Question

a) 4ab = 5cd ( gạch ngang trên đầu )

CMR abcd chia hết cho 9

Answer 1

Ta có 4\(\overline{ab}\) = 5\(\overline{cd}\) \(\Rightarrow\) \(\overline{ab}\) = \(\dfrac{5}{4}\) \(\overline{cd}\) .

Có : \(\overline{abcd}\) = 100\(\overline{ab}\) + \(\overline{cd}\) = \(\dfrac{5}{4}\). 100\(\overline{cd}\) + \(\overline{cd}\) = 125\(\overline{cd}\) + \(\overline{cd}\) = 126\(\overline{cd}\) .

Vì 126 \(⋮\) 9 \(\Rightarrow\) 126\(\overline{cd}\) \(⋮\) 9 hay \(\overline{abcd}\) \(⋮\) 9

Vậy nếu 4\(\overline{ab}\) = 5\(\overline{cd}\) thì \(\overline{abcd}\) \(⋮\) 9.