Repeated digit arithmetic

All numbers are multiples of eleven. Divide them individually to get 1+2+3+4+5+6+7+8+9 If you cannot work it out from there, then I look forward to seeing you in McDonald's

Since every term in the numerator is a multiple of 11, we can break up the numerator into its separate components, and then divide by 11. We get

$\begin{aligned} \frac{ 11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99 } { 11 } & = \frac{11}{11} + \frac{22}{11} + \frac{33}{11} + \frac{44}{11} + \frac{55}{11} + \frac{66}{11} + \frac{77}{11} + \frac{88}{11} + \frac{99}{11} \\ & = 1 + 2 + 3 + 4 +5 + 6 + 7 + 8 + 9 \\ & = 45. \\ \end{aligned}$

Divide each number by 11 and then add them up to get

$=45$

Take common 11 from numerator. Then cancel out 11 from numerator and denominator. Then add the remaining numbers in numerator. You got the answer.

Take 11 out as the common factor. We are left with 1+2+...+9. Use the formula for sigma n = n * (n+1)/2 where n = 9.

Taking 11 as common and dividing with 11 below. Then add remaining.

11=87=99-99=84--2=3