a) \(\dfrac{3}{5}=\dfrac{21}{35};\dfrac{4}{7}=\dfrac{20}{35}\)

b) \(\dfrac{5}{6}=\dfrac{45}{54};\dfrac{7}{9}=\dfrac{42}{54}\)

`MSC:12`

`2/3=(2xx4)/(3xx4)=8/12` và `5/12`

`2/3=`\(\dfrac{2\times4}{3\times4}\)`=8/12` và `5/12`

Vì mẫu số chung là \(12\) nên phân số \(\dfrac{5}{12}\) không phải quy đồng .

Ta thấy \(12\div3=4\) vậy cả tử số và mẫu số của phân số \(\dfrac{2}{3}\) nhân với \(4\)

Ta có :

  \(\dfrac{2}{3}=\dfrac{2\times4}{3\times4}=\dfrac{8}{12}\)

Vậy hai phân số đó là : \(\dfrac{8}{12}\) và \(\dfrac{5}{12}\)

a) \(\dfrac{2}{5}=\dfrac{4}{10}\)

\(\dfrac{4}{10}>\dfrac{3}{10}\)

b) \(\dfrac{5}{6}=\dfrac{10}{12}\)

\(\dfrac{7}{12}< \dfrac{10}{12}\)

c) \(\dfrac{1}{2}=\dfrac{2}{4}\)

\(\dfrac{3}{4}< \dfrac{2}{4}\)

d) \(\dfrac{8}{3}=\dfrac{56}{21}\)

\(\dfrac{56}{21}>\dfrac{11}{21}\)

1) 

\(\dfrac{3}{4}=\dfrac{3\times3}{4\times3}=\dfrac{9}{12}\) 

\(\dfrac{2}{12}\) (giữ nguyên)

2)

\(\dfrac{1}{4}=\dfrac{1\times3}{4\times3}=\dfrac{3}{12}\)

\(\dfrac{2}{3}=\dfrac{2\times4}{3\times4}=\dfrac{8}{12}\)

a) \(\dfrac{3}{4}\) và \(\dfrac{2}{12}\)

\(\dfrac{3}{4}=\dfrac{3\times3}{4\times3}=\dfrac{9}{12}\) ; giữ nguyên \(\dfrac{2}{12}\)

Quy đồng mẫu số hai phân số \(\dfrac{3}{4}\) và \(\dfrac{2}{12}\) được hai phân số \(\dfrac{9}{12}\) và \(\dfrac{2}{12}\).

b) \(\dfrac{1}{4}\) và \(\dfrac{2}{3}\)

\(\dfrac{1}{4}=\dfrac{1\times3}{4\times3}=\dfrac{3}{12}\) ; \(\dfrac{2}{3}=\dfrac{2\times4}{3\times4}=\dfrac{8}{12}\)

Quy đồng mẫu số hai phân số \(\dfrac{1}{4}\) và \(\dfrac{2}{3}\) được hai phân số \(\dfrac{3}{12}\) và \(\dfrac{8}{12}\).

Ta có: \(\dfrac{5}{7} = \dfrac{{5.4}}{{7.4}} = \dfrac{{20}}{{28}}\) và \(\dfrac{{ - 3}}{4} = \dfrac{{ - 3.7}}{{4.7}} = \dfrac{{ - 21}}{{28}}\)

Như vậy, \(\dfrac{{20}}{{28}} + \dfrac{{ - 21}}{{28}} = \dfrac{{20 + \left( { - 21} \right)}}{{28}} =  \dfrac{-1}{{28}}\)

a) \(\dfrac{3}{4}=\dfrac{3\cdot5}{4\cdot5}=\dfrac{15}{20}\\ \dfrac{2}{5}=\dfrac{2\cdot4}{5\cdot4}=\dfrac{8}{20}\)

b) \(\dfrac{5}{12}=\dfrac{5\cdot3}{12\cdot3}=\dfrac{15}{36}\\ \dfrac{11}{36}=\dfrac{11}{36}\)

c) \(\dfrac{2}{3}=\dfrac{2\cdot4\cdot5}{3\cdot4\cdot5}=\dfrac{40}{60}\\ \dfrac{3}{4}=\dfrac{3\cdot3\cdot5}{4\cdot3\cdot5}=\dfrac{45}{60}\\ \dfrac{4}{5}=\dfrac{4\cdot3\cdot4}{5\cdot3\cdot4}=\dfrac{48}{60}\)

a) \(\dfrac{3}{4}\) và \(\dfrac{2}{5}\)

Mẫu số chung: 20

\(\dfrac{3}{4}=\dfrac{3.5}{4.5}=\dfrac{15}{20}\)

\(\dfrac{2}{5}=\dfrac{2.4}{5.4}=\dfrac{8}{20}\)

b) \(\dfrac{5}{12}\) và \(\dfrac{11}{36}\)

Mẫu số chung: 36

\(\dfrac{5}{12}=\dfrac{5.3}{12.3}=\dfrac{15}{36}\)

c) \(\dfrac{2}{3};\dfrac{3}{4}\) và \(\dfrac{4}{5}\)

Mẫu số chung: 60

\(\dfrac{2}{3}=\dfrac{2.20}{3.20}=\dfrac{40}{60}\\ \dfrac{3}{4}=\dfrac{3.15}{4.15}=\dfrac{45}{60}\\ \dfrac{4}{5}=\dfrac{4.12}{5.12}=\dfrac{48}{60}\)

a) MTC=20

 \(\dfrac{3}{4}=\dfrac{15}{20}\)

\(\dfrac{2}{5}=\dfrac{8}{20}\)

b) MTC=36 

\(\dfrac{5}{12}=\dfrac{15}{36}\)

\(\dfrac{11}{36}=\dfrac{11}{36}\)

c) MTC=60

\(\dfrac{2}{3}=\dfrac{40}{60}\)

\(\dfrac{3}{4}=\dfrac{45}{60}\)

\(\dfrac{4}{5}=\dfrac{48}{60}\)

a) \(\dfrac{2}{36}=\dfrac{1}{18}\)

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

b) \(\dfrac{10}{25}=\dfrac{2}{5}\)

\(\dfrac{14}{40}=\dfrac{7}{20}\)

a) \(\dfrac{3}{4}=\dfrac{3\times4}{4\times4}=\dfrac{12}{16}\)

b) \(\dfrac{1}{3}=\dfrac{1\times3}{3\times3}=\dfrac{3}{9}\)

c) \(\dfrac{5}{6}=\dfrac{5\times3}{6\times3}=\dfrac{15}{18}\)

a) \(\dfrac{2}{3}=\dfrac{2.8}{3.8}=\dfrac{16}{24}\)

\(\dfrac{5}{8}=\dfrac{5.3}{8.3}=\dfrac{15}{24}\)

b) \(\dfrac{1}{4}=\dfrac{1.3}{4.3}=\dfrac{3}{12}\)

\(\dfrac{7}{12}=\dfrac{7.1}{12.1}=\dfrac{7}{12}\)

c) \(\dfrac{5}{6}=\dfrac{5.4}{6.4}=\dfrac{20}{24}\)

\(\dfrac{3}{8}=\dfrac{3.3}{8.3}=\dfrac{9}{24}\)

a) 58=5.38.3=152458=5.38.3=1524

b) 712=7.112.1=712712=7.112.1=712

c) 38=3.38.3=924

a) 58=5.38.3=152458=5.38.3=1524

b) 712=7.112.1=712712=7.112.1=712

c) 38=3.38.3=924

+ Quy đồng mẫu các phân số: \(\dfrac{3}{4}\) và \(\dfrac{5}{6}\):

\(BCNN\left( {6,4} \right) = 12\)

Thừa số phụ: \(12:4 = 3; 12:6=2\)

Ta có: \(\dfrac{3}{4} = \dfrac{{3.3}}{{4.3}} = \dfrac{9}{{12}}\\\dfrac{5}{6} = \dfrac{{5.2}}{{6.2}} = \dfrac{{10}}{{12}}\)

+ So sánh hai phân số cùng mẫu:

Vì 9 < 10 nên \(\dfrac{9}{{12}} < \dfrac{{10}}{{12}}\) nên \(\dfrac{3}{4} < \dfrac{5}{6}\).