rút gọn các phân số
a,23/24 b,35/34 c,47/410 d,511/58 e,62/42
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a: \(=\dfrac{6\left(12-7\right)}{60}=\dfrac{6\cdot5}{6\cdot10}=\dfrac{5}{10}=\dfrac{1}{2}\)
b: \(=\dfrac{35\cdot\left(18-1\right)}{34\cdot7}=5\cdot\dfrac{1}{2}=\dfrac{5}{2}\)
c: \(=\dfrac{42\left(1-11\right)}{21\cdot\left(-15\right)}=2\cdot\dfrac{-10}{-15}=2\cdot\dfrac{2}{3}=\dfrac{4}{3}\)
d: \(=\dfrac{2^5\cdot3^2}{2^5\cdot3^3}=\dfrac{1}{3}\)
e: \(=\dfrac{-36\cdot14}{27\left(14+7\right)}=\dfrac{-36}{27}\cdot\dfrac{14}{21}=\dfrac{-4}{3}\cdot\dfrac{2}{3}=-\dfrac{8}{9}\)
a, 24/-42 = -24/42= -4x6/7x6 =-4/7
b,-24/36 = -2x12/3x12 =-2/3
c,-8/56= -1x8/7x8 =-1/7
d,29/-87= -29/87 =-1x29/3x29 =-1/3
e, -3x35/42x9 =-1x3x5x7/6x7x3x3 =-1x5/3x6 =-5/18
f,-45045 / 6006000=-45x1001 /6000x1001=45/6000=3x15/15x400=3/400
\(a.\frac{-4}{7},b.\frac{-2}{3},c.\frac{-1}{7},d.\frac{-1}{3},e.\frac{-5}{18},f.\frac{-3}{400}\)
a) $420-(71+420)$
$=420-71-420$
$=-71$
b) $(35-120)+(120+410-35)$
$=35-120+120+410-35$
$=(35-35)+(-120+120)+410$
$=410$
c) $(320-15+49)-(85-51)$
$=320-15+49-85+51$
$=320+(-15-85)+(49+51)$
$=320+(-100)+100$
$=320$
d) $-(312+59)-(41+400+88)$
$=-312-59-41-400-88$
$=(-312-88)+(-59-41)-400$
$=-400+(-100)-400$
$=-500-400$
$=-900$
e) $(430-731)-(-731+430-56)$
$=430-731+731-430+56$
$=(430-430)+(-731+731)+56$
$=56$
f) $(1352-47)-(53-1000+1352)$
$=1352-47-53+1000-1352$
$=(1352-1352)+(-47-53)+1000$
$=(-100)+1000$
$=1000-100$
$=900$
h) $(-42)-(370+58)-(120-370)$
$=-42-370-58-120+370$
$=(-42-58)+(-370+370)-120$
$=-100-120$
$=-220$
$Toru$
a ) − 1 < 1 ; b ) 9 15 > 7 15 ; c ) − 1 2 > − 7 12 ; d ) 71 20 < 4
a) Ta có : a + 1 > a - 1
=> \(\frac{1}{a+1}\) < \(\frac{1}{a-1}\)
a) \(\frac{1}{a+1}< \frac{1}{a}< \frac{1}{a-1}\Rightarrow\frac{1}{a+1}< \frac{1}{a-1}\)
b) \(\frac{23}{47}< \frac{23}{45}< \frac{24}{45}\Rightarrow\frac{23}{47}< \frac{24}{45}\)
c) \(\frac{12}{17}>\frac{1}{2}>\frac{7}{15}\Rightarrow\frac{12}{17}>\frac{7}{15}\)
d) \(\frac{34}{43}< \frac{35}{43}< \frac{35}{42}\Rightarrow\frac{34}{43}< \frac{35}{42}\)
a: 14/35=2/5
b: 23/62=23/62
c: -33/143=-3/11
d: -53/81=-53/81
e: \(\dfrac{2^2\cdot5^2}{2^5\cdot5^4}=\dfrac{1}{2^3\cdot5^2}=\dfrac{1}{8\cdot25}=\dfrac{1}{200}\)
a) \(\frac{2^3}{2^4}=\frac{2^3}{2^3.2}=\frac{1}{2}\)
b) \(\frac{3^5}{3^4}=\frac{3^4.3}{3^4}=3\)
c) \(\frac{4^7}{4^{10}}=\frac{4^7}{4^7.4^3}=\frac{1}{4^3}=\frac{1}{64}\)
d) \(\frac{5^{11}}{5^8}=\frac{5^8.5^3}{5^8}=5^3=125\)
e) \(\frac{6^2}{4^2}=\frac{2^2.3^2}{\left(2^2\right)^2}=\frac{3^2}{2^2}=\frac{9}{4}\)
a) \(\frac{2^3}{2^4}\)= \(\frac{8}{16}\)= \(\frac{1}{2}\)
b) \(\frac{3^5}{3^4}\)= \(\frac{243}{81}\)= \(\frac{3}{1}\)= 3