Answer
`a,` Ta có:
`1/5 = {1 xx 24}/{5 xx 24} = {24}/120`
`8/10 = {8 xx 12}/{10 xx 12} = 96/120`
`9/15 = {9 xx 8}/{15 xx 8} = 72/120`
`3/10 = {3 xx 12}/{10 xx 12} = 36/120`
`9/12 = {9 xx 10}/{12 xx 10} = 90/120`
`3/8 = {3 xx 15}/{8 xx 15} = 45/120`
$\text{Vì}$ $24 < 36 < 45 < 72 < 90 < 96$ $\text{nên}$ $\dfrac{24}{120} < \dfrac{36}{120} < \dfrac{45}{120} < \dfrac{72}{120} < \dfrac{90}{120} < \dfrac{96}{120}$
`-> 1/5 < 3/10 < 3/8 < 9/15 < 9/12 < 8/10`
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`b,` Rút gọn:
`24/16 = {24 : 8}/{16 : 8} = 3/2`
`20/25 = {20 : 5}/{25 : 5} = 4/5`
`20/55 = {20 : 5}/{55 : 5} = 4/11`
Ta có:
`1/7 = {1 xx 110}/{7 xx 110} = 100/770`
`3/7 = {3 xx 110}/{7 xx 110} = 330/770`
`1 = 770/770`
`5/2 = {5 xx 385}/{2 xx 385} = {1925}/770`
`3/2 = {3 xx 385}/{2 xx 385} = {1155}/770`
`4/5 = {4 xx 154}/{5 xx 154} = 616/770`
`4/11 = {4 xx 70}/{11xx 70} = 280/770`
Vì $100 < 280 < 330 < 616 < 770 < 1155$ nên `100/770 < 280/770 < 330/770 < 616/770 < 770/770 < {1155}/770`
`-> 1/7 < 20/55 < 3/7 < 20/25 < 1 < 24/16 < 5/2`
