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a] 4/12 ; 5/12 ; 11/2 ; 1/4

b] 1 ; 9/12; 12/5 ; 11/3

c] 8/21; 6/11;8/7

d] 2/3 ;2/7 15/2

a]1/3  5/12     11/2       1/4

b]1      3/4         12/5         33/9

c]8/21      6/11        8/7

d]2/3        2/7          15/2

1) \(373737.73-37.737373\)

\(=37.10101.73-37.73.10101\)

\(=0\)

2) \(19.41414141-41.19191919\)

\(=19.41.1010101-41.19.1010101\)

\(=0\)

3) \(123456.456789456789-456789.123456123456\)

\(=123456.456789.1000001-456789.123456.1000001\)

\(=0\)

4) \(250.12.7\)

\(=250.4.3.7\)

\(=\left(250.4\right).\left(3.7\right)\)

\(=1000.21\)

\(=21000\)

5) \(24.125.9\)

\(=3.8.125.9\)

\(=\left(3.9\right).\left(8.125\right)\)

\(=27.1000\)

\(=27000\)

6) \(125.44.18\)

\(=125.4.11.2.9\)

\(=\left(125.4.2\right).\left(11.9\right)\)

\(=1000.99\)

\(=99000\)

7) \(8.24.6+12.4.52+2.22.24\)

\(=48.24+48.52+48.22\)

\(=48\left(24+52+22\right)\)

\(=48.98\)

\(=48\left(100-2\right)\)

\(=48.100-48.2\)

\(=4800-96\)

\(=4704\)

8) \(18.58.2-9.27.4+12.69.3\)

\(=36.58-36.27+36.69\)

\(=36\left(58-27+69\right)\)

\(=36.100=3600\)

9) \(30.85.3+18.72.5-45.37.2-9.20.10\)

\(=90.85+90.72-90.37-90.20\)

\(=90\left(85+72-37-20\right)\)

\(=90.100=9000\)

\(\dfrac{7}{18}=\dfrac{7.4}{18.4}=\dfrac{28}{72}\); \(\dfrac{9}{8}=\dfrac{9.9}{8.9}=\dfrac{81}{72}\)

\(\dfrac{2}{3}=\dfrac{2.20}{3.20}=\dfrac{40}{60};\dfrac{3}{4}=\dfrac{3.15}{4.15}=\dfrac{45}{60};\dfrac{6}{5}=\dfrac{6.12}{5.12}=\dfrac{72}{60}\)

\(\dfrac{13}{12}=\dfrac{13.5}{12.5}=\dfrac{65}{60};\dfrac{5}{6}=\dfrac{5.10}{6.10}=\dfrac{50}{60};\dfrac{4}{5}=\dfrac{4.12}{12.5}=\dfrac{48}{60}\)

\(\dfrac{9}{8}=\dfrac{9.8}{8.6}=\dfrac{72}{48};\dfrac{7}{24}=\dfrac{7.2}{24.2}=\dfrac{14}{48};\dfrac{41}{48}\)

a: 4/3=32/24

5/8=15/24

b: 4/5=36/45

5/9=25/45

c: 4/9=16/36

7/12=21/36

d: 1/2=6/12

2/3=8/12

7/12=7/12

4/3 và 5/8 

\(\dfrac{4}{3}=\dfrac{4x8}{3x8}=\dfrac{32}{24}\)

 \(\dfrac{5}{8}=\dfrac{5x3}{8x3}=\dfrac{15}{24}\)

4/5 và 5/9 

\(\dfrac{4}{5}=\dfrac{4x9}{5x9}=\dfrac{36}{45}\)

\(\dfrac{5}{9}=\dfrac{5x5}{9x5}=\dfrac{25}{45}\)

4/9 và 7/12 

  \(\dfrac{4}{9}=\dfrac{4x12}{9x12}=\dfrac{48}{108}\)

\(\dfrac{7}{12}=\dfrac{7x9}{12x9}=\dfrac{63}{108}\)

1/2 ; 2/3 và 7/12 

\(\dfrac{1}{2}=\dfrac{1x6}{2x6}=\dfrac{6}{12}\)

\(\dfrac{2}{3}=\dfrac{2x4}{3x4}=\dfrac{8}{12}\)

\(\dfrac{7}{12}=\dfrac{7x1}{12x1}=\dfrac{7}{12}\)

a: =-5-7-8-3=-26

b: =-4-2-5-6=-17

c: =-8-11-4-2=-25

d: -9-15-6-3=-30

e: =-12-9-3-8=-32

\(1.\sqrt{\left(5+\sqrt{7}\right)^2}-\sqrt{8-2\sqrt{7}}=5+\sqrt{7}-\sqrt{7-2\sqrt{7}+1}=5+\sqrt{7}-\sqrt{7}+1=6\)

\(2.\sqrt{\left(\sqrt{3}+1\right)^2}-\sqrt{4-2\sqrt{3}}=\sqrt{3}+1-\sqrt{3-2\sqrt{3}+1}=\sqrt{3}+1-\sqrt{3}+1=2\)

\(3.VT=\sqrt{11}-\sqrt{20-6\sqrt{11}}=\sqrt{11}-\sqrt{11-2.3\sqrt{11}+9}=\sqrt{11}-\sqrt{11}+3=3=VP\)

Vậy , đẳng thức được chứng minh .

\(4.VT=\sqrt{41+12\sqrt{5}}-\sqrt{41-12\sqrt{5}}=\sqrt{36+2.6\sqrt{5}+5}-\sqrt{36-2.6\sqrt{5}+5}=6+\sqrt{5}-6+\sqrt{5}=2\sqrt{5}=VP\)

Vậy , đẳng thức được chứng minh .