\(1,\\ \dfrac{3}{5}=\dfrac{21}{35};\dfrac{4}{7}=\dfrac{20}{35}\\ \dfrac{2}{3}=\dfrac{4}{6};\dfrac{5}{6}=\dfrac{5}{6}\\ \dfrac{4}{9}=\dfrac{8}{18};\dfrac{1}{6}=\dfrac{3}{18}\\ 2,\\ \dfrac{5}{9}=\dfrac{10}{18};\dfrac{7}{8}=\dfrac{14}{16};\dfrac{24}{42}=\dfrac{12}{21}\)

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

\(\dfrac{2}{3}=\dfrac{4}{6};\dfrac{5}{6}=\dfrac{5}{6}\)

\(\dfrac{4}{9}=\dfrac{16}{36};\dfrac{1}{6}=\dfrac{6}{36}\)

2. \(\dfrac{5}{9}=\dfrac{10}{18}\)

\(\dfrac{7}{8}=\dfrac{14}{16}\)

\(\dfrac{24}{42}=\dfrac{12}{21}\)

\(\dfrac{-54}{72}=\dfrac{-3}{4}\); \(\dfrac{42}{36}=\dfrac{7}{6}\);  \(\dfrac{2}{-3}=\dfrac{2}{-3}\)

\(\Rightarrow BCNN\left(4,6,-3\right)=12\)

Quy đồng

\(\dfrac{-3}{4}=\dfrac{-3.3}{4.3}=\dfrac{-9}{12}\)

\(\dfrac{7}{6}=\dfrac{7.2}{6.2}=\dfrac{14}{12}\)

\(\dfrac{2}{-3}=\dfrac{2.\left(-4\right)}{\left(-3\right).\left(-4\right)}=\dfrac{-8}{12}\)

ta có 2/3 = 2x4/3x 4=8/12 và giữ nguyên phân số 5/12

vậy quy đồng 2 phân số 2/3 và 5/12 được 2 phân số 8/12 và 5/12

90/72 = 90:18/72:18 = 5/4

72/42 = 72:6/42:6 = 12/7

ídsdsdddđ

Kết quả là 8/12 và 5/12 là đúng

-9/6; -5/6; -9/6

90/45; -90/45; -35/45

Quy đồng mẫu số các phân số \(\frac{49}{-42};\frac{-45}{81};\frac{-24}{45}\)

Rút gọn các phân số ta được : \(\frac{49}{-42}=\frac{-49}{42}=\frac{-7}{6}\); \(\frac{-45}{81}=\frac{-5}{9}\); \(\frac{-24}{45}=\frac{-8}{15}\)

Ta có : 6 = 2 . 3

            9 = 3²

            15 = 3 . 5 

=> BCNN(6, 9, 15) = 2 . 3² . 5 = 90

90 : 6 = 15

90 : 9 = 10

90 : 15 = 6

=> \(\frac{-7}{6}=\frac{-7\cdot15}{6\cdot15}=\frac{-105}{90}\); \(\frac{-5}{9}=\frac{-5\cdot10}{9\cdot10}=\frac{-50}{90}\); \(\frac{-8}{15}=\frac{-8\cdot6}{15\cdot6}=\frac{-48}{90}\)

49/-42 = 7/-6 = -7/6
-45/81 = -5/9
-24/45 = -8/15
BCNN(6;9;15) = 90
-7/6 = -105/90
-5/9 = -50/90
-8/15 = -48/90
Vậy 49/-42 = -105/9 ; -45/81 = -50/90 ; -24/45 = -48/90
Chúc bạn học tốt!
 

a ) 1 2 < 5 6 b ) 4 7 > 5 9 ; c ) − 3 7 > − 4 9 d ) − 7 8 < 35 − 42

\(\dfrac{1}{42}+\dfrac{1}{30}+\dfrac{1}{12}+\dfrac{1}{6}+\dfrac{1}{2}\)
\(=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{30}+\dfrac{1}{42}\)
\(=\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{5\times6}+\dfrac{1}{6\times7}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}\)
\(=1-\dfrac{1}{4}+\dfrac{1}{5}-\dfrac{1}{7}\)
\(=\dfrac{140}{140}-\dfrac{35}{140}+\dfrac{28}{140}-\dfrac{20}{140}\)
\(=\dfrac{113}{140}\)

\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{30}+\dfrac{1}{42}\)

\(=\dfrac{1}{2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{5.6}+\dfrac{1}{6.7}\)

\(=\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}\)

\(=1-\dfrac{1}{4}+\dfrac{1}{5}-\dfrac{1}{7}=\dfrac{140-35+28-20}{140}=\dfrac{113}{140}\)

Mình nghĩ đề bài cần thêm 1/20 mới tính nhanh được