Explicație pas cu pas:
a)
[tex] \frac{343434}{252525} = \frac{10101 \cdot 34}{10101 \cdot 25} = \frac{34}{25} \\ [/tex]
[tex]\frac{3434}{2525} = \frac{101 \cdot 34}{101 \cdot 25} = \frac{34}{25} \\ [/tex]
=>
[tex]\frac{343434}{252525} = \frac{3434}{2525} \\ [/tex]
b)
[tex]\frac{\overline {abab}}{\overline {cdcd}} = \frac{1000a + 100b + 10a + 1b}{1000c + 100d + 10c + d} = \frac{1010a + 101b}{1010c + 101d} = \\ = \frac{101(10a + b)}{101(10c + d)} = \frac{10a + b}{10c + d} = \frac{\overline {ab}}{\overline {cd}} \\ [/tex]
[tex]\implies \frac{\overline {abab}}{\overline {cdcd}} = \frac{\overline {ab}}{\overline {cd}} \\[/tex]
