rút gọn các phân số
a)15.47-47.16/-15-32
b)123.5-123.17/36.82
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a)36/48>12/48
=>6/8>3/12
b)135/225<180/225
=>15/25<36/45
c)1575/2835>1323/2835
=>15/27>49/105
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a)
`6/9=2/3`
`6/24=1/4`
`48/96=1/2`
`42/98=3/7`
b)
`24/36=2/3`
`18/30=3/5`
`15/120=1/8`
`80/240=1/3`
a)\(\dfrac{6}{9}=\dfrac{6:3}{9:3}=\dfrac{2}{3}\)
\(\dfrac{6}{24}=\dfrac{6:6}{24:6}=\dfrac{1}{4}\)
\(\dfrac{48}{96}=\dfrac{48:48}{96:48}=\dfrac{1}{2}\)
\(\dfrac{42}{98}=\dfrac{42:14}{98:14}=\dfrac{3}{7}\)
b)\(\dfrac{24}{36}=\dfrac{24:12}{36:12}=\dfrac{2}{3}\)
\(\dfrac{18}{30}=\dfrac{18:6}{30:6}=\dfrac{3}{5}\)
\(\dfrac{15}{120}=\dfrac{15:15}{120:15}=\dfrac{1}{8}\)
\(\dfrac{80}{240}=\dfrac{80:80}{240:80}=\dfrac{1}{3}\)
a ) 2 - 3 2 = 2 - 3 = 2 - 3
(vì 2 - √3 > 0 do 2 = √4 mà √4 > √3)
b ) 3 - 11 2 = 3 - 11 = 11 - 3
(vì √11 - 3 > 0 do 3 = √9 mà √11 > √9)
c) 2√a2 = 2|a| = 2a với a ≥ 0
d ) 3 a - 2 2 = 3 a - 2 = 3 2 - a
(vì a < 2 nên 2 – a > 0)
Câu 3:
a) \(\dfrac{12}{36}=\dfrac{12:12}{36:12}=\dfrac{1}{3}\)
\(\dfrac{-16}{20}=\dfrac{-16:4}{20:4}=\dfrac{-4}{5}\)
b) \(\dfrac{21}{105}=\dfrac{21:21}{105:21}=\dfrac{1}{5}\)
\(\dfrac{35}{150}=\dfrac{35:5}{150:5}=\dfrac{7}{30}\)
Câu 4:
a) \(\dfrac{3}{10}+\dfrac{5}{10}=\dfrac{3+5}{10}=\dfrac{8}{10}=\dfrac{4}{5}\)
b) Ta có: \(\left(-27\right)\cdot36+64\cdot\left(-27\right)+23\cdot\left(-100\right)\)
\(=\left(-27\right)\cdot\left(64+36\right)+23\cdot\left(-100\right)\)
\(=-27\cdot100-23\cdot100\)
\(=100\left(-27-23\right)\)
\(=-50\cdot100=-5000\)
c) \(\dfrac{5}{8}+\dfrac{3}{12}=\dfrac{15}{24}+\dfrac{6}{24}=\dfrac{21}{24}=\dfrac{7}{8}\)
d) Ta có: \(\dfrac{-2}{17}+\dfrac{3}{19}+\dfrac{-15}{17}+\dfrac{16}{19}+\dfrac{5}{6}\)
\(=\left(-\dfrac{2}{17}+\dfrac{-15}{17}\right)+\left(\dfrac{3}{19}+\dfrac{16}{19}\right)+\dfrac{5}{6}\)
\(=-1+1+\dfrac{5}{6}\)
\(=\dfrac{5}{6}\)
a) \(\dfrac{2727-101}{3.303+404}=\dfrac{2626}{909+404}=\dfrac{2626}{1313}=2\)
b) \(\dfrac{8.9-4.15}{12.7-180}=\dfrac{72-60}{84-180}=\dfrac{12}{-96}=\dfrac{-1}{8}\)
c) \(\dfrac{-19}{3^2.7.11}=\dfrac{-19}{9.7.11}=\dfrac{-19}{63.11}=\dfrac{-19}{693}\)
d) \(\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\dfrac{2^{12}.3^{10}+120.6^9}{2^{12}.3^{12}-6^{11}}=\dfrac{2^2.6^{10}+20.6.6^9}{6^{12}-6^{11}}=\dfrac{4.6^{10}+20.6^{10}}{6^{11}\left(6-1\right)}=\dfrac{\left(4+20\right).6^{10}}{5.6^{11}}=\dfrac{24}{30}=\dfrac{4}{5}\)
a) = 47x(15-16)/-47
= -47/-47 =1
b) = 123x(5-17)/24x 123
= -12/24= -1/2