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\(\dfrac{205}{107}\),\(\dfrac{20}{23}\),\(\dfrac{7}{10}\),\(\dfrac{214}{315}\),\(\dfrac{-5}{8}\),\(\dfrac{-16}{19}\)
a: \(\dfrac{-5}{6}=\dfrac{-20}{24};\dfrac{7}{8}=\dfrac{21}{24};\dfrac{7}{24}=\dfrac{7}{24};\dfrac{-3}{4}=-\dfrac{18}{24};\dfrac{2}{3}=\dfrac{16}{24}\)
Do đó: \(\dfrac{-5}{6}< -\dfrac{3}{4}< \dfrac{7}{24}< \dfrac{2}{3}< \dfrac{7}{8}\)
\(\dfrac{7}{8}=\dfrac{119}{136};\dfrac{16}{17}=\dfrac{128}{136}\)
mà 119<128
nên 7/8<16/17
DO đó: -5/6<-3/4<7/24<2/3<7/8<16/17
b: \(\dfrac{-5}{8}=\dfrac{-95}{8\cdot19};\dfrac{-16}{19}=\dfrac{-128}{19\cdot8}\)
Do đó: -5/8>-16/19
\(\dfrac{7}{10}=0.7;\dfrac{20}{23}\simeq0.87;\dfrac{214}{315}\simeq0.68;\dfrac{205}{107}>1\)
Do đó: \(\dfrac{205}{107}>\dfrac{20}{23}>\dfrac{7}{10}>\dfrac{214}{315}>-\dfrac{5}{8}>-\dfrac{16}{19}\)
\(a,\dfrac{-5}{8};\dfrac{7}{10};\dfrac{16}{19};\dfrac{20}{23}\)
\(\Rightarrow\dfrac{20}{23}>\dfrac{16}{19}>\dfrac{7}{10}>\dfrac{-5}{8}\)
Vậy \(\dfrac{20}{23}>\dfrac{16}{19}>\dfrac{7}{10}>\dfrac{-5}{8}\)
\(b,\dfrac{5\times6+6\times7}{5\times5+20}\)và \(\dfrac{8\times9-4\times15}{12\times7-180}\)
Xét : \(\dfrac{5\times6+6\times7}{5\times5+20}\)
\(=\dfrac{\left(5+7\right)\times6}{5\times5+5\times4}\)
\(=\dfrac{12\times6}{\left(5+4\right)\times5}\)
\(=\dfrac{72}{9\times5}\)
\(=\dfrac{72}{45}\)
\(=\dfrac{8}{5}\)
Xét : \(\dfrac{8\times9-4\times15}{12\times7-180}\)
\(=\dfrac{72-60}{84-180}\)
\(=\dfrac{12}{-96}\)
\(=\dfrac{-1}{8}\)
Quy đồng \(\dfrac{8}{5}=\dfrac{8\times8}{5\times8}=\dfrac{64}{40}\\ \dfrac{-1}{8}=\dfrac{\left(-1\right)\times5}{8\times5}=\dfrac{-5}{40}\)
Vì \(\dfrac{64}{40}>\dfrac{-5}{40}\)
\(\Rightarrow\dfrac{8}{5}>\dfrac{-1}{8}\)
\(\Rightarrow\dfrac{5\times6+6\times7}{5\times5+20}>\dfrac{8\times9-4\times15}{12\times7-180}\)
Vậy \(\dfrac{5\times6+6\times7}{5\times5+20}>\dfrac{8\times9-4\times15}{12\times7-180}\)
1) \(\dfrac{3}{2}\) : \(\dfrac{9}{4}\) =\(\dfrac{3}{2}\)x\(\dfrac{4}{9}\)=\(\dfrac{12}{18}\)=\(\dfrac{2}{3}\)
2)\(\dfrac{48}{55}\) : \(\dfrac{12}{11}\)= \(\dfrac{48}{55}\) x\(\dfrac{11}{12}\)= \(\)\(\dfrac{528}{660}\)=\(\dfrac{4}{5}\)
3)\(\dfrac{7}{10}\) : \(\dfrac{7}{5}\)=\(\dfrac{7}{10}\) x \(\dfrac{5}{7}\)= \(\dfrac{35}{70}\)=\(\dfrac{1}{2}\)
4)\(\dfrac{6}{7}\) : \(\dfrac{8}{7}\) = \(\dfrac{6}{7}\) x \(\dfrac{7}{8}\) =\(\dfrac{42}{56}\)=\(\dfrac{3}{4}\)
Sắp xếp các thương theo thứ tự tăng dần :\(\dfrac{1}{2}\);\(\dfrac{2}{3}\);\(\dfrac{3}{4}\);\(\dfrac{4}{5}\)
\(\Rightarrow\)\(\dfrac{7}{10}\) : \(\dfrac{7}{5}\) ; \(\dfrac{3}{2}\) :\(\dfrac{9}{4}\) ; \(\dfrac{6}{7}\) : \(\dfrac{8}{7}\) ; \(\dfrac{48}{55}\):\(\dfrac{12}{11}\).
a: \(\dfrac{-7}{12}=\dfrac{-7\cdot5}{12\cdot5}=\dfrac{-35}{60};\dfrac{-1}{-15}=\dfrac{1}{15}=\dfrac{4}{60};\dfrac{-5}{4}=\dfrac{-5\cdot15}{4\cdot15}=-\dfrac{75}{60}\)
\(\dfrac{3}{-5}=\dfrac{-3}{5}=\dfrac{-3\cdot12}{5\cdot12}=-\dfrac{36}{60}\)
mà -75<-36<-35<4
nên \(-\dfrac{75}{60}< -\dfrac{36}{60}< -\dfrac{35}{60}< \dfrac{4}{60}\)
=>\(\dfrac{-5}{4}< \dfrac{3}{-5}< \dfrac{-7}{12}< \dfrac{-1}{-15}\)
b: \(\dfrac{-8}{25}+\dfrac{22}{23}+\dfrac{-17}{25}\)
\(=\left(-\dfrac{8}{25}-\dfrac{17}{25}\right)+\dfrac{22}{23}\)
\(=-1+\dfrac{22}{23}=-\dfrac{1}{23}\)
đây là tính nhanh à nếu tính bình thường thì tính may tính là ra
a) 17/23 . 8/16 . 23/17. (-80) . 3/4
= (17/23 . 23/17) . (8/16 . 3/4) . (-80)
= 1 . 3/8 . (-80)
= 3/8 . (-80)
= -30
b) 5/11 . 18/29 - 5/11 . 8/29 + 5/11 . 19/29
= 5/11 . (18/29 - 8/29 + 19/29)
= 5/11 . 1
= 5/11
c)(13/23 + 1313/2323 - 131313/232323).(1/3+1/4 -7/12)
= (13/23 + 1313/2323 - 131313/232323).0
= 0
d) 12/2x2 . 22/2x3 . 32/3x4 . 42/4x5 . 52/5x6 . 62/6x7 . 72/7x8 . 82/8x9 . 92/9x10
= 1/2 . 2/3 . 3/4 . 4/5 . 5/6 . 6/7 . 7/8 . 8/9 .9/10
= 1/10
Khó nhìn quá. Bạn thông cảm nhé! 
a) Ta có: \(\dfrac{19}{33}=\dfrac{38}{66};\dfrac{6}{12}=\dfrac{1}{2}=\dfrac{33}{66};\dfrac{13}{22}=\dfrac{39}{66}\)
Mà \(\dfrac{33}{66}< \dfrac{38}{66}< \dfrac{39}{66}\Rightarrow\dfrac{6}{12}< \dfrac{19}{33}< \dfrac{13}{22}\)
Vậy các số hữu tỉ được sắp xếp theo thứ tự tăng dần là: \(\dfrac{6}{12};\dfrac{19}{33};\dfrac{13}{22}\)
b) Ta có:
\(\dfrac{-18}{12}=\dfrac{-3}{2}=\dfrac{-105}{70};\dfrac{-10}{7}=\dfrac{-100}{70};\dfrac{-8}{5}=\dfrac{-112}{70}\)
Mà \(\dfrac{-112}{70}< \dfrac{-105}{70}< \dfrac{-100}{70}\Rightarrow\dfrac{-8}{5}< \dfrac{-18}{12}< \dfrac{-10}{7}\)
Vậy các số hữu tỉ được sắp xếp theo thứ tự tăng dần là: \(\dfrac{-8}{5};\dfrac{-18}{12};\dfrac{-10}{7}\)
a. \(\dfrac{19}{33};\dfrac{6}{12};\dfrac{13}{22}\) ( \(MC=132\) )
Quy đồng : \(\dfrac{19}{33}=\dfrac{76}{132}\) ; \(\dfrac{6}{12}=\dfrac{66}{132}\) ; \(\dfrac{13}{22}=\dfrac{78}{132}\)
Vì \(\dfrac{66}{132}< \dfrac{76}{132}< \dfrac{78}{132}\) => \(\dfrac{6}{12}< \dfrac{19}{33}< \dfrac{13}{22}\)
b. \(\dfrac{-18}{12};\dfrac{-10}{7};\dfrac{-8}{5}\) ( \(MC=420\) )
Quy đồng : \(\dfrac{-18}{12}=\dfrac{-630}{420}\) ; \(\dfrac{-10}{7}=\dfrac{-600}{420}\) ; \(\dfrac{-8}{5}=\dfrac{-672}{420}\)
Vì : \(\dfrac{-672}{420}< \dfrac{-630}{420}< \dfrac{-600}{420}\) => \(\dfrac{-8}{5}< \dfrac{-18}{12}< \dfrac{-10}{7}\)
a. \(\dfrac{5}{7}+\dfrac{9}{23}+\dfrac{-12}{7}+\dfrac{14}{23}\)
= \(\left(\dfrac{5}{7}+\dfrac{-12}{7}\right)+\left(\dfrac{9}{23}+\dfrac{14}{23}\right)\)
= \(\left(-1\right)+1=0\)
b. \(\left(7-2\dfrac{3}{5}\right).2\dfrac{4}{33}-2\dfrac{3}{5}:\dfrac{1}{2}+\dfrac{7}{5}\)
= \(\dfrac{22}{5}.2\dfrac{4}{33}-\dfrac{26}{5}+\dfrac{7}{5}\)
= \(\dfrac{28}{3}-\dfrac{33}{5}=\dfrac{41}{15}\)
c\(\dfrac{-7}{9}:\dfrac{8}{15}+\dfrac{-7}{9}.\dfrac{7}{15}+5\dfrac{7}{9}\)
= \(\dfrac{-56}{135}+\dfrac{-49}{135}+5\dfrac{7}{9}\)
= \(\dfrac{-7}{9}+5\dfrac{7}{9}=5\)
d. \(\left(16\dfrac{3}{8}-19\dfrac{3}{4}\right)-\left(12\dfrac{3}{8}-17\dfrac{3}{4}\right)\)
= \(16\dfrac{3}{8}-19\dfrac{3}{4}-12\dfrac{3}{8}+17\dfrac{3}{4}\)
= \(\left(16\dfrac{3}{8}-12\dfrac{3}{8}\right)-\left(19\dfrac{3}{4}-17\dfrac{3}{4}\right)\)
=\(4+2=6\)
a)\(\dfrac{5}{7}+\dfrac{9}{23}+\dfrac{-12}{7}+\dfrac{14}{23}\)
=\(\left(\dfrac{5}{7}-\dfrac{12}{7}\right)+\left(\dfrac{9}{23}+\dfrac{14}{23}\right)=-1+1=0\)
b)\(\left(7-2\dfrac{3}{5}\right).2\dfrac{4}{33}-2\dfrac{3}{5}:\dfrac{1}{2}+\dfrac{7}{5}\)
=\(\dfrac{22}{5}.\dfrac{70}{33}-\dfrac{13}{5}.2+\dfrac{7}{5}\)
=\(\dfrac{28}{3}-\dfrac{26}{5}+\dfrac{7}{5}=\dfrac{83}{15}\)
Các câu sau tương tự
a) \(\dfrac{-5}{6}=\dfrac{-340}{408}\);\(\dfrac{7}{8}=\dfrac{357}{408}\);\(\dfrac{7}{24}=\dfrac{119}{408}\)
\(\dfrac{16}{17}=\dfrac{384}{408}\); \(\dfrac{-3}{4}=\dfrac{-306}{408}\); \(\dfrac{2}{3}=\dfrac{272}{408}\)
Do đó: \(\dfrac{-5}{6}< \dfrac{-3}{4}< \dfrac{7}{24}< \dfrac{2}{3}< \dfrac{7}{8}< \dfrac{16}{17}\)