a. \(\dfrac{1}{5}\) đã tối giản

\(\dfrac{4}{120}=\dfrac{1}{30}\)

\(\dfrac{-50}{60}=\dfrac{-5}{6}\)

Quy đồng: \(BCNN\left(5,30,6\right)=30\)

\(\Rightarrow\dfrac{1}{5}=\dfrac{1.6}{5.6}=\dfrac{6}{30};\dfrac{1}{30}=\dfrac{1.1}{30.1}=\dfrac{1}{30};\dfrac{-5}{6}=\dfrac{-5.5}{6.5}=\dfrac{-25}{30}\)

b. \(\dfrac{-25}{30}< \dfrac{1}{30}< \dfrac{6}{30}\)

a,\(\dfrac{4}{120}=\dfrac{1}{30};\dfrac{-50}{60}=\dfrac{-5}{6}\)  

\(\dfrac{1}{5}=\dfrac{1.6}{5.6}=\dfrac{6}{30};\dfrac{1}{30};\dfrac{-5}{6}=\dfrac{-5.5}{6.5}=\dfrac{-25}{30}\)

b, Vì \(\dfrac{6}{30}>\dfrac{1}{30}>\dfrac{-25}{30}\) nên => \(\dfrac{4}{120}>\dfrac{1}{30}>\dfrac{-50}{60}\)

Rút gọn :
10/15=2/3 ; 12/16=3/4 
Quy đồng : 
2/3 = 8/12 
3/4=9/12

a) \(\dfrac{21}{15}\) + \(\dfrac{2}{5}\) = \(\dfrac{9}{5}\)
b)  \(\dfrac{6}{16}\) + \(\dfrac{1}{8}\) = \(\dfrac{1}{2}\)

c)  \(\dfrac{3}{12}\) + \(\dfrac{3}{4}\) = 1

a: \(\dfrac{1}{8}+\dfrac{5}{8}=\dfrac{1+5}{8}=\dfrac{6}{8}=\dfrac{3}{4}\)

b: \(\dfrac{1}{15}+\dfrac{4}{15}=\dfrac{1+4}{15}=\dfrac{5}{15}=\dfrac{1}{3}\)

c: \(\dfrac{5}{9}+\dfrac{7}{9}=\dfrac{5+7}{9}=\dfrac{12}{9}=\dfrac{4}{3}\)

d: \(\dfrac{23}{100}+\dfrac{27}{100}=\dfrac{23+27}{100}=\dfrac{50}{100}=\dfrac{1}{2}\)

a) 18+58=1+58=68=3418+58=1+58=68=34

b) 115+415=1+415=515=13115+415=1+415=515=13

c) 59+79=5+79=129=4359+79=5+79=129=43

d) 23100+27100=23+27100=50100=12

a) \(\left\{{}\begin{matrix}\dfrac{1}{5}=\dfrac{1.6}{5.6}=\dfrac{6}{30}\\\dfrac{1}{6}=\dfrac{1.5}{6.5}=\dfrac{5}{30}\\\dfrac{2}{15}=\dfrac{2.2}{15.2}=\dfrac{4}{30}\\\dfrac{1}{10}=\dfrac{1.3}{10.3}=\dfrac{3}{30}\end{matrix}\right.\)

Quy luật: Tử số của mỗi phân số cách nhau \(1\) đơn vị, cùng chung mẫu số là \(30\).

Phân số tiếp theo: \(\dfrac{2}{30}=\dfrac{1}{15}\)

b) \(\left\{{}\begin{matrix}\dfrac{1}{9}=\dfrac{1.5}{9.5}=\dfrac{5}{45}\\\dfrac{1}{15}=\dfrac{1.3}{15.3}=\dfrac{3}{45}\end{matrix}\right.\)

Quy luật: Tử số của mỗi phân số cách nhau \(1\) đơn vị, cùng chung mẫu số là \(45\).

Phân số tiếp theo: \(\dfrac{1}{45}\)

a, \(\dfrac{6}{30};\dfrac{5}{30};\dfrac{4}{30};\dfrac{3}{30};\dfrac{2}{30}\)

b,\(\dfrac{5}{45};\dfrac{4}{45};\dfrac{3}{45};\dfrac{2}{45};\dfrac{1}{45}\)

\(a,\dfrac{6}{30};\dfrac{5}{30};\dfrac{4}{30};\dfrac{3}{30};\dfrac{2}{30}\)

\(b,\dfrac{5}{45};\dfrac{4}{45};\dfrac{3}{45};\dfrac{2}{45};\dfrac{1}{45}\)

a)

Phân số đã tối giản: \(\dfrac{2}{3}\); \(\dfrac{5}{17}\);\(\dfrac{1}{10}\)Phân số nào chưa tối giản: \(\dfrac{9}{21}\); \(\dfrac{10}{15}\); \(\dfrac{7}{14}\) 

b) Rút gọn

\(\dfrac{21}{9}\) = \(\dfrac{7}{3}\)
\(\dfrac{10}{15}\) = \(\dfrac{2}{3}\)
\(\dfrac{7}{14}\) = \(\dfrac{1}{2}\)

a) Phân số tối giản là: \(\dfrac{2}{3};\dfrac{5}{17};\dfrac{1}{10}.\)

 Phân số chưa tối giản là: \(\dfrac{9}{21};\dfrac{10}{15};\dfrac{7}{14}\)

b)

 \(\dfrac{10}{15}=\dfrac{10:5}{15:5}=\dfrac{2}{3}\\ \dfrac{7}{14}=\dfrac{7:7}{14:7}=\dfrac{1}{2}\)

Lời giải:

a. $\frac{5}{9}=\frac{5\times 2}{9\times 2}=\frac{10}{18}$
b. $\frac{9}{20}=\frac{9\times 3}{20\times 3}=\frac{27}{60}$

a) \(\dfrac{5}{9}=\dfrac{5\times2}{9\times2}=\dfrac{10}{18}\)

b) \(\dfrac{9}{20}=\dfrac{9\times3}{20\times3}=\dfrac{27}{60}\)

\(a)\) Mẫu số chung: 45.

\(\dfrac{2}{5}=\dfrac{2\times7}{5\times7}=\dfrac{14}{45}\\ \dfrac{13}{15}=\dfrac{13\times3}{15\times3}=\dfrac{39}{45}\\ \dfrac{19}{45}\)

b) Mẫu số chung: 16.

\(\dfrac{1}{2}=\dfrac{1\times8}{2\times8}=\dfrac{8}{16}\\ \dfrac{3}{8}=\dfrac{3\times2}{8\times2}=\dfrac{6}{16}\\ \dfrac{5}{4}=\dfrac{5\times4}{4\times4}=\dfrac{\dfrac{20}{16}\\ 7}{16}\)

a: \(\dfrac{15}{8}-\dfrac{13}{8}=\dfrac{15-13}{8}=\dfrac{2}{8}=\dfrac{1}{4}\)

b: \(\dfrac{7}{15}-\dfrac{2}{15}=\dfrac{7-2}{15}=\dfrac{5}{15}=\dfrac{1}{3}\)

c: \(\dfrac{11}{12}-\dfrac{2}{12}=\dfrac{11-2}{12}=\dfrac{9}{12}=\dfrac{3}{4}\)

d: \(\dfrac{19}{7}-\dfrac{5}{7}=\dfrac{19-5}{7}=\dfrac{14}{7}=2\)