

\(\frac{12}{9}=\frac{12:3}{9:3}=\frac{4}{3}\)

\(\frac{8}{4}=\frac{8:4}{4:4}=\frac{2}{1}\)

\(\frac{5}{6}\)giữ nguyên

\(\frac{10}{5}\)=\(\frac{10:5}{5:5}\)=\(\frac{2}{1}\)=\(2\)

\(\frac{12}{9}\)=\(\frac{12:3}{9:3}\)=\(\frac{4}{3}\)

\(\frac{8}{4}\)=\(\frac{8:4}{4:4}\)=\(\frac{2}{1}\)=\(2\)

\(\frac{5}{6}\)là phân số tối giản.

a) Số:

\(\dfrac{12}{18}\) = \(\dfrac{6}{9}\)  = \(\dfrac{2}{3}\) 

b) Rút gọn các phân số:
\(\dfrac{12}{48}\) = \(\dfrac{1}{4}\)

\(\dfrac{80}{100}\)= \(\dfrac{4}{5}\) 

\(\dfrac{75}{125}\) = \(\dfrac{3}{5}\) 

\(\dfrac{15}{25}=\dfrac{15:5}{25:5}=\dfrac{3}{5}\\ \dfrac{24}{28}=\dfrac{24:4}{28:4}=\dfrac{6}{7}\\ \dfrac{18}{33}=\dfrac{18:3}{33:3}=\dfrac{6}{11}\\ \dfrac{12}{36}=\dfrac{12:12}{36:12}=\dfrac{1}{3}.\)

\(\dfrac{15}{25}=\dfrac{3}{5}\)

\(\dfrac{24}{28}=\dfrac{6}{7}\)

\(\dfrac{18}{33}=\dfrac{6}{11}\)

\(\dfrac{12}{36}=\dfrac{1}{3}\)

\(\dfrac{15}{25}=\dfrac{15:5}{25:5}=\dfrac{3}{5}\\ \dfrac{24}{28}=\dfrac{24:4}{28:4}=\dfrac{6}{7}\\ \dfrac{18}{33}=\dfrac{18:3}{33:3}=\dfrac{6}{11}\\ \dfrac{12}{36}=\dfrac{12:12}{36:12}=\dfrac{1}{3}\)

-2/3

4/7

-5/3

1/3

\(\dfrac{8}{-12}=\dfrac{-8}{12}=\dfrac{-2}{3}\)

\(\dfrac{400}{700}=\dfrac{4}{7}\)

\(\dfrac{-10}{6}=\dfrac{-5}{3}\)

\(\dfrac{-35}{-105}=\dfrac{35}{105}=\dfrac{1}{3}\)

Bài 1:

a) \(a=2\cdot3\cdot5\cdot43\)

\(b=7200=2^5\cdot3^2\cdot5^2\)

\(c-4680=2^3\cdot3^2\cdot5\cdot13\)

b) \(\dfrac{8440}{5910}=\dfrac{8440:10}{5910:10}=\dfrac{844}{591}\)

\(\dfrac{1245}{3450}=\dfrac{1245:15}{3450:15}=\dfrac{83}{230}\)

Bài 2:

a) Ước nguyên tố của 140 là:

\(ƯNT\left(140\right)=\left\{2;5;7\right\}\)

Ước nguyên tố của 138 là:
\(ƯNT\left(138\right)=\left\{3;23;2\right\}\)

b) \(A=\dfrac{2^{10}+4^6}{8^4}\)

\(A=\dfrac{2^{10}+2^{12}}{2^{12}}\)

\(A=\dfrac{2^{10}\cdot\left(1+2^2\right)}{2^{12}}\)

\(A=\dfrac{1+4}{2^2}\)

\(A=\dfrac{5}{4}\)

\(B=\dfrac{6^{10}+15\cdot2^{10}\cdot3^9}{12\cdot8^3\cdot27^3}\)

\(B=\dfrac{2^{10}\cdot3^{10}+5\cdot2^{10}\cdot3^{10}}{2^{11}\cdot3^{10}}\)

\(B=\dfrac{2^{10}\cdot3^{10}\cdot\left(1+5\right)}{2^{11}\cdot3^{10}}\)

\(B=\dfrac{1+5}{2}\)

\(B=3\)

2/5,2/3,3/7,1/3,12/25