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a) \(\frac{5252}{7575}=\frac{52}{75};\frac{525252}{757575}=\frac{52}{75}\)
Vậy cả 3 phân số trên bằng nhau
b) \(\frac{1313}{1515}=\frac{13}{15};\frac{131313}{151515}=\frac{13}{15}\)
Vậy các phân số trên bằng nhau
\(\frac{52}{73}=\frac{52\cdot101}{73\cdot101}=\frac{5252}{7373}\)
\(\frac{52}{73}=\frac{52\cdot10101}{73\cdot10101}=\frac{525252}{737373}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có abab/cdcd=abab:101/cdcd:101=ab/cd
ababab/cdcdcd=ababab:10101/cdcdcd:10101=ab/cd
Vì ab/cd=ab/cd nên abab/cdcd= ababab/cdcdcd
\(\frac{abab}{cdcd}=\frac{ab.101}{cd.101}=\frac{ab}{cd}\)
\(\frac{ababab}{cdcdcd}=\frac{ab.10101}{cd.10101}=\frac{ab}{cd}\)
VẬY \(\frac{abab}{cdcd}=\frac{ababab}{cdcdcd}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Hai phân số sau có bằng nhau không?
=\(\frac{ab}{cd}\)
\(\Rightarrow\) Hai phan so đều bằng nhau.
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a) a b = a . ( − 1 ) b . ( − 1 ) = − a − b
b) ta có:
a b a b ¯ c d c d ¯ = a b a b ¯ : 101 c d c d ¯ : 101 = a b ¯ c d ¯ ; a b a b a b ¯ c d c d ¯ c d = a b a b a b ¯ : 10101 c d c d ¯ c d:10101 = a b ¯ c d ¯
do đó: a b a b ¯ c d c d ¯ = a b a b a b ¯ c d c d ¯ c d
c) a b a b ¯ a b a b a b ¯ = a b a b ¯ : a b ¯ a b a b a b ¯ : a b ¯ = 101 10101
![](https://rs.olm.vn/images/avt/0.png?1311)
1,
ta có : \(\frac{\overline{abab}}{\overline{cdcd}}=\frac{\overline{abab}:101}{\overline{cdcd}:101}=\frac{\overline{ab}}{\overline{cd}}\) ; \(\frac{\overline{ababab}}{\overline{cdcdcd}}=\frac{\overline{ababab}:10101}{\overline{cdcdcd}:10101}=\frac{\overline{ab}}{\overline{cd}}\)
Vậy \(\frac{\overline{abab}}{\overline{cdcd}}=\frac{\overline{ababab}}{\overline{cdcdcd}}\)
2,
\(\frac{1}{2}.\frac{1}{b}=\frac{2}{4}\)
\(\Rightarrow\frac{1.1}{2.b}=\frac{2}{4}\)
\(\Rightarrow\frac{1}{2.b}=\frac{1}{2}\)
\(\Rightarrow2.b=2\)
\(\Rightarrow b=2:2=1\)
\(\frac{abab}{cdcd}=\frac{abab:101}{cdcd:101}=\frac{ab}{cd}\)
mà \(\frac{ababab}{cdcdcd}=\frac{ababab:10101}{cdcdcd:10101}=\frac{ab}{cd}\)
=> \(\frac{abab}{cdcd}=\frac{ababab}{cdcdcd}\)
vậy...
câu 2
\(\frac{1}{2}.\frac{1}{b}=\frac{2}{4}\\ \Rightarrow\frac{1}{b}=\frac{2}{4}:\frac{1}{2}=1\\ \Rightarrow b=1\)
vậy....
![](https://rs.olm.vn/images/avt/0.png?1311)
a b a b ¯ c d c d ¯ = a b ¯ c d ¯ . 101 101 = a b ¯ c d ¯
a b a b a b ¯ c d c d c d ¯ = a b ¯ c d ¯ . 10101 10101 = a b ¯ c d ¯
⇒ a b a b ¯ c d c d ¯ = a b a b a b ¯ c d c d c d ¯
![](https://rs.olm.vn/images/avt/0.png?1311)
a b a b ¯ c d c d ¯ = 101 a b ¯ 101 c d ¯ = a b ¯ c d ¯ ; a b a b a b ¯ c d c d c d ¯ = 10101 a b ¯ 10101 c d ¯ = a b ¯ c d ¯
⇒ a b a b ¯ c d c d ¯ = a b a b a b ¯ c d c d c d ¯
\(\frac{52}{75}=\frac{52.101}{75.101}=\frac{5252}{7575};\frac{52}{75}=\frac{52.10101}{75.10101}=\frac{525252}{757575}\)
\(\frac{13}{15}=\frac{13.101}{15.101}=\frac{1313}{1515};\frac{13}{15}=\frac{13.10101}{15.10101}=\frac{131313}{151515}\)
\(\frac{ab}{cd}=\frac{101ab}{101cd}=\frac{abab}{cdcd};\frac{ab}{cd}=\frac{10101ab}{10101cd}=\frac{ababab}{cdcdcd}\)
ai k minh minh k lai
chia các vế với 1001 và 100001