what number, when added to both the numerator and to the denominator of 8/11, gives 2/3?
We have
[8 + N] / [11 + N] = 2/3 cross-multiply
2[11+N]= 3[8 + N] simplify
22 + 2N = 24 + 3N subtract 24, 2N from both sides
-2 = N
Check
[8 - 2]/ [11- 2] =
6/9 =
2/3