3) So sánh các số:
a) 3247 và 6433 b) (\(\dfrac{1}{2}\) )30 và ( \(\dfrac{1}{3}\) )20
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`a)1<3`
`=>1/5<3/5`
`b)21>9`
`=>8/21<8/9`
`c)3/5<5/5=1`
`d)7/5>5/5=1`
a) \(\dfrac{2}{5}=\dfrac{4}{10}\)
\(\dfrac{4}{10}>\dfrac{3}{10}\)
b) \(\dfrac{5}{6}=\dfrac{10}{12}\)
\(\dfrac{7}{12}< \dfrac{10}{12}\)
c) \(\dfrac{1}{2}=\dfrac{2}{4}\)
\(\dfrac{3}{4}< \dfrac{2}{4}\)
d) \(\dfrac{8}{3}=\dfrac{56}{21}\)
\(\dfrac{56}{21}>\dfrac{11}{21}\)
`3/7-2/5`
`=1/35>0`
`=>3/7>2/5`
`b,9>8`
`=>1/9<1/8`
`=>5/9<5/8`
`d,8/7>1`
`7/8<1`
`=>8/7>7/8`
a) \(< \)
b) \(>\)
c) \(< \)
d) \(>\)
e) \(< \)
g) \(>\)
h) \(>\)
k) \(>\)
a)\(\dfrac{3}{7}=\dfrac{3.8}{7.8}=\dfrac{24}{56};\dfrac{5}{8}=\dfrac{5.7}{8.7}=\dfrac{35}{56}\)
b)\(\dfrac{7}{10}=\dfrac{7.2}{10.2}=\dfrac{14}{20};\dfrac{3}{20}\)
c)\(\dfrac{9}{20}=\dfrac{9.9}{20.9}=\dfrac{81}{180};\dfrac{2}{9}=\dfrac{2.20}{9.20}=\dfrac{40}{180}\)
a) Gọi tử số của phân số càn tìm là x
Theo đề bài ta có:
\(\dfrac{-2}{5}< \dfrac{x}{30}< \dfrac{-1}{6}\)
\(\Rightarrow\dfrac{-12}{30}< \dfrac{x}{30}< \dfrac{-5}{30}\)
\(\Rightarrow x=\left\{-11;-10;-9;-8;-7;-6\right\}\)
Bài 1:
a: Sửa đề: 1/3^200
1/2^300=(1/8)^100
1/3^200=(1/9)^100
mà 1/8>1/9
nên 1/2^300>1/3^200
b: 1/5^199>1/5^200=1/25^100
1/3^300=1/27^100
mà 25^100<27^100
nên 1/5^199>1/3^300
a) \(\dfrac{2}{3}=\dfrac{2.8}{3.8}=\dfrac{16}{24}\)
\(\dfrac{5}{8}=\dfrac{5.3}{8.3}=\dfrac{15}{24}\)
b) \(\dfrac{1}{4}=\dfrac{1.3}{4.3}=\dfrac{3}{12}\)
\(\dfrac{7}{12}=\dfrac{7.1}{12.1}=\dfrac{7}{12}\)
c) \(\dfrac{5}{6}=\dfrac{5.4}{6.4}=\dfrac{20}{24}\)
\(\dfrac{3}{8}=\dfrac{3.3}{8.3}=\dfrac{9}{24}\)
a) 23=2.83.8=162423=2.83.8=1624
58=5.38.3=152458=5.38.3=1524
b) 14=1.34.3=31214=1.34.3=312
712=7.112.1=712712=7.112.1=712
c) 56=5.46.4=202456=5.46.4=2024
38=3.38.3=924
Lời giải:
a.
$32^{47}=(2^5)^{47}=2^{5.47}=2^{235}$
$64^{33}=(2^6)^{33}=2^{6.33}=2^{198}$
Vì $2^{235}> 2^{198}$ nên $32^{47}> 64^{33}$
b.
$(\frac{1}{2})^{30}=\frac{1}{2^{30}}=\frac{1}{8^{10}}$
$(\frac{1}{3})^{20}=\frac{1}{3^{20}}=\frac{1}{9^{10}}$
Hiển nhiên $8^{10}< 9^{10}\Rightarrow \frac{1}{8^{10}}> \frac{1}{9^{10}}$
$\Rightarrow (\frac{1}{2})^{30}> (\frac{1}{3})^{20}$