Question

vì sao:ab +ba chia hết cho 11?

Answer 1

Ta có:

\(\overline{ab}+\overline{ba}=10a+b+10b+a=\left(10a+a\right)+\left(10b+b\right)=11a+11b=11\left(a+b\right)⋮11\)

\(\Rightarrow\overline{ab}+\overline{ba}⋮11\left(đpcm\right)\)

Answer 2

Ta có ab+ba=a.10+b.1+b.10+a.1

                      = (a.10+a.1)+(b.1+b.10)

                      = a.(10+1)+b.(10+1)

                      = a.11+b.11

Vì \(11⋮11\)

\(\Rightarrow a.11+b.11⋮11\)

hay ab+ba chia hết cho 11